Related papers: Lattice models and Monte Carlo methods for simulat…

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements.…

Fabrication of DNA nanostructures primarily follows two fundamental rules. First, DNA oligonucleotides mutually combine by Watson-Crick base pairing rules between complementary base sequences. Second, the geometrical compatibility of the…

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major…

The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have…

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential…

Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation…

The geometric, aesthetic, and mathematical elegance of origami is being recognized as a powerful pathway to self-assembly of micro and nano-scale machines with programmable mechanical properties. The typical approach to designing the…

The collective behavior of the shortest DNA oligomers in high concentration aqueous solutions is an unexplored frontier of DNA science and technology. Here we broaden the realm of DNA nanoscience by demonstrating that single-component…

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular…

Complementary DNA strands in solution reliably hybridize to form stable duplexes. We study the kinetics of the hybridization process and the mechanisms by which two initially isolated strands come together to form a stable double helix. We…

DNA-coated particles are promising as building blocks for functional and finite-sized assemblies because they can be programmed with orthogonal interactions owing to the sequence-specific hybridization of DNA strands. To fully exploit this…

We propose an off-lattice model for a self-avoiding homopolymer chain with two different competing attractive interactions, mimicking the hydrophobic effect and the hydrogen bond formation respectively. By means of Monte Carlo simulations,…

We develop the hybrid Monte Carlo method for simulations of single off-lattice polymer chains. We discuss implementation and choice of simulation parameters in some detail. The performance of the algorithm is tested on models for…

Lattice Monte Carlo simulations are used to study the phase behavior of self-assembling ordered mesoporous materials formed by an organic template with amphiphilic properties and an inorganic precursor in a model solvent. Three classes of…

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a…

We introduce an efficient, scalable Monte Carlo algorithm to simulate cross-linked architectures of freely-jointed and discrete worm-like chains. Bond movement is based on the discrete tractrix construction, which effects conformational…

Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However,…

Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. By bridging the lattice geometry and rigid-folding kinematics, this study…

Molecular electronics and other technologies whose components comprise individual molecules have been pursued for half a century because the molecular scale represents the limit of miniaturisation of objects whose structure is tuneable for…