Adaptively Biased Molecular Dynamics for Free Energy Calculations

We present an Adaptively Biased Molecular Dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using non-equilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential, and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters, and an $O(t)$ numerical cost with molecular dynamics time $t$. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.Comment: Revised version to appear in Journal of Chemical Physic

Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions

Giant Coulomb broadening and Raman lasing on ionic transitions

CW generation of anti-Stokes Raman laser on a number of blue-green argon-ion lines (4p-4s, 4p-3d) has been demonstrated with optical pumping from metastable levels 3d'^2G, 3d^4F. It is found, that the population transfer rate is increased by a factor of 3-5 (and hence, the output power of such Raman laser) owing to Coulomb diffusion in the velocity space. Measured are the excitation and relaxation rates for the metastable level. The Bennett hole on the metastable level has been recorded using the probe field technique. It has been shown that the Coulomb diffusion changes shape of the contour to exponential cusp profile while its width becomes 100 times the Lorentzian one and reaches values close to the Doppler width. Such a giant broadening is also confirmed by the shape of the absorption saturation curve.Comment: RevTex 18 pages, 5 figure

Neoclassical Theory of Elementary Charges with Spin of 1/2

We advance here our neoclassical theory of elementary charges by integrating into it the concept of spin of 1/2. The developed spinorial version of our theory has many important features identical to those of the Dirac theory such as the gyromagnetic ratio, expressions for currents including the spin current, and antimatter states. In our theory the concepts of charge and anticharge relate naturally to their "spin" in its rest frame in two opposite directions. An important difference with the Dirac theory is that both the charge and anticharge energies are positive whereas their frequencies have opposite signs

Intermittency and regularity issues in 3D Navier-Stokes turbulence

Two related open problems in the theory of 3D Navier-Stokes turbulence are discussed in this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation-range intermittency was first discovered experimentally by Batchelor and Townsend over fifty years ago. It is characterized by spatio-temporal binary behaviour in which long, quiescent periods in the velocity signal are interrupted by short, active `events' during which there are violent fluctuations away from the average. The second and related problem is whether solutions of the 3D Navier-Stokes equations develop finite time singularities during these events. This paper shows that Leray's weak solutions of the three-dimensional incompressible Navier-Stokes equations can have a binary character in time. The time-axis is split into `good' and `bad' intervals: on the `good' intervals solutions are bounded and regular, whereas singularities are still possible within the `bad' intervals. An estimate for the width of the latter is very small and decreases with increasing Reynolds number. It also decreases relative to the lengths of the good intervals as the Reynolds number increases. Within these `bad' intervals, lower bounds on the local energy dissipation rate and other quantities, such as \|\bu(\cdot, t)\|_{\infty} and \|\nabla\bu(\cdot, t)\|_{\infty}, are very large, resulting in strong dynamics at sub-Kolmogorov scales. Intersections of bad intervals for $n\geq 1$ are related to Scheffer's potentially singular set in time. It is also proved that the Navier-Stokes equations are conditionally regular provided, in a given `bad' interval, the energy has a lower bound that is decaying exponentially in time.Comment: 36 pages, 3 figures and 6 Table

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

The decay of turbulence in rotating flows

We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to $k^4$. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that separate the decay of two-dimensional from three-dimensional modes, and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered.Comment: Sections reordered to address comments by referee

Optical Characterisation of Suspended Particles in the Mackenzie River Plume (Canadian Arctic Ocean) and Implications for Ocean Colour Remote Sensing

Climate change significantly impacts Arctic shelf regions in terms of air temperature, ultraviolet radiation, melting of sea ice, precipitation, thawing of permafrost and coastal erosion. Direct consequences have been observed on the increasing Arctic river flow and a large amount of organic carbon sequestered in soils at high latitudes since the last glacial maximum can be expected to be delivered to the Arctic Ocean during the coming decade. Monitoring the fluxes and fate of this terrigenous organic carbon is problematic in such sparsely populated regions unless remote sensing techniques can be developed and proved to be operational. The main objective of this study is to develop an ocean colour algorithm to operationally monitor dynamics of suspended particulate matter (SPM) on the Mackenzie River continental shelf (Canadian Arctic Ocean) using satellite imagery. The water optical properties are documented across the study area and related to concentrations of SPM and particulate organic carbon (POC). Robust SPM and POC : SPM proxies are identified, such as the light backscattering and attenuation coefficients, and relationships are established between these optical and biogeochemical parameters. Following a semi-analytical approach, a regional SPM quantification relationship is obtained for the inversion of the water reflectance signal into SPM concentration. This relationship is reproduced based on independent field optical measurements. It is successfully applied to a selection of MODIS satellite data which allow estimating fluxes at the river mouth and monitoring the extension and dynamics of the Mackenzie River surface plume in 2009, 2010 and 2011. Good agreement is obtained with field observations representative of the whole water column in the river delta zone where terrigenous SPM is mainly constrained (out of short periods of maximum river outflow). Most of the seaward export of SPM is observed to occur within the west side of the river mouth. Future work will require the validation of the developed SPM regional algorithm based on match-ups with field measurements, then the routine application to ocean colour satellite data in order to better estimate the fluxes and fate of SPM and POC delivered by the Mackenzie River to the Arctic Ocean