Pattern universes

In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.     

Reentrant behavior of magnetic ordered phase in spin-crossover solids with quenched disordered ligand field

The Ising-like model of spin-crossover solid compounds with quenched random ligand field has been investigated by the mean-field (infinite-range) approximation. An exact solution for the problem is found within the replica formalism. The magnetic diagrams are obtained; the relations between the intermolecular coupling and the temperature as well as the reentrant phenomena of the magnetic ordered phase are discussed.     

Biocatalytic Feedback‐Controlled Non‐Newtonian Fluids

Non‐Newtonian fluids are ubiquitous in daily life and industrial applications. Herein, we report an intelligent fluidic system integrating two distinct non‐Newtonian rheological properties mediated by an autocatalytic enzyme reaction. Associative polyelectrolytes bearing a small amount of ionic and alkyl groups are engineered: by carefully balancing the charge density and the hydrophobic effect, the polymer solutions demonstrate a unique shear thickening property at low pH while shear thinning at high pH. The urea‐urease clock reaction is utilized to program a feedback‐induced pH change, leading to a strong upturn of the nonlinear viscoelastic properties. As long as the chemical fuel is supplied, two distinct non‐Newtonian states can be achieved with a tunable lifetime span. As a proof of concept, we demonstrate how the physical energy‐driven nonequilibrium properties can be manipulated by a chemical‐fueled process.     

Instabilities of soap film structures in square cuboid frame

ABSTRACT

Through the simulations performed with the Surface Evolver, we explored the T1s and the eight-fold vertex related topological changes in the square cuboid frame by changing the axial ratio λ and the liquid fraction ?. A stability diagram is provided to illustrate the instabilities encountered in any quasi-static process. Metastable film configurations are always accompanied by pre-emptive instabilities, while the instabilities of stable film configurations are not triggered until the central quadrilateral film steadily vanishes.     

Exact coexistence surfaces containing double critical points for a three-component solution on the Bethe,honeycomb, and square lattices

A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponent near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.     

One-dimensional model with rotational and liquid-crystalline phase transitions

A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water.