Inertial Time Research Articles

Hopf–pitchfork bifurcation in an inertial two-neuron system with time delay

In this paper, we have considered a delayed differential equation modeling two-neuron system with both inertial terms and time delay. By studying the distribution of the eigenvalues of the corresponding transcendental characteristic equation of the linearization of this equation, we derive the critical values where Hopf–pitchfork bifurcation occurs. Then, by computing the normal forms for the system, the bifurcation diagrams are obtained. Furthermore, we find some interesting phenomena, such as the coexistence of two asymptotically stable states, two stable periodic orbits, and two attractive quasi-periodic motions, which are verified both theoretically and numerically.

Assessing the fidelity of surface currents from a coastal ocean model and HF radar using drifting buoys in the Middle Atlantic Bight

The rapid expansion of urbanization along the world’s coastal areas requires a more comprehensive and accurate understanding of the coastal ocean. Over the past several decades, numerical ocean circulation models have tried to provide such insight, based on our developing understanding of physical ocean processes. The systematic establishment of coastal ocean observation systems adopting cutting-edge technology, such as high frequency (HF) radar, satellite sensing, and gliders, has put such ocean model predictions to the test, by providing comprehensive observational datasets for the validation of numerical model forecasts. The New York Harbor Observing and Prediction System (NYHOPS) is a comprehensive system for understanding coastal ocean processes on the continental shelf waters of New York and New Jersey. To increase confidence in the system’s ocean circulation predictions in that area, a detailed validation exercise was carried out using HF radar and Lagrangian drifter-derived surface currents from three drifters obtained between March and October 2010. During that period, the root mean square (RMS) differences of both the east–west and north–south currents between NYHOPS and HF radar were approximately 15 cm s−1. Harmonic analysis of NYHOPS and HF radar surface currents shows similar tidal ellipse parameters for the dominant M2 tide, with a mean difference of 2.4 cm s−1 in the semi-major axis and 1.4 cm s−1 in the semi-minor axis and 3° in orientation and 10° in phase. Surface currents derived independently from drifters along their trajectories showed that NYHOPS and HF radar yielded similarly accurate results. RMS errors when compared to currents derived along the trajectory of the three drifters were approximately 10 cm s−1. Overall, the analysis suggests that NYHOPS and HF radar had similar skill in estimating the currents over the continental shelf waters of the Middle Atlantic Bight during this time period. An ensemble-based set of particle tracking simulations using one drifter which was tracked for 11 days showed that the ensemble mean separation generally increases with time in a linear fashion. The separation distance is not dominated by high frequency or short spatial scale wavelengths suggesting that both the NYHOPS and HF radar currents are representing tidal and inertial time scales correctly and resolving some of the smaller scale eddies. The growing ensemble mean separation distance is dominated by errors in the mean flow causing the drifters to slowly diverge from their observed positions. The separation distance for both HF radar and NYHOPS stays below 30 km after 5 days, and the two technologies have similar tracking skill at the 95 % level. For comparison, the ensemble mean distance of a drifter from its initial release location (persistence assumption) is estimated to be greater than 70 km in 5 days.

Isotropization at small scales of rotating helically driven turbulence

AbstractWe present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami ($\mathit{ABC}$) forcing, creating helical flow. The Zeman scale ${\ell }_{\Omega } $ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $307{2}^{3} $ points, with Rossby and Reynolds numbers, respectively, equal to $0. 07$ and $2. 7\ensuremath{\times} 1{0}^{4} $. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond ${\ell }_{\Omega } $ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at ${\ell }_{\Omega } $, a clear sign of recovery of three-dimensionality in the small scales.

Are OPERA neutrinos faster than light because of non-inertial reference frames?

Recent results from the OPERA experiment reported a neutrino beam traveling faster than light. The experiment measured the neutrino time of flight (TOF) over a baseline from the CERN to the Gran Sasso site. The neutrino beam arrives 60 ns earlier than a light ray would do. Because the result has an enormous impact on science, it might be worth double-checking the time definitions with respect to the non-inertial system in which the neutrino travel time was measured. Potential problems in the OPERA data analysis connected with the definition of the reference frame and time synchronization are emphasized. We aim to investigate the synchronization of non-inertial clocks on Earth by relating this time to the proper time of an inertial observer at Solar System Barycenter(SSB). The Tempo2 software was used to time-stamp events observed on the geoid with respect to the SSB inertial observer time. Neutrino results from OPERA might carry the fingerprint of non-inertial effects. The CERN-Gran Sasso clock synchronization is accomplished by applying corrections that depend on special and general relativistic time dilation effects at the clocks, depending on the position of the clocks in the solar system gravitational well. As a consequence, TOF distributions are centered on values shorter by tens of ns than expected, integrating over a period from April to December, longer if otherwise. It is worth remarking that the OPERA runs have always been carried out from April/May to November. If the analysis by Tempo2 holds for the OPERA experiment, the excellent measurement by the OPERA collaboration will turn into a proof of the General Relativity theory in a weak field approximation. The analysis presented here is falsifiable because it predicts that performing the experiment from January to March/April, the neutrino beam will be detected to arrive 50 ns later than light.

On Damped Wave Diffusion of Oxygen in Pancreatic Islets: Parabolic and Hyperbolic Models

Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are; 1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia ; 2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front ， τ = Xp; 4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.

Continuous and discontinuous transitions in geophysical turbulence

In geophysical turbulent flows, it is customary to have two or more attractors (typically responsible for low-frequency variability). Such a phenomenon is investigated in the dynamics of two-dimensional and quasi-geostrophic turbulence. In the inertial limit, with a time scale separation (between spin-up time and inertial time), the attractors are concentrated near a set of steady states of the inviscid equations. Statistical mechanical approaches help us determine which of these steady states are eligible. Then, we can establish phase diagrams, where phase transition lines delimitate regions corresponding to different regimes, i.e., different flow structures. The latter can be related to the different (say, two) regimes, which the Kuroshio alternatively finds itself into (bistability). Our present aim is to classify the bifurcations -given the two inertial equilibria—when tuning an external parameter. We give a general theory predicting whether the transitions are continuous (second-order) or discontinuous (first-order). The continuity or discontinuity depends on the value of some moments of the potential vorticity. We discuss applications to oceanic (Kuroshio) and experimental geophysical flows.

Rotating helical turbulence: three-dimensionalization or self-similarity in the small scales?

We present numerical evidence on how three-dimensionalization is recovered at small scale in rotating turbulence with helical forcing provided by a Beltrami flow. The relevant ranges (large-scale inverse cascade of energy, anisotropic and isotropic direct cascades of energy and helicity, dissipative) are each moderately resolved. These results stem from large direct numerical simulations on grids of either 15363 or 30723 points. In the latter case, the scale at which the inertial wave time and the eddy turn-over time are equal is found to be more than one order of magnitude larger than the dissipation scale. We also examine how the presence of such an intermediate scale could affect truncation due to the use of a helical spectral Large Eddy Simulation procedure which can allow for extending the analysis to a wider range of parameters. Finally, the self-similarity of the direct cascade of energy to small scales for rotating flows, observed recently in numerical simulations as well as in several laboratory experiments, will be discussed briefly for its scaling properties and its conformal invariance.

A local lagrangian analysis of passive particle advection in a gas flow field

A local analysis is performed to study the departure from passive advection by small inertial particles based on a Lagrangian framework. The analysis considers heavy particles immersed in a gaseous flow and is restricted to short times, making it relevant to the PIV technique. A necessary (but not sufficient condition) for passive particle advection of inertial particles is that the quantity Λ max τ p be much smaller than one, where Λ max is the largest modulus of the eigenvalues corresponding to the velocity gradient tensor. This allows for the inertial and passive time scales to match beyond the initial transient, and consequently for the respective trajectories to remain relatively close. Due to this important role regarding advection behavior, Λ max τ p is offered as a definition of a local Stokes number, St Λ . Since this quantity is a field quantity, it directly provides indication of when and where passive advection by particles can be expected. A departure equation is obtained in one-dimension, where the influence of initial velocity and gravity are explicitly shown. If the flow is irrotational, the higher dimensional analysis reduces to a set of decoupled one-dimensional equations acting along each respective eigenvector of the velocity gradient tensor. A similar expression is found for the case of a purely temporal flow field.

Observing system simulation experiments with ensemble Kalman filters in Nantucket Sound, Massachusetts

[1] Observing system simulation experiments (OSSEs) were performed for Nantucket Sound, Massachusetts, as a pilot study for the design of optimal monitoring networks in the coastal ocean. Experiments were carried out using the ensemble Kalman filter (EnKF) for data assimilation with ensemble transform Kalman filter (EnTKF) and proper orthogonal decomposition (POD) for selecting the optimal monitoring sites. The singular evolutive interpolated Kalman filter (SEIK) was compared with EnKF for the data assimilation efficiency. Running the unstructured grid Finite-Volume Community Ocean Model (FVCOM) with perturbed initial fields of currents, water temperature, and salinity show that in this shallow coastal system, the velocity and surface elevation are able to restore themselves back to the true state over an inertial time scale after perturbation without data assimilation, while the water temperature and salinity are not. This suggests that in this vertically well mixed region with strong tidal influence, monitoring should be targeted at water properties rather than velocities. By placing measurement sites at an entrance or exit or a location with the maximum signal variance (EnTKF) or at extrema of the dominant EOF spatial modes (POD), we evaluated the capability of EnTKF and POD in designing the optimal monitoring site for the forecast model system in this region. The results suggest that understanding the multiscale dynamical nature of the system is essential in designing an optimal monitoring network since “optimal” sites suggested by an assimilation method may only represent a local-scale feature that has little influence on a region-wide system. Comparing EnKF and SEIK simulations shows that SEIK can significantly improve the data assimilation efficiency by reducing the ensemble number and increasing the convergence rate.

Clustering of settling charged particles in turbulence: theory and experiments

Atmospheric clouds, electrosprays and protoplanetary nebula (dusty plasma) contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. We have developed a theoretical description of the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions (RDFs) to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ‘terminal’ speed to the turbulence dissipation velocity scale) and the settling parameter (the ratio of the gravitational terminal speed to the turbulence dissipation velocity scale). The theory is compared to measured RDFs for water particles in homogeneous, isotropic air turbulence. The RDFs are obtained from particle positions measured in three dimensions using digital holography. The measurements verify the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ‘gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity.

Pressure-coupled vaporization response of n-pentane fuel droplet at subcritical and supercritical conditions

The dynamic response of a liquid fuel droplet to externally impressed pressure oscillations is studied comprehensively over a wide range of mean pressures. Both subcritical and supercritical conditions are considered. The formulation treats a complete set of conservation equations and incorporates real fluid thermodynamics and transport theories. As a specific example, the situation with isolated n-pentane droplets in nitrogen is studied at various forcing frequencies. Results are correlated with the liquid thermal inertial time, instantaneous droplet radius, and oscillation frequency. The magnitude of the vaporization response increases with increasing pressure, mainly due to the decreased enthalpy of vaporization at high pressures. The increased sensitivity of droplet thermophysical properties to ambient flow variations at high pressures also plays a role. The phase angle of the vaporization response function, however, appears to be independent of the ambient pressure. An abrupt increase in the response function takes place when the droplet surface reaches its critical mixing state. A major factor contributing to this phenomenon is the abnormal variations of fluid thermophysical properties near the critical mixing point.

Scattering of gravity waves by potential vorticity in a shallow-water fluid

The influence of a geostrophically balanced or potential vorticity (PV) containing background flow on the propagation of a coherent gravity wave is examined in a rotating shallow-water model. Over inertial time scales, we find that the gravity wave energy is scattered into other modes of similar wavelength, but with different directions of propagation. We attribute this response to nonlinear resonant interactions between the PV and gravity wave modes, despite the absence of any exchange of energy between the two, and show that the response is consistent with resonant triad theory. We first consider the scattering of a gravity wave mode due to a single PV mode, and compare the theoretical response to numerical solutions. This is followed by consideration of the propagation of a coherent gravity mode through a turbulent PV background. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.

ChemInform Abstract: The Electrodynamic Chamber: A Tool for Studying High-Temperature Kinetics Involving Liquid and Solid Particles

Abstract This review presents the development and application of a new approach for studying single particle kinetics that can provide new insights into particulate combustion. The new approach uses the capability of suspending a charged particle motionless at a fixed position in an electrodynamic chamber (EDC). The particle is heated by means of laser radiation. The new approach combines the capabilities of classical thermogravimetric and calorimetric approaches with those of drop tube experiments without some of the accompanied limitations. In this approach the particle can be well characterized prior to reaction. If after the reaction the particle is still suspended it can be further characterized in the chamber then it can be captured and off-line characterization can be carried out. The method is presently capable of providing information prior to, during, and past reaction on the mass, size, density, heat capacity, light absorptivity, porosity, phase transition, reaction enthalpies, thermal and inertial characteristic times, ignition temperatures and ignition delay times. The issues connected with heating with laser radiation include (1) the nature of internal electromagnetic field within the particle, (2) transient heat changes, and (3) photophoretic phenomena. In order to reach the desired temperature by radiation a laser beam has to be focused to a size of the particle diameter. Small movement of the particle may upset the heat balance. It is thus of essential importance to develop methods that will control the particle motionless at the center of the chamber in spite of the changes in the force balance it may experience. A feature of this technique is that the surroundings are at ambient temperature (300 K). The lack of external source (other than laser radiation) permits the steady determination of the heat release rates and the measure of heat capacities. Also, secondary reactions in the boundary layer such as CO oxidation are minimized enabling one to concentrate on the surface reactions. Ignition studies in the presence of controlled external heating can provide new insights into particulate ignition. High relative gas velocities surrounding the particle can be achieved thus simulating reactions under high flow fields. The present approach is however not without its drawbacks. Thermoionic emission can lead to problems of particle stability and the small sample size limits gas analysis to major products. The present review provides a discussion of the capabilities and limitations of the electrodynamic chamber for high temperature applications. The review discusses in detail the methodology of the EDC. Theoretical aspects of the important processes and phenomena in conjunction with the operation of the EDC are provided. The motivation of the detailed theoretical presentation is twofold: (1) To provide the user with tools necessary to estimate the operation conditions of the specific system. (2) To evaluate the force balance from phenomena taking place during the heterogeneous reaction not connected with the reaction and correct the interpretation of the results accordingly.

Three-Dimensional Structure and Temporal Evolution of Submesoscale Thermohaline Intrusions in the North Pacific Subtropical Frontal Zone

AbstractFour instances of persistent intrusive deformation of the North Pacific Subtropical Front were tagged individually by a Lagrangian float and tracked for several days. Each feature was mapped in three dimensions using repeat towed observations referenced to the float. Isohaline surface deformations in the frontal zone included sheetlike folds elongated in the alongfront direction and narrow tongues extending across the front. All deformations appeared as protrusions of relatively cold, and fresh, water across the front. No corresponding features of the opposite sign or isolated lenslike structures were observed. The sheets were O(10 m) thick, protruded about 10 km into the warm saline side of the front, and were coherent for 10–30 km along the front. Having about the same thickness and cross-frontal extent as the sheets, tongues extended less than 5 km along the front. All of the intrusions persisted as long as they were followed, several days to one week. Their structures evolved on both inertial (23 h) and subinertial (∼10 days) time scales in response to differential lateral advection. The water mass surrounding the intrusions participated in gradual anticyclonic rotation as a part of a mesoscale meander of the subtropical front. The intrusions may be interpreted as a manifestation of three-dimensional submesoscale turbulence of the frontal zone, driven by the mesoscale. Absence of large features of the opposite sign may be indicative of the asymmetry of the underlying dynamics.

Frictional aging, de-aging, and re-aging in a monolayer-coated micromachined interface

Measurements on monolayer-coated polycrystalline silicon surfaces have shown that the static friction coefficient ${\ensuremath{\mu}}_{s}$ strongly depends on loading parameters including hold time and normal hold force by Corwin and de Boer [J. Microelectromech. Syst. 18, 250 (2009)]. In that work, ${\ensuremath{\mu}}_{s}$ was measured by keeping the tangential force constant and lowering normal force until motion occurred. Results indicated that ${\ensuremath{\mu}}_{s}$ also depends strongly on normal force ramp-down rate. Here, we postulate that if the normal load is lowered instantaneously, the time for the block to begin moving, the ``release time'' ${t}_{r}$, will be greater than the inertial response time, which is on the order of $5\text{ }\ensuremath{\mu}\text{s}$. We measure the release time and find that it spans nearly six decades from less than $100\text{ }\ensuremath{\mu}\text{s}$ to almost 50 s. Release time depends on the loading and unloading history through all three of the parameters varied: hold time, hold force, and release force. An empirical model incorporating all three of these parameters fits the release time data over the full range. Release time decreases after the contacting surfaces are held together at increasing hold force levels and this qualitatively explains a previous observation that static friction aging is suppressed with increasing normal force at a fixed tangential load in this interfacial system. We further quantitatively relate the previous ${\ensuremath{\mu}}_{s}$ loading dependence on all three parameters to the release time model established here by introducing a ``re-aging'' parameter. This work firmly establishes that release time is a more fundamental parameter than the static friction coefficient and is the origin of static friction coefficient dependencies in this micromachined interface.

Modeling and study of dynamic performance of a valveless micropump

This work presents an approximate nonlinear analytical model for the problem of fluid–structural interaction in a valveless micropump. The model is constructed using the lumped-mass approach and takes into account the inertial force and time variation of mass density of the working fluid within the micropump chamber, pressure viscous losses of the flow through the diffuser/nozzle elements and the structural geometric nonlinearity due to the membrane mid-plane stretching. It consists of a set of coupled partial integro-differential equations which is reduced to a third order nonlinear coupled fluid-plate vibration equation by using the assumed mode method to approximate the plate dynamic deflection. An approximate analytical solution for the nonlinear vibration model is carried out using the harmonic balance method and is used to investigate the effect of various system parameters on the performance of the micropump. The obtained model and approximate analytical results are compared with those available in the open literature. The approximate analytical results show that, depending on the micropump physical parameters and membrane driving frequency, the working fluid stiffness, which arise in the present model as a result of taking into account the variation of the fluid density with time, and the membrane geometric nonlinearity can have significant effects on the predicted micropump performance and can lead to a complex nonlinear dynamic behavior. The accuracy of these results is subject to a future numerical validation of the presented approximate theoretical model.

Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh–Taylor (CRT) instability and a spiral Kelvin–Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface.

Comparison of Solutions from Parabolic and Hyperbolic Models for Transient Heat Conduction in Semi-Infinite Medium

The expression for the transient temperature during damped wave conduction and relaxation developed by Baumeister and Hamill by the method of Laplace transforms was further integrated. A Chebyshev polynomial approximation was used for the integrand with a modified Bessel composite function in space and time. A telescoping power series leads to a more useful expression for the transient temperature. By the method of relativistic transformation, the transient temperature during damped wave conduction and relaxation was developed. There are four regimes to the solution. These include: (i) a regime comprising a Bessel composite function in space and time, (ii) another regime comprising a modified Bessel composite function in space and time, (iii) the temperature solution at the wave front was also developed separately, and (iv) the fourth regime at a given location X in the medium is at times less than the inertial thermal lag time. In this regime, the temperature was found to be unchanged at the initial condition. The solution for the transient temperature from the method of relativistic transformation is compared side by side with the solution for the transient temperature from the method of Chebyshev economization. Both solutions are within 12% of each other. For conditions close to the wave front, the solution from the Chebyshev economization is expected to be close to the exact solution and was found to be within 2% of the solution from the method of relativistic transformation. Far from the wave front, i.e., close to the surface, the numerical error from the method of Chebyshev economization is expected to be significant and verified by a specific example. The solution for transient surface heat flux from the parabolic Fourier heart conduction model and the hyperbolic damped wave conduction and relaxation models are compared with each other. For τ > 1/2 the parabolic and hyperbolic solutions are within 10% of each other. The parabolic model has a “blow-up” as τ → 0, and the hyperbolic model is devoid of singularities. The transient temperature from the Chebyshev economization is within an average of 25% of the error function solution for the parabolic Fourier heat conduction model. A penetration distance beyond which there is no effect of the step change in the boundary is predicted using the relativistic transformation model.

Solvent control of the soft angular potential in hydroxyl-pi hydrogen bonds: inertial orientational dynamics.

Ultrafast polarization and wavelength selective IR pump-probe spectroscopy is used to measure the inertial and long time orientational dynamics of pi-hydrogen bonding complexes. Inertial orientational relaxation is sensitive to the angular potential associated with the hydrogen bond. The complexes studied are composed of phenol-OD (hydroxyl hydrogen replaced by deuterium) and various pi-base solvents with different electron donating or withdrawing substituents (chlorobenzene, bromobenzene, benzene, toluene, p-xylene, mesitylene, 1-pentyne). The different substituents provide experimental control of the hydrogen bond strength. The inertial orientational relaxation of the complexes, measured at the center frequency of each line, is independent of the hydrogen bond strength, demonstrating the insensitivity of the OD inertial dynamics, and therefore the H-bond angular potential, to the hydrogen bond strength. OD stretch absorption bands are inhomogeneously broadened through interactions with the solvent. The hydrogen bonding complexes all have similar wavelength dependent inertial orientational relaxation across their inhomogeneously broadened OD stretch absorption lines. The wavelength dependence of the inertial reorientation across each line arises because of a correlation between local solvent structure and the angular potential. These two results imply that local solvent structure acts as the controlling influence in determining the extent of inertial orientational relaxation, and therefore the angular potential, and that variation in the pi-hydrogen bond strength is of secondary importance.

Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed two-dimensional spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation time scale and an inertial time scale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation is proposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles not only in terms of kinematics but also in terms of forces.