Search results for "Mathematics"
showing 10 items of 22031 documents
Force probe simulations of a reversibly rebinding system: Impact of pulling device stiffness.
2017
We present a detailed study of the parameter dependence of force probe molecular dynamics (FPMD) simulations. Using a well studied calix[4]arene catenane dimer as a model system, we systematically vary the pulling velocity and the stiffness of the applied external potential. This allows us to investigate how the results of pulling simulations operating in the constant velocity mode (force-ramp mode) depend on the details of the simulation setup. The system studied has the further advantage of showing reversible rebinding meaning that we can monitor the opening and the rebinding transition. Many models designed to extract kinetic information from rupture force distributions work in the limit…
Introducing Memory in Coarse-Grained Molecular Simulations
2021
[Image: see text] Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori–Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In…
Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble …
2015
Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles …
Nonlinear response theory for Markov processes II: Fifth-order response functions
2017
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012)). For sinusoidal fields the $5\om$-component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurence of such a hump as compared to a …
Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved a…
2008
The theory and implementation of approximate coupled-cluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general single-determinant reference functions. While the extension of iterative approximate models to the non-Hartree-Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for non-Hartree-Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree-Fock-base…
Quantum Dynamics of the 17O + 32O2 Collision Process
2016
We report full quantum integral and differential cross sections and rate constants for the 17O + 32O2 reactive process. This constitutes the first quantum scattering study of the 17O16O16O system. We emphasize the comparison with the 18O + 32O2 collision in close connection to the mass-independent fractionation (hereafter referred to as MIF) puzzle for ozone in atmospheric chemistry. We find similar general trends in the cross sections and rate constants for both rare isotopes, but we note some singular behaviors peculiar to the use of 17O isotope, particularly at the lowest collision energies.
Matrix isolation and quantum chemical studies on the H2O2–SO2complex
2004
Complexation and photochemical reactions of hydrogen peroxide and sulfur dioxide have been studied in solid Ar, Kr and Xe. Complexes between H2O2 and SO2 are characterized using Fourier transform infrared spectroscopy and ab initio calculations. In solid Ar, the H2O2–SO2 complex absorptions are found at wavenumbers of 3572.8, 3518.7, 3511.2, 3504.3, 1340.3, 1280.2 and 1149.9 cm−1. In Kr and Xe matrices, the bonded OH stretching frequencies deviate from the values in Ar, and we propose that the matrix surrounding influences the structure of the H2O2–SO2 complex. UV photolysis of the H2O2–SO2 was also studied in solid Ar, Kr and Xe. This photolysis produces mainly a complex between sulfur tri…
Smoothed Spherical Truncation based on Fuzzy Membership Functions: Application to the Molecular Encoding.
2019
A novel spherical truncation method, based on fuzzy membership functions, is introduced to truncate interatomic (or interaminoacid) relations according to smoothing values computed from fuzzy membership degrees. In this method, the molecules are circumscribed into a sphere, so that the geometric centers of the molecules are the centers of the spheres. The fuzzy membership degree of each atom (or aminoacid) is computed from its distance with respect to the geometric center of the molecule, by using a fuzzy membership function. So, the smoothing value to be applied in the truncation of a relation (or interaction) is computed by averaging the fuzzy membership degrees of the atoms (or aminoacid…
Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology
2016
This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called “contextuality-by-default,” and then discuss generalizations of the theory to arbitrary systems of arbitrary random variables.
Harmonic morphisms in nonlinear potential theory
1992
This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.