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Rouse Emborg posted an update 6 months ago
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study and any derivation of an algebraic relation between the two do not seem to exist. Here, we explore the nature of this entropy-diffusion relation in three deterministic systems where an accurate estimate of both can be carried out. We study three deterministic model systems (a) the motion of a single point particle with constant energy in a two-dimensional periodic potential energy landscape, (b) the same in the regular Lorentz gas where a point particle with constant energy moves between collisions with hard disk scatterers, and (c) the motion of a point particle among the boxes with small apertures. These models exhibit diffusive motion in the limit where ergodicity is shown to exist. We estimate the self-diffusion coefficient of the particle by employing computer simulations and entropy by quadrature methods using Boltzmann’s formula. We observe an interesting crossover in the diffusion-entropy relation in some specific regions, which is attributed to the emergence of correlated returns. The crossover could herald a breakdown of the Rosenfeld-like exponential scaling between the two, as observed at low temperatures. Later, we modify the exponential relation to account for the correlated motions and present a detailed analysis of the dynamical entropy obtained via the Lyapunov exponent, which is rather an important quantity in the study of deterministic systems.Surface nanobubbles have potential applications in the manipulation of nanoscale and biological materials, waste-water treatment, and surface cleaning. These spherically capped bubbles of gas can exist in stable diffusive equilibrium on chemically patterned or rough hydrophobic surfaces, under supersaturated conditions. Previous studies have investigated their long-term response to pressure variations, which is governed by the surrounding liquid’s local supersaturation; however, not much is known about their short-term response to rapid pressure changes, i.e., their cavitation dynamics. Here, we present molecular dynamics simulations of a surface nanobubble subjected to an external oscillating pressure field. The surface nanobubble is found to oscillate with a pinned contact line, while still retaining a mostly spherical cap shape. Kenpaullone concentration The amplitude-frequency response is typical of an underdamped system, with a peak amplitude near the estimated natural frequency, despite the strong viscous effects at the nanoscale. This peak is enhanced by the surface nanobubble’s high internal gas pressure, a result of the Laplace pressure. We find that accurately capturing the gas pressure, bubble volume, and pinned growth mode is important for estimating the natural frequency, and we propose a simple model for the surface nanobubble frequency response, with comparisons made to other common models for a spherical bubble, a constant contact angle surface bubble, and a bubble entrapped within a cylindrical micropore. This work reveals the initial stages of growth of cavitation nanobubbles on surfaces, common in heterogeneous nucleation, where classical models based on spherical bubble growth break down.An adaptation of the full configuration interaction quantum Monte Carlo (FCIQMC) method is presented for correlated electron problems containing heavy elements and the presence of significant relativistic effects. The modified algorithm allows for the sampling of the four-component spinors of the Dirac-Coulomb(-Breit) Hamiltonian within the relativistic no-pair approximation. The loss of spin symmetry and the general requirement for complex-valued Hamiltonian matrix elements are the most immediate considerations in expanding the scope of FCIQMC into the relativistic domain, and the alternatives for their efficient implementation are motivated and demonstrated. For the canonical correlated four-component chemical benchmark application of thallium hydride, we show that the necessary modifications do not particularly adversely affect the convergence of the systematic (initiator) error to the exact correlation energy for FCIQMC calculations, which is primarily dictated by the sparsity of the wavefunction, allowing the computational effort to somewhat bypass the formal increases in Hilbert space dimension for these problems. We apply the method to the larger problem of the spectroscopic constants of tin oxide, correlating 28 electrons in 122 Kramers-paired spinors, finding good agreement with experimental and prior theoretical relativistic studies.We study the aqueous solvation dynamics of lithium ions using nuclear magnetic resonance spectroscopy, molecular dynamics, and viscosity measurements. Several relaxation mechanisms are examined to explain the strong increases of spin-lattice relaxation toward high concentrations. The use of both 6Li and 7Li isotopes is helpful to identify the quadrupolar contribution to the relaxation rate. In particular, it is found that the quadrupolar interaction constitutes the strongest contribution above a concentration of ∼10 molal. The next-strongest contribution arises from interactions that scale with the square of the gyromagnetic ratio (mostly the dipolar interaction), and the experimental relaxation rates appear to be fully accounted for when these mechanisms are combined over the concentration range up to the saturation concentration. The study of solvation dynamics, particularly at high concentrations, could be of relevance for electrolyte dynamics in aqueous Li-ion rechargeable batteries.Subsystem time-dependent density-functional theory (sTDDFT) making use of approximate non-additive kinetic energy (NAKE) functionals is known to be capable of describing excitation energy transfer processes in a variety of applications. Here, we show that sTDDFT, especially when combined with projection-based embedding (PbE), can be employed for the entire range of photo-induced electronic couplings essential for modeling photophysical properties of complex chemical and biological systems and therefore represents a complete toolbox for this class of problems. This means that it is capable of capturing the interaction/coupling associated with local- and charge-transfer (CT) excitons. However, this requires the choice of a reasonable diabatic basis. We therefore propose different diabatization strategies of the virtual orbital space in PbE-sTDDFT and show how CT excitations can be included in sTDDFT using NAKE functionals via a phenomenological approach. Finally, these electronic couplings are compared to couplings from a multistate fragment excitation difference (FED)-fragment charge difference (FCD) diabatization procedure.
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