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Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and…
Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials…
Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich…
Spatially-periodic channels are increasingly attracting attention as an efficient alternative to packed columns for a number of analytical and engineering processes. In incompressible flows, the periodic geometry allows to compute the flow…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Two primary challenges stand in the way of practical large-scale quantum computation, namely achieving sufficiently low error rate quantum gates and implementing interesting quantum algorithms with a physically reasonable number of qubits.…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an…
The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications…
Metallic glasses possess outstanding mechanical and physical properties, making them promising candidates for advanced structural and functional applications; however, the lack of understanding and control over their glass transition and…
A novel Genetic Algorithm is described that is suitable for determining the global minimum energy configurations of crystal structures and which can also be used as a polymorph search technique. This algorithm requires no prior assumptions…
Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path integral Monte Carlo (PIMC) approach [J. Chem. Phys. {\bf 121}, 12696 (2004)]. The reduced electronic dynamics is…
In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract…
We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental group of the link complement over all meridional presentations…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
The critical point is a fixed point in finite-size scaling. To quantify the behaviour of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…