On the "generalized Generalized Langevin Equation"

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. In contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation, but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows to relate the Taylor expansion of the memory kernel to data that is accessible in MD simulations and experiments, thus allowing to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions, and is shown to be consistent with direct measurements from simulations

Cooling rate, heating rate and aging effects in glassy water

We report a molecular dynamics simulation study of the properties of the potential energy landscape sampled by a system of water molecules during the process of generating a glass by cooling, and during the process of regenerating the equilibrium liquid by heating the glass. We study the dependence of these processes on the cooling/heating rates as well as on the role of aging (the time elapsed in the glass state). We compare the properties of the potential energy landscape sampled during these processes with the corresponding properties sampled in the liquid equilibrium state to elucidate under which conditions glass configurations can be associated with equilibrium liquid configurations.Comment: to be published in Phys. Rev. E (rapid comunication

Intermittent permeation of cylindrical nanopores by water

Molecular Dynamics simulations of water molecules in nanometre sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is {\emph{intermittent}} on a nanosecond timescale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulk-like. Its behaviour differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract into a highly layered structure inside the channel.Comment: 4 pages, 4 figure

Assessment of the validity of intermolecular potential models used in molecular dynamics simulations by extended x-ray absorption fine structure spectroscopy:A case study of Sr2+ in methanol solution

Molecular dynamics simulations have been carried out for Sr2+ in methanol using different Sr2+ Lennard-Jones parameters and methanol models. X-ray absorption fine structure. (EXAFS) spectroscopy has been employed to assess the reliability of the ion-ion and ion-methanol potential functions used in the simulations. Radial distribution functions of Sr2+ in methanol have been. calculated for each simulation and compared with the EXAFS experimental data. This procedure has allowed the determinations of reliable Sr2+-methanol models which have been used in longer simulations providing an accurate description of the dynamic and structural properties of this system

Free energy of hydrophobic hydration:A molecular dynamics study of noble gases in water

The potential utility and limitations of two methods to determine free energy differences from molecular dynamics simulations (MD) are studied. The computation of the free energy of hydration of the inert gases serves as a simple but illustrative example. Good results are obtained for the inert gases from a perturbation treatment, using a reference ensemble obtained from a MD simulation of a cavity in water, if these atoms are comparable in size to the cavity and the calculated free energy differences are small. This limits the applicability of the perturbation treatment of a small number of cases. Larger free energy differences can be obtained with reasonable accuracy from MD simulations with continuously changing interaction parameters. This integration method is more generally applicable, but makes an additional simulation necessary

Magnetic friction due to vortex fluctuation

We use Monte Carlo and molecular dynamics simulation to study a magnetic tip-sample interaction. Our interest is to understand the mechanism of heat dissipation when the forces involved in the system are magnetic in essence. We consider a magnetic crystalline substrate composed of several layers interacting magnetically with a tip. The set is put thermally in equilibrium at temperature T by using a numerical Monte Carlo technique. By using that configuration we study its dynamical evolution by integrating numerically the equations of motion. Our results suggests that the heat dissipation in this system is closed related to the appearing of vortices in the sample.Comment: 6 pages, 41 figure

Cooperative Origin of Low-Density Domains in Liquid Water

We study the size of clusters formed by water molecules possessing large enough tetrahedrality with respect to their nearest neighbors. Using Monte Carlo simulation of the SPC/E model of water, together with a geometric analysis based on Voronoi tessellation, we find that regions of lower density than the bulk are formed by accretion of molecules into clusters exceeding a minimum size. Clusters are predominantly linear objects and become less compact as they grow until they reach a size beyond which further accretion is not accompanied by a density decrease. The results suggest that the formation of "ice-like" regions in liquid water is cooperative.Comment: 16 pages, 6 figure

A phase II study of high dose epirubicin in unresectable non small cell lung cancer.

Epirubicin (EPI), a doxorubicin analogue, is reported to have equal antitumour activity with lower cardiac and systemic toxicity. Recently, the maximum tolerated dose of this drug has been revised upwards with reported increased response rates in several malignancies. We initiated a phase II study of high-dose EPI as initial treatment for patients with advanced non-small cell lung cancer (NSCLC) (stage III and IV). Between May 1988 and November 1989, 25 patients were entered. The starting dose of EPI was 135 mg m-2, with dose attenuations and escalations of 15 mg m-2 based on mid-cycle evaluation of toxicity. Treatment was repeated every 3 weeks. Nine partial responses (36%, 95% CI: 18-57.5%) and 11 patients with disease stabilisation (44%) were observed. Median (range) time to progression was 19 (3-70) weeks. Median (range) survival is 32 (9-116+) weeks. There were no treatment related deaths. Major side effects were leukocytopenia WHO grade III/IV (23% of courses) and mucositis WHO grade II/III (15% of courses). In two patients left ventricular ejection fraction decreased greater than 15% compared to baseline values after a cumulative Epirubicin dose of 435 mg m-2, and therefore went off study. In none of the patients clinical signs of congestive heart failure were observed. We conclude from our data that high-dose EPI, contrary to previous negative studies using lower doses of EPI, ranks amongst the most active regimens against advanced NSCLC. Toxicity of high-dose EPI is moderate. Further evaluation of this compound in combination regimens is recommended

Physics of the liquid-liquid critical point

Within the inherent structure (IS) thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A {\bf 25}, 978 (1982)] we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape (PEL) responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.Comment: Physical Review Letters, in publicatio

High frequency longitudinal and transverse dynamics in water

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q,\omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed. The study of their temperature- and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c_0) (viscous limit) to the infinite frequency sound velocity (c_\infinity) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q,\omega) as soon as the purely viscous regime is left.Comment: 28 pages, 12 figure