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Conventional molecular dynamics simulations macromolecules require long computational times because the most interesting motions are very slow compared with the fast oscillations of bond lengths and bond angles that limit the integration…
Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within R^5 with an inner product different from the usual one. This model enables efficient…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend…
Many areas of chemistry are devoted to the challenge of understanding, predicting, and controlling the behavior of strongly localized electrons. Examples include molecular magnetism and luminescence, color centers in crystals,…
We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of…
Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…
Rigid bodies, made of smaller composite beads, are commonly used to simulate anisotropic particles with molecular dynamics or Monte Carlo methods. To accurately represent the particle shape and to obtain smooth and realistic effective pair…
A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the…
A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or…
Seismic imaging is the numerical process of creating a volumetric representation of the subsurface geological structures from elastic waves recorded at the surface of the Earth. As such, it is widely utilized in the energy and construction…
Room-temperature metals and semi-metals which consist of a gas of bound electrons in a near-continuum band structure can be classified as cold quantum plasmas. This insight suggests that Particle-in-Cell (PIC) simulations, traditionally…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x…
Mesoscopic molecular dynamics simulations are used to determine the large scale structure of several binary polymer mixtures of various chemical architecture, concentration, and thermodynamic conditions. By implementing an analytical…