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Soft materials, such as colloidal suspensions, polymer solutions, and biological systems, are typically multicomponent mixtures of macromolecules and simpler components (e.g., microions, monomers, solvent) that can assemble into complex…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…
We introduce the concept of a soft ditopological space as the "soft generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Erturk, S. Dost,…
We provide an informal discussion of pattern formation in a finite universe. The global size and shape of the universe is revealed in the pattern of hot and cold spots in the cosmic microwave background. Topological pattern formation can be…
Earth's water, intrinsic oxidation state, and metal core density are fundamental chemical features of our planet. Studies of exoplanets provide a useful context for elucidating the source of these chemical traits. Planet formation and…
This article provides a detailed review on the generalized dynamics of soft-matter quasicrystals developed recent years. Comparing to solid quasicrystals consisted mainly with metallic alloys, soft-matter quasicrystals have been observed in…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Galaxies, in particular disc galaxies, contain a number of structures and substructures with well defined morphological, photometric and kinematic properties. Considerable theoretical effort has been put into explaining their formation and…
The mass physical and dynamic properties of marine mud deposits are a function of the interaction among a maximum of four sediment Phases as follows: (1) clay mineral solids that often include silt and sand size particles of different…
Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…
Magma oceans are a common result of the high degree of heating that occurs during planet formation. It is thought that almost all of the large rocky bodies in the Solar System went through at least one magma ocean phase. In this paper, we…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
Life on Earth emerged at the interface of the geosphere, hydrosphere and atmosphere. This setting serves as our basis for how biological systems originate on rocky planets. Often overlooked, however, is the fact that the chemical nature of…
Granular materials, composed of discrete solid grains, can be modeled as simple mechanical systems. However, these materials can undergo spontaneous slow deformation, or creep, even under small forces and while in apparent mechanical…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
The spontaneous formation of patterns in dynamical systems is a rich phenomenon that transcends scientific boundaries. Here, we report our observation of coupled optical-atomic pattern formation, which results in the creation of…
Planetary systems can evolve dynamically even after the planets themselves have fully formed, and there is circumstantial evidence that most planetary systems become unstable after the disappearance of the gaseous protoplanetary disk.…
Where did elementary particles come from? What mechanisms are responsible for their occurrence and maintenance? Are they compound or truly elementary? Is vacuum primordial soup where elementary particles are born? Are quantum behavior and…