Related papers: Mapping the magic numbers in binary Lennard-Jones …
Using state-of-the-art rare-event sampling simulations, we precisely characterize the nucleation of liquid droplets from a supersaturated Lennard-Jones gas and uncover a key physical feature: critical clusters nucleate with a density that…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
A simple pair potential, which equilibrium pair separation can be varied under a fixed interaction range, has been proposed. The new potential can make both face-centered-cubic(fcc) and body-centered-cubic(bcc) structure stable by simply…
In this work, we employ density functional theory (DFT) to explore the structure of boron clusters doped with two chromium atoms (B$_7$Cr$_2$). The results show that the most stable structure is a bipyramidal configuration formed by a B$_7$…
The emergence of CsCl bulk structure in (CsCl)nCs+ cluster ions is investigated using a mixed quantum-mechanical/semiempirical theoretical approach. We find that rhombic dodecahedral fragments (with bulk CsCl symmetry) are more stable than…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of $n$ points into dimension $O(\log n)$ with low distortion of their distances. This dimension bound is tight…
For several decades, globular clusters have been considered the best example of simple stellar populations, hosting coeval and chemical homogeneous stars. The last decade of spectroscopic and photometric studies has revealed a more complex…
Almost all the polymer crystals have several polymorphic modifications. Their structure and existence conditions, as well as transitions between them are not understood even in the case of the 'model' polymer polyethylene (PE). For analysis…
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We…
The dynamic and static critical behavior of five binary Lennard-Jones liquid mixtures, close to their continuous demixing points (belonging to the so-called model H' dynamic universality class), are studied computationally by combining…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.
Given a natural number N, one may ask what configuration of N points on the two-sphere minimizes the discrete generalized Coulomb energy. If one applies a gradient-based numerical optimization to this problem, one encounters many…
Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We…
Zinc and cadmium clusters interacting with a Gupta potential have previously been identified as prototypical metallic systems that exhibiting disordered cluster structures. Here, putative global minima of the potential energy have been…
We consider a two-dimensional athermal binary mixture of Lennard-Jones particles with persistent random active forces. The liquid phase of this system for active forces exceeding a threshold value exhibits self-organization with long-range…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…