Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

A molecular-statistical theory of coil–rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic mechanisms. The first mechanism resembles a low dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.

Adsorption in Mixtures with Competing Interactions

A binary mixture of oppositely charged particles with additional short-range attraction between like particles and short-range repulsion between different ones in the neighborhood of a substrate preferentially adsorbing the first component is studied by molecular dynamics simulations. The studied thermodynamic states correspond to an approach to the gas–crystal coexistence. Dependence of the near-surface structure, adsorption and selective adsorption on the strength of the wall–particle interactions and the gas density is determined. We find that alternating layers or bilayers of particles of the two components are formed, but the number of the adsorbed layers, their orientation and the ordered patterns formed inside these layers could be quite different for different substrates and gas density. Different structures are associated with different numbers of adsorbed layers, and for strong attraction the thickness of the adsorbed film can be as large as seven particle diameters. In all cases, similar amount of particles of the two components is adsorbed, because of the long-range attraction between different particles.

Stability analysis of swarming model with time delays

A swarming model is a model that describes the behavior of the social aggregation of a large group of animals or the community of humans. In this work, the swarming model that includes the short-range repulsion and long-range attraction with the presence of time delay is investigated. Moreover, the convergence to a consensus representing dispersion and cohesion properties is proved by using the Lyapunov functional approach. Finally, numerical results are provided to demonstrate the effect of time delay on the motion of the group of agents.

Stable emergent formations for a swarm of autonomous car-like vehicles

A biological swarm is an ideal multi-agent system that collectively self-organizes into bounded, if not stable, formations. A mathematical model, developed appropriately from some principle of swarming, should enable one, therefore, to study formation strategies for multiple autonomous robots. In this article, based on the hypothesis that swarming is an interplay between long-range attraction and short-range repulsion between the individuals in the swarm, a planar individual-based or Lagrangian swarm model is constructed using the Direct Method of Lyapunov. While attraction ensures the swarm is cohesive, meaning that the individuals in the swarm remain close to each other at all times, repulsion ensures that the swarm is well-spaced, meaning that no two individuals in the swarm occupy the same space at the same time. Via a novel Lyapunov-like function with attractive and repulsive components, the article establishes the global existence, uniqueness, and boundedness of solutions about the centroid. This paves the way to prove that the swarm model, governed by a system of first-order ordinary differential equations (ODEs), is cohesive and well-spaced. The article goes on to show that the artificial swarm can collectively self-organize into two stable formations: (i) a constant arrangement about the centroid when the system has equilibrium points, and (ii) a highly parallel formation when the system does not have equilibrium points. Computer simulations not only illustrate these but also reveal other emergent patterns such as swirling structures and random-like walks. As an application, we tailor the model accordingly and propose new autonomous steering laws giving rise to pattern-forming for multiple nonholonomic car-like vehicles.

Local interactions and their group-level consequences in flocking jackdaws

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula ) in flocks containing 2–338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

The Amphoteric and Hydrophilic Properties of Cartilage Surface in Mammalian Joints: Interfacial Tension and Molecular Dynamics Simulation Studies

In this paper, we explain the amphoteric character of the cartilage surface by studying a lipid bilayer model built from phospholipids. We examined the interfacial tension values and molecular dynamics simulation in solutions of varying pH. The effects of negative and positive charge density (or fixed charges) on the (cartilage/cartilage) friction coefficient were investigated. In physiological (or synovial) fluid, after the isoelectric point (pI), the curve of interfacial tension decreases rapidly as it reaches pH 7.4 and then approaches a constant value at higher pH. It was shown that the curve of the interfacial tension curve exhibits a maximum value at the isoelectric point with a Gaussian shape feature. The phospholipid bilayers facilitate an almost frictionless contact in the joint. Moreover, the slippage of the bilayer and the short-range repulsion between the surfaces of the negatively charged cartilage surfaces are the main determinants of the low frictional properties of the joint.

Charge density distributions and electron scattering form factors of 19F, 27Al and 25Mg nuclei

An effective two-body density operator for point nucleon system folded with two-body correlation functions, which take account of the effect of the strong short range repulsion and the strong tensor force in the nucleon-nucleon forces, is produced and used to derive an explicit form for ground state two-body charge density distributions (2BCDD's) and elastic electron scattering form factors F (q) for 19F, 27Al and 25Mg nuclei. It is found that the inclusion of the two-body short range correlations (SRC) has the feature of reducing the central part of the 2BCDD's significantly and increasing the tail part of them slightly, i.e. it tends to increase the probability of transferring the protons from the central region of the nucleus towards its surface and to increase the root mean square charge radius ˂ r 2˃ 1/2 of the nucleus and then makes the nucleus to be less rigid than the case when there is no (SRC). It is also found that the effects of two body tensor correlations (TCs) on 2BCDD's and ˂ r 2˃ 1/2 are in opposite direction to those of (SRC).

Роль кулоновского взаимодействия электронов адсорбата и субстрата: модель поверхностного димера

Coulomb interaction in adsorption system is reduced to the short-range repulsion of the electrons of adsorbed particle and substrate surface atom which are considered as the surface dimer. It is shown that the account of such an interaction leads to the increase of charge transfer between the dimer’s components and decrease of charge transfer between dimer and metallic substrate due to the Fermi level variation.