相关论文: Symmetric functions and the phase problem in cryst…

The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…

In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a…

We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We…

Generative models trained on public databases of protein structures, most of which have been determined by X-ray crystallography, now provide powerful priors for structure prediction. However, they are not readily conditioned on the…

The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be…

We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…

We develop the foundations of the deformation theory of compact complete affine space forms and affine crystallographic groups. Using methods from the theory of linear algebraic groups we show that these deformation spaces inherit an…

A new method for direct evaluation of both crystalline structure, bulk modulus B_0, and bulk-modulus pressure derivative B'_0 of solid materials with complex crystal structures is presented. The explicit and exact results presented here…

The application of generative models in crystal structure prediction (CSP) has gained significant attention. Conditional generation--particularly the generation of crystal structures with specified stability or other physical properties has…

Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…

Sub-angstrom spatial resolution of electron density coupled with sub-femtosecond temporal resolution is required to directly observe the dynamics of the electronic structure of a molecule after photoinitiation or some other ultrafast…

We consider various trace formulas for the cubic Schrodinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian…

Colored planar rook algebra is a semigroup algebra in which the basis element has a diagrammatic description. The category of finite dimensional modules over this algebra is completely reducible and suitable functors are defined on this…

We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…

Single-crystal X-ray diffraction (SC-XRD) is the gold standard technique to characterize crystal structures in solid state. Despite significant advances in automation for structure solution, the refinement stage still depends heavily on…

A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semi-analytic approach allows efficient and accurate…

The use of strongly bent crystals in spectrometers for pulses of a hard x-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated…

We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases…

The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…

In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…