Light Induced Inverse-Square Law Interactions between Nanoparticles: "Mock Gravity" at the Nanoscale.

The interaction forces between identical resonant molecules or nanoparticles, optically induced by a quasimonochromatic isotropic random light field, are theoretically analyzed. In general, the interaction force exhibits a far-field oscillatory behavior at separation distances larger than the light wavelength. However, we show that the oscillations disappear when the frequency of the random field is tuned to an absorption Fröhlich resonance, at which the real part of the particle's electric polarizability is zero. At the resonant condition, the interaction forces follow a long-range gravitylike inverse square distance law which holds for both near- and far-field separation distances.

Sectoral multipole focused beams.

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are "sectoral" multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams.

Optofluidic control of the dispersion of nanoscale dumbbells.

Previous research has shown that gold nanoparticles immersed in water in an optical vortex lattice formed by the perpendicular intersection of two standing light waves with a π/2rad phase difference will experience enhanced dispersion that scales with the intensity of the incident laser. We show that flexible nanoscale dumbbells (created by attaching two such gold particles by means of a polymer chain) in the same field display different types of motion depending on the chain length and field intensity. We have not disregarded the secondary optical forces due to light scattering. The dumbbells may disperse, rotate, or remain trapped. For some values of the parameters, the (enhanced) dispersion possesses a displacement distribution with exponential tails, making the motion anomalous, though Brownian.

Solvent Hydrodynamics Enhances the Collective Diffusion of Membrane Lipids.

The collective motion of membrane lipids over hundreds of nanometers and nanoseconds plays an essential role in the formation of submicron complexes of lipids and proteins in the cell membrane. These dynamics are difficult to access experimentally and are currently poorly understood. One of the conclusions of the celebrated Saffman-Debrück (SD) theory is that lipid disturbances smaller than the Saffman length (microns) are not affected by the hydrodynamics of the embedding solvent. Using molecular dynamics and coarse-grained models with implicit hydrodynamics we show that this is not true. Hydrodynamic interactions between the membrane and the solvent strongly enhance the short-time collective diffusion of lipids at all scales. The momentum transferred between the membrane and the solvent in the normal direction (not considered by the SD theory) propagates tangentially over the membrane inducing long-ranged repulsive forces amongst lipids. As a consequence, the lipid collective diffusion coefficient increases proportionally to the disturbance wavelength. We find quantitative agreement with the predicted anomalous diffusion in quasi-two-dimensional dynamics, observed in colloids confined to a plane but embedded in a three-dimensional solvent.

Collective colloid diffusion under soft two-dimensional confinement.

This work presents a numerical and theoretical investigation of the collective dynamics of colloids in an unbounded solution but trapped in a harmonic potential. Under strict two-dimensional confinement (infinitely stiff trap) the collective colloidal diffusion is enhanced and diverges at zero wave number (like k^{-1}), due to the hydrodynamic propagation of the confining force across the layer. The analytic solution for the collective diffusion of colloids under a Gaussian trap of width δ still shows enhanced diffusion for large wavelengths kδ<1, while a gradual transition to normal diffusion for kδ>1. At intermediate and short wavelengths, we illustrate to what extent the hydrodynamic enhancement of diffusion is masked by the conservative forces between colloids. At very large wavelengths, the collective diffusion becomes faster than the solvent momentum transport and a transition from Stokesian dynamics to inertial dynamics takes place. Using our inertial coupling method code (resolving fluid inertia), we study this transition by performing simulations at small Schmidt number. Simulations confirm theoretical predictions for the k→0 limit [Phys. Rev. E 90, 062314 (2014)PLEEE81539-375510.1103/PhysRevE.90.062314] showing negative density-density time correlations. However, at finite k simulations show deviations from the theory.

Thermodynamics of adaptive molecular resolution.

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ=U(1)-U(0) The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al, J. Chem. Phys. 142, 064115, 2015 (doi:10.1063/1.4907006)) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as 'real' thermodynamic variablesThis article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Statistical mechanics of Hamiltonian adaptive resolution simulations.

The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.

Minimal model for acoustic forces on Brownian particles.

We present a generalization of inertial coupling (IC) [Balboa Usabiaga et al., J. Comput. Phys. 235, 701 (2013)], which permits the resolution of radiation forces on small particles with arbitrary acoustic contrast factor. The IC method is based on a Eulerian-Lagrangian approach: particles move in continuum space while the fluid equations are solved in a regular mesh (here we use the finite volume method). Thermal fluctuations in the fluid stress, important below the micron scale, are also taken into account following the Landau-Lifshitz fluid description. Each particle is described by a minimal cost resolution which consists of a single small kernel (bell-shaped function) concomitant to the particle. The main role of the particle kernel is to interpolate fluid properties and spread particle forces. Here, we extend the kernel functionality to allow for an arbitrary particle compressibility. The particle-fluid force is obtained from an imposed "no-slip" constraint which enforces similar particle and kernel fluid velocities. This coupling is instantaneous and permits the capture of the fast, nonlinear effects underlying the radiation forces on particles. Acoustic forces arise because of an excess either in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions shows that the present generalization of the IC method correctly reproduces both contributions. Due to its low computational cost, the present method allows for simulations with many [O(10(4))] particles using a standard graphical processor unit.

Nonreflecting boundaries for ultrasound in fluctuating hydrodynamics of open systems.

We present a formulation for nonreflecting boundaries in fluctuating hydrodynamics. Nonreflecting boundary conditions are designed to evacuate sound waves out of the computational domain, thus allowing one to deal with open systems and to avoid finite size effects associated with periodic boundaries. Thermodynamic consistency for the fluctuation of the total mass and momentum of the open system is ensured by a fluctuation-dissipation balance which controls the amplitude of the sound waves generated by stress fluctuations near the boundary. We consider equilibrium and out-of-equilibrium situations (forced sound) in liquid water at ambient conditions and argon ranging from gas to liquid densities. Nonreflecting boundaries for fluctuating hydrodynamics make feasible simulations of ultrasound in microfluidic devices.

Hydrodynamics of nanoscopic capillary waves.

The dynamics of nanoscopic capillary waves on simple liquid surfaces is analyzed using molecular dynamics simulations. Each Fourier mode of the surface is obtained from the molecular positions, and its time behavior compared with the hydrodynamic prediction. We trace the transition from propagating to overdamped modes, at short wavelengths. The damping rate is in very good agreement with the hydrodynamic theory up to surprisingly small wavelengths, of about four molecular diameters, but only if the wave number dependent surface tension is considered. At shorter scales, surface tension hydrodynamics break down and we find a transition to a molecular diffusion regime.

Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids.

We present a hybrid protocol designed to couple the dynamics of a nanoscopic region of liquid described at atomistic level with a fluctuating hydrodynamics description of the surrounding liquid. The hybrid technique is based on the exchange of fluxes and it is shown to respect the conservation laws of fluid mechanics. This fact allows us to solve unsteady flows involving shear and sound waves crossing the interface of both domains. In equilibrium we find perfect agreement with the grand-canonical ensemble at low and moderate densities, while within the nanoscopic volumes considered, mass fluctuation (both in hybrid and full MD simulations) becomes slightly larger than predicted by the thermodynamic limit. Stress fluctuations across the hybrid interface are shown to have a seamless profile. Nonequilibrium scenarios involving shear (startup of Couette flow) and longitudinal flow (sound waves) are also illustrated.

Fluctuating hydrodynamic modeling of fluids at the nanoscale.

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales [De Fabritiis, Phys. Rev. Lett. 97, 134501 (2006)]. However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider nonequilibrium states involving diffusion and convection in cavities with no-slip boundary conditions.

Multiscale modeling of liquids with molecular specificity.

The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which addresses this problem by keeping the full molecular nature of the system where it is of interest and coarse graining it elsewhere. This is made possible by coupling molecular dynamics with a mesoscopic description of realistic liquids based on Landau's fluctuating hydrodynamics. We show that our scheme correctly couples hydrodynamics and that fluctuations, at both the molecular and continuum levels, are thermodynamically consistent. Hybrid simulations of sound waves in bulk water and reflected by a lipid monolayer are presented as illustrations of the scheme.

Determination of the chemical potential using energy-biased sampling.

An energy-biased method to evaluate ensemble averages requiring test-particle insertion is presented. The method is based on biasing the sampling within the subdomains of the test-particle configurational space with energies smaller than a given value freely assigned. These energy wells are located via unbiased random insertion over the whole configurational space and are sampled using the so-called Hit-and-Run algorithm, which uniformly samples compact regions of any shape immersed in a space of arbitrary dimensions. Because the bias is defined in terms of the energy landscape it can be exactly corrected to obtain the unbiased distribution. The test-particle energy distribution is then combined with the Bennett relation for the evaluation of the chemical potential. We apply this protocol to a system with relatively small probability of low-energy test-particle insertion, liquid argon at high density and low temperature, and show that the energy-biased Bennett method is around five times more efficient than the standard Bennett method. A similar performance gain is observed in the reconstruction of the energy distribution.

Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow.

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C-->P and P-->C) that conveys mass, momentum, and energy fluxes. The contribution of the hybrid scheme hereby presented is twofold. First, it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C-->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature, and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.

Effects of thermal boundary conditions and cavity tilt on hydrothermal waves: suppression of oscillations.

Hydrothermal waves are longitudinal modes responsible for the onset of oscillations of low-Prandtl number flows inside end-heated cavities. We consider the flow induced by the hydrothermal wave in a rectangular enclosure whose differentially-heated side is tilted alpha degrees from the vertical position. An analytical approximation to the neutral curve and dispersion relation obtained by the Galerkin procedure is shown to quantitatively agree with the exact numerical solution of the stability problem. The analytical expressions are then used to dissect the effect of the Prandtl and Biot numbers and the inclination on the wave stability. In conducting walls the critical Rayleigh R(cr) and wave number m(cr) tend to a constant value at low Pr, while the critical frequency f(cr) approximately Pr(-1/12). In adiabatic walls all these critical parameters increase like Pr(1/2). The boundaries can be considered to be poorly insulated if Bi>Pr, and in this case the critical parameters increase like Bi(1/2). On the other hand, R(cr) and m(cr) reach a minimum value at intermediate inclinations, while the critical frequency steadily increases with alpha. A closed equation for the frequency is also derived. This equation correctly forecasts the critical frequency in the unbounded domain and also the fundamental frequency measured in confined flows, as revealed by comparison with previous experiments and hereby presented numerical calculations for varying alpha. An important conclusion of the study is that for any arbitrarily small value of Pr the hydrothermal wave can be suppressed by heating the cavity above a theoretically predicted (Pr-dependent) angle. This prediction is of great relevance in the application domain (viz. the crystal growth from melts by the Bridgman technique).

Convection patterns in end-heated inclined enclosures.

The natural convection in inclined side-heated rectangular boxes with adiabatic walls is theoretically and numerically investigated. The study is focused on the characterization of the convection patterns arising at the core of the basic steady unicellular flow and covers the whole range of Prandtl numbers (0< or = Pr < or = infinity) and inclinations (from alpha=0 degrees, heated-from-below vertical cavities, to alpha=180 degrees ). The onset of the flow instabilities depends on the core Rayleigh number R identical with K Ra, defined in terms of the local streamwise temperature gradient, K Delta T/L. The critical value of R for transversal and longitudinal modes is determined by the linear stability analysis of the basic plane-parallel flow, which also provides the stability diagram in the (Pr-alpha) chart. Anyhow, the effect of confinement can decisively change the stability properties of the core: if the steady unicell reaches the boundary layer regime (BLR) the local temperature gradient vanishes at the core leaving a completely stable core region. A theoretical determination of the frontier of the BLR in the space of parameters (alpha, R, and cavity size) yields an extra criterion of stability that has been displayed in the stability diagram. As confirmed by numerical calculations, the core-flow instabilities can only develop for Pr