Competing Interactions and Patterns in Nanoworld
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Contents:
Patterns in octupolar systems 2. Ordering entropy 2. Famous competition between a short- and a long-range interaction 3. Localized particles 3. Competition between the ferromagnetic exchange and the dipolar Stripe domains in Ising-like systems a Scaling theory b Orientation of the domain walls c Labyrinthine and chevron patterns d Bubbles 3. Ordering in systems of vector-spins a On periodic lattices mono-domain, vortex structure b On aperiodic lattices quasiferromagnetic configuration 3.
Competition between the antiferromagnetic exchange and the dipolar interaction 3. Neural networks 3. DNA model with competing interactions 3. Delocalized particles 3. Self-assembled domain patterns on a solid surface 3. Self-organization in Langmuir monolayers 3. Stripe patterns in diblock copolymers 3.
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Patterns in ferrofluids 3. Colloidal crystals 3. Planar magnetic colloidal crystals 3. Dynamic self-assembly at a liquid-air interface She classifies phenomena by the type of competing interaction involved to better present the underlying principles and universal laws governing the behavior of various systems, covering the basics of self-competition, competition between a short-range and a long-range interaction, competition between interactions on a scale of similar length, interplay between anisotropies and inter-particle interactions, and dynamic selforganization.
She provides comprehensive references for each topic.
Vedmedenko's interdisciplinary approach and logical organization makes what is a very complex topic easy to follow, and the examples are useful for a variety of applications. Press, pp. Choksi R. Pure Appl. Nonlinear Sci. Seul M. Yu, B. Kohn, R. In: International Congress of Mathematicians. Muratov, C. Thesis, Boston University, Google Scholar. E 66 , , pp.
View on Wiley Online Library. Communications in Mathematical Physics. To include a comma in your tag, surround the tag with double quotes. Introduction 1. Petrich D. In order to set up a list of libraries that you have access to, you must first login or sign up.
Care C. Emery V. Chen L. Nyrkova I. Ohta T. Bates F. Matsen M. Stillinger F.
Glotzer S. In: Novaga, M.
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Pisa: Edizioni della Normale, Google Scholar. Ren X. SIAM J. Interfaces Free Bound. Alberti G. Sharp interface functional. Nishiura Y. Petrich D. The recent discovery of 'type In particular, some typical characteristics of the observed vortex patterns e. In this paper, we consider a model competing range interaction potential which is repulsive for the short range and attractive for the longer range. In principle, this type of interaction potential could be used as a model for various systems with non-monotonic inter-particle interaction, e.
Competing Interactions And Patterns In Nanoworld 2007
We investigate the pattern formation in 2D systems for various interaction potential profiles; for example, we distinguish 'soft-core' and 'hard-core' interactions and analyze the transitions between different types of patterns. Based on this analysis, we construct a 'morphology diagram' for various interaction parameters and particle densities.
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We propose a new approach to characterizing the different morphologies: instead of qualitative characterization of the patterns e. In particular, the obtained patterns are analyzed in terms of the radial distribution function RDF and additional quantities characterizing, e.
The paper is organized as follows. These units can be specified, depending on the system. The interaction force is then given by. Indeed, for. By setting the force equal to zero, the coefficient a is given by. We study pattern formation in a system of interacting point-like particles using the Langevin equations.
Note that in this way the interaction in our system is finite-range. To obtain stable particle patterns, we performed simulated annealing simulations of interacting particles.
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For this purpose, particles were initially randomly distributed inside the simulation region at some suitable non-zero temperature. Then the temperature was gradually reduced to zero, and the simulation was continued until the total force acting on any single particle became much smaller than typical forces in the system. Figure 1. The main panel and the inset panel show the change in the force profile due to an increase of r c and b , respectively. Thus, increasing b facilitates stabilization of the minimum inter-particle distance at r c. In other words, an increase of b results in hardening of the core in the interaction force 3 , i.
In this subsection, we analyze pattern formation in the absence of additional pinning. The influence of random pinning on the pattern formation will be discussed in the next subsection. In addition, the interaction between the clusters decaying exponentially for long distances within the interaction range becomes negligible for inter-cluster distance of the order of a few to several r 0. As r c increases, the clusters expand.
For 2. Figure 2. Figure 3. We analyzed in detail the intermediate regime i. The distribution of particles becomes more uniform, with only a few small voids. Figure 4. Our calculations show that the obtained patterns are very sensitive to variations in r c. Thus, if r c slightly decreases e. However, since the decrease of r c increases the attractive component of the inter-particle interaction this occurs at a much higher density.
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- Analysis of pattern formation in systems with competing range interactions.
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For even smaller values of r c , i. To further study the stability of the patterns, here we analyze the influence of the cut-off procedure and the annealing time used in our simulations.
Systems displaying competing interactions of some kind are widespread - much more, in fact, as commonly anticipated (magnetic and. Systems displaying competing interactions of some kind are widespread - much more, in fact, as commonly anticipated (magnetic and Ising-type interactions or.
Alternatively, we consider the effect of additional weak pinning and modify the inter-particle interaction by introducing a weak repulsive tail.
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