The beta sheet is a common motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands) connected laterally by at least two or three backbone hydrogen bonds, forming a generally twisted, pleated sheet. A β-strand is a stretch of polypeptide chain typically 3 to 10 amino acids long with backbone in an extended conformation. The supramolecular association of β-sheets has been implicated in the formation of the fibrils and protein aggregates observed in amyloidosis, Alzheimer's disease and other proteinopathies.
Topology is the part of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension.
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions or to non-Euclidean spaces such as hyperbolic space.
Carbon is capable of forming many allotropes due to its valency. Well-known forms of carbon include diamond and graphite. In recent decades, many more allotropes have been discovered and researched, including ball shapes such as buckminsterfullerene and sheets such as graphene. Larger-scale structures of carbon include nanotubes, nanobuds and nanoribbons. Other unusual forms of carbon exist at very high temperatures or extreme pressures. Around 500 hypothetical 3‑periodic allotropes of carbon are known at the present time, according to the Samara Carbon Allotrope Database (SACADA).
Nanomaterials describe, in principle, materials of which a single unit is sized between 1 and 100 nm.
Graphene is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds.
Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers – specifically polypeptides – formed from sequences of amino acids, which are the monomers of the polymer. A single amino acid monomer may also be called a residue, which indicates a repeating unit of a polymer. Proteins form by amino acids undergoing condensation reactions, in which the amino acids lose one water molecule per reaction in order to attach to one another with a peptide bond. By convention, a chain under 30 amino acids is often identified as a peptide, rather than a protein. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions, such as hydrogen bonding, ionic interactions, Van der Waals forces, and hydrophobic packing. To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional structure. This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo-electron microscopy (cryo-EM) and dual polarisation interferometry, to determine the structure of proteins.
A trabecula is a small, often microscopic, tissue element in the form of a small beam, strut or rod that supports or anchors a framework of parts within a body or organ. A trabecula generally has a mechanical function, and is usually composed of dense collagenous tissue. It can be composed of other material such as muscle and bone. In the heart, muscles form trabeculae carneae and septomarginal trabeculae. Cancellous bone is formed from groupings of trabeculated bone tissue.
Auxetics are typical structures of the representative mechanical meta-materials. Mechanical meta-materials are structures whose mechanical properties are artificially derived from sophisticated structures and refer to unique structures that do not take place in nature. Herein, the basic concept of meta implies something that goes beyond naturally occurring substances. Generally, materials have a positive Poisson's ratio. Unlike general materials, Auxetics are structures or materials that have a negative Poisson's ratio. In terms of general materials, it is noted that while elongating along the x axis, the length in the y axis is decreased. Interestingly, in terms of the auxetic structure, while it expands along the x axis, y axis also expands simultaneously. In other words, elongation occurs in both directions, causing a rapid decrease in volume.
ν=-ε(trans)/ε(axial)
Graphene nanoribbons are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine the edge and nanoscale size effect in graphene.
In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.
Mechanical metamaterials are artificial materials with mechanical properties that are defined by their mesostructure in addition to than their composition. They can be seen as a counterpart to the rather well-known family of optical metamaterials. They are often also termed elastodynamic metamaterials and include acoustic metamaterials as a special case of vanishing shear. Their mechanical properties can be designed to have values which cannot be found in nature.
Salvatore Torquato is an American theoretical scientist born in Falerna, Italy. His research work has impacted a variety of fields, including physics, chemistry, applied and pure mathematics, materials science, engineering, and biological physics. He is the Lewis Bernard Professor of Natural Sciences in the department of chemistry and Princeton Institute for the Science and Technology of Materials at Princeton University. He has been a senior faculty fellow in the Princeton Center for Theoretical Science, an enterprise dedicated to exploring frontiers across the theoretical natural sciences. He is also an associated faculty member in three departments or programs at Princeton University: physics, applied and computational mathematics, and mechanical and aerospace engineering. On multiple occasions, he was a member of the schools of mathematics and natural sciences at the Institute for Advanced Study, Princeton, New Jersey.
Aerographene or graphene aerogel is the least dense solid known to exist, at 160 g/m3. The material reportedly can be produced at the scale of cubic meters.
Borophene is a crystalline atomic monolayer of boron, i.e., it is a two-dimensional allotrope of boron and also known as boron sheet. First predicted by theory in the mid-1990s, different borophene structures were experimentally confirmed in 2015.
Ulam's packing conjecture, named for Stanislaw Ulam, is a conjecture about the highest possible packing density of identical convex solids in three-dimensional Euclidean space. The conjecture says that the optimal density for packing congruent spheres is smaller than that for any other convex body. That is, according to the conjecture, the ball is the convex solid which forces the largest fraction of space to remain empty in its optimal packing structure. This conjecture is therefore related to the Kepler conjecture about sphere packing. Since the solution to the Kepler conjecture establishes that identical balls must leave ≈25.95% of the space empty, Ulam's conjecture is equivalent to the statement that no other convex solid forces that much space to be left empty.
A carbon nanothread is a sp3-bonded, one-dimensional carbon crystalline nanomaterial. The tetrahedral sp3-bonding of its carbon is similar to that of diamond. Nanothreads are only a few atoms across, more than 300,000 times thinner than a human hair. They consist of a stiff, strong carbon core surrounded by hydrogen atoms. Carbon nanotubes, although also one-dimensional nanomaterials, in contrast have sp2-carbon bonding as is found in graphite. The smallest carbon nanothread has a diameter of only 0.2 nanometers, much smaller than the diameter of a single-wall carbon nanotube.
A graphene morphology is any of the structures related to, and formed from, single sheets of graphene. 'Graphene' is typically used to refer to the crystalline monolayer of the naturally occurring material graphite. Due to quantum confinement of electrons within the material at these low dimensions, small differences in graphene morphology can greatly impact the physical and chemical properties of these materials. Commonly studied graphene morphologies include the monolayer sheets, bilayer sheets, graphene nanoribbons and other 3D structures formed from stacking of the monolayer sheets.
Titanium foams exhibit high specific strength, high energy absorption, excellent corrosion resistance and biocompatibility. These materials are ideally suited for applications within the aerospace industry. An inherent resistance to corrosion allows the foam to be a desirable candidate for various filtering applications. Further, titanium's physiological inertness makes its porous form a promising candidate for biomedical implantation devices. The largest advantage in fabricating titanium foams is that the mechanical and functional properties can be adjusted through manufacturing manipulations that vary porosity and cell morphology. The high appeal of titanium foams is directly correlated to a multi-industry demand for advancement in this technology.
