Random conical tilt reconstruction without particle picking in cryo-electron microscopy

A method is described to reconstruct the 3D molecular structure without the need for particle picking in the random conical tilt scheme. The results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy.

On the termination of the X-ray constrained wavefunction procedure: reformulation of the method for an unequivocal determination of λ

The longstanding problem of determining the correct point at which to stop the calculations in the X-ray constrained wavefunction (XCW) approach is formally solved on solid mathematical grounds, and a new and more physically meaningful variant of the XCW method is proposed.

Growth forms of grid tilings

Growth forms can be used to study a range of crystallographic problems including obtaining exact formulae for coordination sequences, modeling the structures of nanoclusters and calculating topological densities. While they are fully understood in the periodic case, very little is known about them in the quasiperiodic case. Growth forms of quasiperiodic tilings obtained by the grid method are presented.

Diffraction enhancement of symmetry and modular structures

The necessary and sufficient conditions for diffraction enhancement of symmetry in monoarchetypal modular structures are derived.

Generating triply periodic surfaces from crystal structures: the tiling approach and its application to zeolites

Physical properties of objects depend on topological features of the corresponding triply periodic surfaces; thus topological exploration and classification of the surfaces has practical relevance. A general method is developed for generating triply periodic surfaces from triply periodic crystal structures. In 253 zeolite frameworks, 12 surfaces were found to be equivalent to already known triply periodic minimal surfaces (TPMSs), while four surfaces can be treated as new TPMSs.

Realizations of the abstract regular H₃ polyhedra

Regular polyhedra and related structures such as complexes and nets play a prominent role in the study of materials such as crystals, nanotubes and viruses. This work discusses an approach to the theory of realizations of abstract regular polyhedra with an emphasis on the construction of a realization and its decomposition as a blend of subrealizations. To demonstrate the approach, it is applied to the polyhedra whose automorphism groups are abstractly isomorphic to the non-crystallographic Coxeter group H₃.

X-ray third-order nonlinear diffraction in the asymmetric reflection geometry

X-ray third-order nonlinear asymmetrical Bragg diffraction is investigated.

Multidimensional color codes for chair tilings

A color code for chair tilings in arbitrary dimensions is presented. The code can be applied also to other lattice substitution tilings.

Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups

The first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent modulations is presented. An algorithm for uniquely identifying an arbitrary magnetic superspace group with an entry in this tabulation makes it straightforward to establish whether or not two incommensurate magnetic structures with apparently different symmetry operations actually have the same magnetic superspace group, but presented in different settings.

On the growth of the wallpaper groups

Using the method of cone types, the coordination sequences (also known as growth functions) of the wallpaper groups (the 2D crystallographic groups) are computed.

Lev Feigin (1928–2022)

Obituary for Lev Feigin.