Lagrangian statistics of passive tracers in rotating turbulence is investigated by particle tracking velocimetry. A confined and steadily forced turbulent flow is subjected to five different rotation rates. The PDFs of the velocity components clearly reveal the anisotropy induced by background rotation. Although the statistical properties of the horizontal turbulent flow field are approximately isotropic, in agreement with previously reported results by van Bokhoven and coworkers [Phys. Fluids 21, 096601 (2009)], the velocity component parallel to the (vertical) rotation axis gets strongly reduced (compared to the horizontal ones) while the rotation is increased. The auto-correlation coefficients of all three components are progressively enhanced for increasing rotation rates, although the vertical one shows a tendency to decrease for slow rotation rates. The decorrelation is approximately exponential. Lagrangian data compare favorably with previously reported Eulerian data for horizontal velocity components but show a different behavior for the vertical velocity components at higher rotation rates.

In this paper we investigate kinematic simulation (KS) consistency with the theory of Richardson [Proc. Roy. Soc. A 110, 24 (1926)] for two-particle diffusivity. In particular we revisit the sweeping problem. It has been argued by Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).] that due to the lack of sweeping of small scales by large scales in kinematic simulation, the validity of Richardson’s power law might be affected. Here, we argue that the discrepancies between authors on the ability of kinematic simulation to predict Richardson power law may be linked to the inertial subrange they have used. For small inertial subranges, KS is efficient and the significance of the sweeping can be ignored, as a result we limit the KS agreement with the Richardson scaling law $t^3$ for inertial subranges $k_N/k_1⩽10000$. For larger inertial range KS does not fully follow the $t^3$ law. Unfortunately, there is no experimental data to compare KS with and draw conclusions for such large inertial subranges. It cannot be concluded either that the discrepancy between KS and Richardson’s theory for larger inertial subranges is exactly taken into account by the theory developed in Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).].

The role of polymer additives on the turbulent convective flow of a Rayleigh-Taylor system is investigated by means of direct numerical simulations of Oldroyd-B viscoelastic model. The dynamics of polymer elongations follows adiabatically the self-similar evolution of the turbulent mixing layer and shows the appearance of a strong feedback on the flow which originates a cutoff for polymer elongations. The viscoelastic effects on the mixing properties of the flow are twofold. Mixing is appreciably enhanced at large scales (the mixing layer growth rate is larger than that of the purely Newtonian case) and depleted at small scales (thermal plumes are more coherent with respect to the Newtonian case). The observed speed up of the thermal plumes, together with an increase of the correlations between temperature field and vertical velocity, contributes to a significant enhancement of heat transport. Our findings are consistent with a scenario of drag reduction induced by polymers. A weakly nonlinear model proposed by Fermi for the growth of the mixing layer is reported in the Appendix.

We report on the symmetrization phenomenon of a hollow-core vortex in shallow liquid conditions. This phenomenon accompanies the transition of $m$ wave into ($m$ $+$ 1) wave and involves a beat-wave resonance that mediates energy transfer between the background flow and the vortex core. It is shown that this beat wave has a frequency $\frac{m}{(m-1)}$times the frequency of the parent $m$ wave.

The interface thermal resistance becomes more and more important as device miniaturization for better performance renders a large surface-to-volume ratio and invariably requires a device design with multiple materials inducing thermal interfaces across the material heterogeniety. Toward developing a comprehensive computational methodology for thermal transport prediction, incorporating the interface effects in a heterogeneous medium, a novel boundary collision rule is devised in the lattice Boltzmann computational scheme to realize a thermal interface between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for Umklapp process, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution, which is uniquely defined by the energy conservation principle. The Kapitza length and the interface thermal resistance are determined by the relaxation parameter and the local phonon properties. The implementation of the proposed mesoscopic boundary collision rule in the lattice Boltzmann computational framework provides a methodology of predicting the thermal properties of a heterogeneus medium incorporating both normal and Umklapp collision processes of phonon.

An efficient approach for the simulation of ion scattering from solids is proposed. For every encountered atom, we take multiple samples of its thermal displacements among those which result in scattering with high probability to finally reach the detector. As a result, the detector is illuminated by intensive “showers,” where each event of detection must be weighted according to the actual probability of the atom displacement. The computational cost of such simulation is orders of magnitude lower than in the direct approach, and a comprehensive analysis of multiple and plural scattering effects becomes possible. We use this method for two purposes. First, the accuracy of the approximate approaches, developed mainly for ion-beam structural analysis, is verified. Second, the possibility to reproduce a wide class of experimental conditions is used to analyze some basic features of ion-solid collisions: the role of double violent collisions in low-energy ion scattering; the origin of the “surface peak” in scattering from amorphous samples; the low-energy tail in the energy spectra of scattered medium-energy ions due to plural scattering; and the degradation of blocking patterns in two-dimensional angular distributions with increasing depth of scattering. As an example of simulation for ions of MeV energies, we verify the time reversibility for channeling and blocking of 1-MeV protons in a W crystal. The possibilities of analysis that our approach offers may be very useful for various applications, in particular, for structural analysis with atomic resolution.

The quest for high thermal conductivity materials has led to nanocomposites incorporating macromolecular materials with excellent thermal conductivity, such as carbon nanotubes and graphene nanoribbons, in a matrix of poorer thermal conductivity. To minimize the interface thermal resistance the stiff, incorporated materials can be chemically functionalized with various side chains. We report here an efficient theoretical method using normal modes to calculate the thermal conductivity of such systems and show how the participation ratio of these modes can be used to evaluate different choices for functionalization. We use this method to examine how effective different alkane chains improve the heat flux through a graphene nanosheet.

One-dimensional arrays of nucleosomes (DNA-bound histone octamers separated by stretches of linker DNA) fold into higher-order chromatin structures which ultimately make up eukaryotic chromosomes. Chromatin structure formation leads to $10-11$ base pair (bp) discretization of linker lengths caused by the smaller free energy cost of packaging nucleosomes into regular chromatin fibers if their rotational setting (defined by the DNA helical twist) is conserved. We describe nucleosome positions along the fiber using a thermodynamic model of finite-size particles with both intrinsic histone-DNA interactions and an effective two-body potential. We infer one- and two-body energies directly from high-throughput maps of nucleosome positions. We show that higher-order chromatin structure helps explains in vitro and in vivo nucleosome ordering in transcribed regions, and plays a leading role in establishing well-known $10-11$ bp genome-wide periodicity of nucleosome positions.

We have investigated the glass transitions of trihydric alcohols using broadband dielectric spectroscopy, and compare the results with those previously reported for sugar alcohols. Although a systematic glass transition feature related to molecular size has been reported for sugar alcohols, the essential factor governing this feature is still unclear because the number of carbon atoms ($N_{\mathrm{C}}$) and the number of OH groups ($N_{\mathrm{OH}}$) per molecule are identical in sugar alcohols. By examining trihydric alcohols ($N_{\mathrm{C}}\ne N_{\mathrm{OH}}$), we conclude that $N_{\mathrm{OH}}$ is dominant for the characteristics of the slow dynamics, such as fragility and glass transition temperature. This result suggests that the topological structure of the hydrogen-bonding network (coordination number) plays an important role in the glass transition of polyhydric alcohols. Furthermore, the orientational correlation factor evaluated using the Kirkwood-Fröhlich theory reveals a similarity in hydrogen bond formation among a variety of polyhydric alcohols. Based on these two experimental results, we discuss a possible physical picture of the glass transition of polyhydric alcohols.

The glass transition temperature of a broad class of molecules is shown to depend on molecular size. This dependency results from the size dependence of the pair potential. A generalized equation of state is used to estimate how the volume fraction at the glass transition depends on the size of the molecule, for rigid molecule glass-formers. The model shows that at a given pressure and temperature there is a size-induced glass transition: For molecules larger than a critical size, the volume fraction required to support the effective pressure due to particle attractions is above that which characterizes the glassy state. This observation establishes the boundary between nanoparticles, which exist in liquid form only as dispersions in low molecular weight solvents and large molecules which form liquids that have viscosities below those characterized by the glassy state.

We report pattern formation using a slippery ballistic deposition (SBD) model where growth germinates from a single site or from sites distributed periodically on a lattice. By changing the sticking probability $p_s$ and choosing systems with different lattice constants and symmetries, we demonstrate that a variety of patterns can be generated. These patterns can be further used as scaffolds for nanofabrication. We also demonstrate that by choosing a lateral sticking probability $p_l$ at the base that is different than $p_s$, one can control both the early and late time morphologies originating from a seed. Furthermore, we indicate a possible generalization of preparing patterns to higher dimensions that in principle can have potential technological applications for preparing grooves and scaffolds of specific shapes and periodicities.

Using a combination of isothermal-isobaric Monte Carlo and microcanonical molecular dynamics we investigate the relation between structure and self-diffusion in various phases of a model liquid crystal using the Gay-Berne-Kihara potential. These molecules are confined to a mesoscopic slit pore with atomically smooth substrate surfaces. As reported recently [seeM. G. Mazza et al., Phys. Rev. Lett. 105, 227802 (2010)], a reentrant nematic (RN) phase may form at sufficiently high pressures and densities. This phase is characterized by a high degree of nematic order and a substantially enhanced self-diffusivity in the direction of the director $\stackrel{\wedge }{\mathit{n}}$ that exceeds that of the lower-density nematic and an intermittent smectic-$A$ phase by about an order of magnitude. Here we demonstrate that the unique transport behavior in the RN phase may be linked to a confinement-induced packing effect that causes the formation of supramolecular, stringlike conformations. The strings consist of several molecules traveling in the direction of $\stackrel{\wedge }{\mathit{n}}$ as individual “trains” consisting of chains of molecular “cars.”

The features of flame acceleration in channels with wall friction and the deflagration to detonation transition (DDT) are investigated theoretically and using high resolution numerical simulations of two-dimensional reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, and a detailed chemical reaction mechanism for hydrogen-oxygen gaseous mixture. It is shown that in a wide channel, from the beginning, the flame velocity increases exponentially for a short time and then flame acceleration decreases, ending up with the abrupt increase of the combustion wave velocity and the actual transition to detonation. In a thin channel with a width smaller than the critical value, the exponential increase of the flame velocity is not bounded and ends up with the transition to detonation. The transition to detonation occurs due to the pressure pulse, which is formed at the tip of the accelerating flame. The amplitude of the pressure pulse grows exponentially due to a positive feedback coupling between the pressure pulse and the heat released in the reaction. Finally, large amplitude pressure pulse steepens into a strong shock coupled with the reaction zone forming the overdriven detonation. The evolution from a temperature gradient to a detonation via the Zeldovich gradient mechanism and its applicability to the deflagration-to-detonation transition is investigated for combustible materials whose chemistry is governed by chain-branching kinetics. The results of the high resolution simulations are fully consistent with experimental observations of the flame acceleration and DDT.

The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple construction of a quantized representation of these equations and their soliton solutions over a Fock space of bosons or of fermions. The classical nonlinear wave equation becomes a nonlinear equation for an operator. The solution of this equation is constructed through an operator analog of the Hirota transformation. The classical N-soliton solution is the expectation value of the solution operator in an $N$-particle state in the Fock space. The effect of perturbations that modify soliton identity is demonstrated.

The steady-state solidification along the liquid-liquid interface in the monotectic system is discussed. A boundary-integral formulation describing the diffusion in the two liquid phases is given and the corresponding equations for the three interfaces (two solid-liquid interfaces and one liquid-liquid interface) are solved. Scaling relations are extracted from the results and supported by analytic arguments in the limit of small deviation from the monotectic temperature. We present also a complementary phase-field simulation, which proves the stability of the process.

Infiltration of diffusing particles from one material to another, where the diffusion mechanism is either normal or anomalous, is a widely observed phenomenon. Starting with an underlying continuous-time random-walk model, we derive the boundary conditions for the diffusion equations describing this problem. We discuss a simple method showing how the boundary conditions can be determined from equilibrium experiments. When the diffusion processes are close to thermal equilibrium, the boundary conditions are determined by a thermal Boltzmann factor, which in turn controls the solution of the problem.

We develop a Born-Oppenheimer-type formalism for the description of quantum thermal transport across hybrid nanoscale objects. Our formalism is suitable for treating heat transfer in the off-resonant regime, where, e.g., the relevant vibrational modes of the interlocated molecule are high relative to typical bath frequencies, and at low temperatures when tunneling effects dominate. A general expression for the thermal energy current is accomplished in the form of a generalized Landauer formula. In the harmonic limit this expression reduces to the standard Landauer result for heat transfer. In the presence of nonlinearities, multiphonon effects are realized.

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream’s macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gaslike jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.

We investigate a single frictional, inelastic, spherical particle falling under gravity through a symmetric funnel. A recent study showed that, for a frictionless particle in such a system, several anomalous phenomena occur: The particle can stay longer, lose more energy, and exert more impulsive force in a funnel with steeper walls. For frictionless particles, such phenomena exist for many small ranges of funnel angles and are a consequence of the many possible repeated patterns in particle trajectories. However, in reality, friction always exists and it is a natural question whether the anomalous phenomena still exist for frictional particles in such systems. We show that, surprisingly, the inclusion of friction in the dynamics actually dramatically enhances the anomalous phenomena. For frictional particles, the anomalous phenomena exist for all funnel angles steeper than ${45}^{°}$ and are thus more robust than the frictionless case. Furthermore, instead of many possible complicated repeated patterns in particle trajectories, there is a unique repeated pattern for frictional particles. Moreover, this is the simplest possible repeated pattern. We derive an analytical expression for this unique repeated pattern and provide a theoretical explanation for the anomalous phenomena observed in frictional particle systems. We further show that the friction, no matter how small, plays a critical role in the dynamics, that is, the dynamics of the frictionless particle system is singular.

We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation are used, within a Lagrangian framework, to obtain the equations of motion. The free energy consists of both elastic and liquid crystalline contributions, each of which is a function of the material displacement and the orientational order parameter. The model gives dynamics for the material displacement, the scalar order parameter and the nematic director, the latter two of which correspond to the orientational order parameter tensor. Our simulations are carried out by solving the governing equations using an implicit-explicit scheme and the Chebyshev polynomial method. The simulations show that the model can successfully capture the shape changing dynamics of LCEs that have been observed in experiments, and also track the evolution of the order parameter tensor.