Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance.

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve.

Design of Linear Block Copolymers and Star Terpolymers That Produce Two Length Scales at Phase Separation.

Quasicrystals (materials with long-range order but without the usual spatial periodicity of crystals) were discovered in several soft matter systems in the last 20 years. The stability of quasicrystals has been attributed to the presence of two prominent length scales in a specific ratio, which is 1.93 for the 12-fold quasicrystals most commonly found in soft matter.

Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry.

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries.

How does homophily shape the topology of a dynamic network?

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter J∈[-1,1], the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability (1+J)/2 and delete them with probability (1-J)/2.

Density Distribution in Soft Matter Crystals and Quasicrystals.

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centered on lattice sites or via a Fourier sum. Here, we argue that representing instead the logarithm of the density distribution via a Fourier sum is better. We show that truncating such a representation after only a few terms can be highly accurate for soft matter crystals.

Which Wave Numbers Determine the Thermodynamic Stability of Soft Matter Quasicrystals?

For soft matter to form quasicrystals an important ingredient is to have two characteristic length scales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wave numbers should be favored, and the ratio of these wave numbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed.

Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations.

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each.

Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate.

We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions.

Three-Dimensional Icosahedral Phase Field Quasicrystal.

We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state.

Influence of Luddism on innovation diffusion.

We generalize the classical Bass model of innovation diffusion to include a new class of agents-Luddites-that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate.

Soft-core particles freezing to form a quasicrystal and a crystal-liquid phase.

Systems of soft-core particles interacting via a two-scale potential are studied. The potential is responsible for peaks in the structure factor of the liquid state at two different but comparable length scales and a similar bimodal structure is evident in the dispersion relation. Dynamical density functional theory in two dimensions is used to identify two unusual states of this system: a crystal-liquid state, in which the majority of the particles are located on lattice sites but a minority remains free and so behaves like a liquid, and a 12-fold quasicrystalline state.

Characterization of spiraling patterns in spatial rock-paper-scissors games.

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals.

Cyclic dominance in evolutionary games: a review.

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game.

Quasicrystalline order and a crystal-liquid state in a soft-core fluid.

A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory and Brownian dynamics simulations reveal a fluid phase and two crystalline phases with different lattice spacing. Of these the larger lattice spacing phase can form an exotic periodic state with a fraction of highly mobile particles: a crystal liquid.

Three-wave interactions and spatiotemporal chaos.

Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to interact with one wave of the shorter. Consideration of both types of three-wave interactions can generically explain the presence of complex patterns and spatiotemporal chaos.

Skew-varicose instability in two-dimensional generalized Swift-Hohenberg equations.

We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our models to allow exact stripe solutions. In the generalized models, stripes become unstable to the skew-varicose, oscillatory skew-varicose, and cross-roll instabilities, in addition to the usual Eckhaus and zigzag instabilities.

Probing the effects of ligand structure on activity and selectivity of Cr(III) complexes for ethylene oligomerisation and polymerisation.

A series of distorted octahedral Cr(III) complexes containing tridentate S-, S/O- or N-donor ligands comprised of three distinct architectures: facultative {S(CH(2)CH(2)SC(10)H(21))(2) (L(1)) and O(CH(2)CH(2)SC(10)H(21))(2) (L(2))}, tripodal {MeC(CH(2)S(n)C(4)H(9))(3) (L(3)), MeC(CH(2)SC(10)H(21))(3) (L(4))} and macrocyclic {(C(10)H(21))[9]aneN(3) (L(5)), (C(10)H(21))(3)[9]aneN(3) (L(6)), with [9]aneN(3)=1,4,7-triazacyclononane} are reported and characterised spectroscopically. Activation of [CrCl(3)(L)] with MMAO produces very active ethylene trimerisation, oligomerisation and polymerisation catalysts, with significant dependence of the product distribution upon the ligand type present. The properties of the parent [CrCl(3)(L)] complexes are probed by cyclic voltammetry, UV-visible, EPR, EXAFS and XANES measurements, and the effects upon activation with Me(3)Al investigated similarly.

Quasipatterns in parametrically forced systems.

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-frequency forcing, does not select a specific quasipattern: we find, for two different forcing strengths, 12-fold and 14-fold quasipatterns.

Methoxycarbonylation of vinyl acetate catalysed by palladium complexes of bis(ditertiarybutylphosphinomethyl)benzene and related ligands.

High selectivities to methyl acetoxypropanoate esters (b : l up to 3.6 : 1) are obtained from the methoxycarbonylation of vinyl acetate catalysed by palladium complexes of bis(ditertiarybutylphosphinomethyl)benzene in the presence of acid, provided that the acid concentration does not exceed that of the free phosphine.

Cycling chaotic attractors in two models for dynamics with invariant subspaces.

Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddle-type invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors appears by virtue of the fact that the connections are robust within some invariant subspace.

Pattern formation in large domains.

Pattern formation is a phenomenon that arises in a wide variety of physical, chemical and biological situations. A great deal of theoretical progress has been made in understanding the universal aspects of pattern formation in terms of amplitudes of the modes that make up the pattern. Much of the theory has sound mathematical justification, but experiments and numerical simulations over the last decade have revealed complex two-dimensional patterns that do not have a satisfactory theoretical explanation.

Phase resetting effects for robust cycles between chaotic sets.

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible.

Infinities of stable periodic orbits in systems of coupled oscillators.

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor.