Search

Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In the ocean interior, this turbulent mixing is caused mainly by breaking internal waves: generated predominantly by winds and tides, these waves interact nonlinearly, transferring energy downscale, and finally become unstable, break and mix the water column. This paradigm, long parameterized heuristically, still lacks full theoretical explanation. Here, we close this gap using wave-wave interaction theory with input from both localized and global observations. We find near-ubiquitous agreement between first-principle predictions and observed mixing patterns in the global ocean interior. Our findings lay the foundations for a wave-driven mixing parameterization for ocean general circulation models that is entirely physics-based, which is key to reliably represent future climate states that could differ substantially from today's.

One-dimensional chains are used as a fundamental model of condensed matter, and have constituted the starting point for key developments in nonlinear physics and complex systems. The pioneering work in this field was proposed by Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. An intense and fruitful mathematical and physical research followed during these last 70 years. Recently, a fresh look at the mechanisms of thermalization in such systems has been provided through the lens of the Wave Turbulence approach. In this review, we give a critical summary of the results obtained in this framework. We also present a series of open problems and challenges that future work needs to address., Comment: arXiv admin note: text overlap with arXiv:1811.05697 by other authors

Survey researchers are increasingly turning to multimode data collection to deal with declines in survey response rates and increasing costs. An efficient approach offers the less costly modes (e.g., web) followed with a more expensive mode for a subsample of the units (e.g., households) within each primary sampling unit (PSU). We present two alternatives to this traditional design. One alternative subsamples PSUs rather than units to constrain costs. The second is a hybrid design that includes a clustered (two-stage) sample and an independent, unclustered sample. Using a simulation, we demonstrate the hybrid design has considerable advantages., Comment: 60 pages, 5 exhibits, 17 figures, 1 table

Hydrogen is an efficient energy carrier that can be produced from renewable sources, enabling the transition towards CO2-free energy. Hydrogen can be stored for a long period in the solid-state, with suitable alloys. Ti-rich TiFe0.90 compound exhibits a mild activation process for the first hydrogenation, and Ti(Fe,Mn)0.90 substituted alloys can lead to the fine tuning of equilibrium pressure as a function of the final application. In this study, the crystal structure of TiFe(0.90-x)Mnx alloys (x = 0, 0.05 and 0.10) and their deuterides has been determined by in-situ neutron diffraction, while recording Pressure-Composition Isotherms at room temperature. The investigation aims at analysing the influence of Mn for Fe substitution in Ti-rich Ti(Fe,Mn)0.90 alloys on structural properties during reversible deuterium loading, which is still unsolved and seldom explored. After activation, samples have been transferred into custom-made stainless-steel and aluminium alloy cells used for in-situ neutron diffraction experiments during deuterium loading at ILL and ISIS neutron facilities, respectively. The study enables remarkable understanding on hydrogen storage, basic structural knowledge, and support to the industrial application of TiFe-type alloys for integrated hydrogen tank in energy storage systems by determining the volume expansion during deuteration. Furthermore, the study demonstrates that different contents of Mn do not significantly change the volumetric expansion during phase transitions, affecting only the deuterium content for the {\gamma} phase and the cell evolution for the \b{eta} phase. The study confirms that the deuterated structures of the {\gamma} phase upon absorption, \b{eta} and {\alpha} phase upon desorption, correspond to S.G. Cmmm, P2221 and Pm-3m, respectively., Comment: 34 pages, 5 figures, 4 tables, ESI

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we rederive the standard formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale-invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to be energetically disconnected, with potential consequences in the interpretation of wave-turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids like nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e. propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons is described by the wave kinetic equation (WKE), derived directly from the microscopic dynamics. Here, we use the spatially nonhomogeneous WKE of the prototypical $\beta-$ Fermi-Pasta-Ulam-Tsingou (FPUT) model, equipped with thermostats able to set different temperatures at the two ends. Our main findings are as follows: (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wavenumbers. (ii) The high-wavenumber phonons relax to local thermodynamic equilibrium transporting energy diffusively, {\it \`a la Fourier}. (iii) The low-wavenumber phonons are nearly noninteracting and transfer energy ballistically; this latter phenomenon is the analogous of the second sound emission, observed for example in superfluids.

In the use of hydrogen as large-scale energy vector, metal hydrides based on intermetallic compounds play a key role, thanks to mild temperatures and pressures required for the storage. It is increasingly necessary to develop hydrogen-based devices, and in this work, the intermetallic compound TiFe$_{0.85}$Mn$_{0.05}$ is evaluated and selected as H$_2$-carrier for a storage system of 50 kg of H$_2$. A batch of 5 kg of alloy was synthesized at industrial level and characterized through scanning electron microscopy and powder X-ray diffraction, to determine the structure and phase abundance. Moreover, the hydrogen sorption properties were investigated through thermodynamic and kinetic analyses, followed by a long-term cycling study and resistance to O$_2$ and H$_2$O poisoning. Comparing results for alloys with same nominal composition, but prepared either under industrial or laboratory conditions, it was found that the alloy synthesis promotes discrepancies in phase abundance and microstructure and promotes the formation of a passive layer that deeply affect the hydrogen sorption properties. A scheme based on Monte Carlo simulation and structural results was developed to explain the key role of the passive layer (Ti$_3$Fe$_3$O) and of the secondary phases (Ti$_4$Fe$_2$O$_{0.4}$ and $\beta$-Ti$_{80}$(Fe,Mn)$_2$0) in promoting the hydrogenation of the TiFe$_{0.85}$Mn$_{0.05}$. A storage system based on this alloy can be integrated with an electrolyser upstream (25 bar) and a fuel cell downstream (1 bar) at 55 $^\circ$C, storing 1.0 H$_2$ wt.%, displaying fast kinetic, resistance to oxygen, water and nitrogen gas impurities, and stability over more than 250 cycles., Comment: 27+SI pages, 8 figures, 4 tables

We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber - frequency domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a `local' and a `scale-separated' contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed `no-flux' solutions are reinstated to the status of `constant-downscale-flux' solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of `Oceanic Ultraviolet Catastrophe'., Comment: 20 pages, 8 figures

Because substitutions of BH4- anion with Br can stabilize the hexagonal structure of the LiBH4 at room temperature, leading to a high Li-ion conductivity, its thermodynamic stability has been investigated in this work. The binary LiBH4-LiBr system has been explored by means of X-ray diffraction and differential scanning calorimetry, combined with an assessment of thermodynamic properties. The monophasic zone of the hexagonal Li(BH4)1-x(Br)x solid solution has been defined from x=0.30 to x=0.55 at room temperature. Solubility limits have been determined by in-situ X-ray diffraction at various temperatures. For the formation of the h-Li(BH4)0.6(Br)0.4 solid solution, a value of the enthalpy of mixing has been determined experimentally equal to 1.0 kJ/mol. In addition, the enthalpy of melting has been measured for various compositions. Lattice stabilities of LiBH4 and LiBr have been determined by ab initio calculations, using CRYSTAL and VASP codes. Combining results of experiments and theoretical calculations, the LiBH4-LiBr phase diagram has been determined in all composition and temperature range by the CALPHAD method., Comment: 32 pages, 5 figures, 6 tables

The search for suitable materials for solid-state stationary storage of green hydrogen is pushing the implementation of efficient renewable energy systems. This involves rational design and modification of cheap alloys for effective storage in mild conditions of temperature and pressure. Among many intermetallic compounds described in the literature, TiFe-based systems have recently regained vivid interest as materials for practical applications since they are low-cost and they can be tuned to match required pressure and operation conditions. This work aims to provide a comprehensive review of publications involving chemical substitution in TiFe-based compounds for guiding compound design and materials selection in current and future hydrogen storage applications. Mono- and multi-substituted compounds modify TiFe thermodynamics and are beneficial for many hydrogenation properties. They will be reviewed and deeply discussed, with a focus on manganese substitution., Comment: 76 pages, 7 Figures, 5 Tables

We predict negative temperature states in the Discrete Nonlinear Sch\"odinger equation as exact solutions of the associated Wave Kinetic equation. Those solutions are consistent with the classical thermodynamics formalism. Explicit calculation of the entropy as a function of the energy and number of particles is performed analytically. Direct numerical simulations of the DNLS equation are in agreement with theoretical results. We show that the key ingredient for observing negative temperatures in lattices is the boundedness of the dispersion relation in its domain. States with negative temperatures are characterized by an accumulation of particles and energy at wavenumber $k=\pi$.

TiFe intermetallic compound has been extensively studied, owing to its low cost, good volumetric hydrogen density, and easy tailoring of hydrogenation thermodynamics by elemental substitution. All these positive aspects make this material promising for large-scale applications of solid-state hydrogen storage. On the other hand, activation and kinetic issues should be amended and the role of elemental substitution should be further understood. This work investigates the thermodynamic changes induced by the variation of Ti content along the homogeneity range of the TiFe phase (Ti:Fe ratio from 1:1 to 1:0.9) and of the substitution of Mn for Fe between 0 and 5 at.%. In all considered alloys, the major phase is TiFe-type together with minor amounts of TiFe2 or \b{eta}-Ti-type and Ti4Fe2O-type at the Ti-poor and rich side of the TiFe phase domain, respectively. Thermodynamic data agree with the available literature but offer here a comprehensive picture of hydrogenation properties over an extended Ti and Mn compositional range. Moreover, it is demonstrated that Ti-rich alloys display enhanced storage capacities, as long as a limited amount of \b{eta}-Ti is formed. Both Mn and Ti substitutions increase the cell parameter by possibly substituting Fe, lowering the plateau pressures and decreasing the hysteresis of the isotherms. A full picture of the dependence of hydrogen storage properties as a function of the composition will be discussed, together with some observed correlations., Comment: 39 pages, 9 figure, 4 tables, 3 supplementary figures

We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and the horizontal directions. Our results compare favorably with the finescale parametrization of ocean mixing that was proposed in [Polzin et al. (1995)].

The current energy transition imposes a rapid implementation of energy storage systems with high energy density and eminent regeneration and cycling efficiency. Metal hydrides are potential candidates for generalized energy storage, when coupled with fuel cell units and/or batteries. An overview of ongoing research is reported and discussed in this review work on the light of application as hydrogen and heat storage matrices, as well as thin films for hydrogen optical sensors. These include a selection of single-metal hydrides, Ti-V(Fe) based intermetallics, multi-principal element alloys (high-entropy alloys), and a series of novel synthetically accessible metal borohydrides. Metal hydride materials can be as well of important usefulness for MH-based electrodes with high capacity (e.g. MgH2 ~ 2000 mAh g-1) and solid-state electrolytes displaying high ionic conductivity suitable, respectively, for Li-ion and Li/Mg battery technologies. To boost further research and development directions some characterization techniques dedicated to the study of M-H interactions, their equilibrium reactions, and additional quantification of hydrogen concentration in thin film and bulk hydrides are presented at the end of this manuscript.

The present study investigates the partial substitutions of Mn and Cu for Fe in the TiFe-system to gain better understanding of the role of elemental substitution on its hydrogen storage properties. The TiFe0.88-xMn0.02Cux (x = 0, 0.02, 0.04) compositions were studied. From X-Ray Diffraction (XRD) and Electron Probe Micro-Analysis (EPMA), it was found that all alloys are multi-phase, with TiFe as a major phase, together with \b{eta}-Ti and Ti4Fe2O-type as secondary precipitates, of all them containing also Mn and Cu. Increasing the Cu content augments the secondary phase amounts. Low quantity of secondary phases helps the activation of the main TiFe phase for the first hydrogen absorption, but on increasing their amounts, harsher activation occurs. Both Mn and Cu substitutions increase the cell parameter of TiFe, thus decreasing the first plateau pressure. However, Cu substitution rises the second plateau pressure revealing the predominancy of electronic effects associated to this substitution. All samples have fast kinetics and high hydrogen capacity making these substituted compounds promising for large scale stationary applications., Comment: 25 pages, 4 Tables, 4 Figures, 5 ESI Figures, 1 ESI Table

Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $\beta$-FPUT chain, considered a prototypical model for one-dimensional anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, in steady state conditions, the {\it local} wave energy spectrum can be naturally split into modes that are essentially ballistic (non-interacting or scarcely interacting) and kinetic modes (interacting enough to relax to local thermodynamic equilibrium). We show numerically that the well-known divergence of the energy conductivity is related to how the transition region between these two sets of modes shifts in $k$-space with the system size $L$, due to properties of the collision integral of the system. Moreover, we show that the kinetic modes are responsible for a macroscopic behavior compatible with Fourier's law. Our work sheds light on the long-standing problem of the applicability of standard thermodynamics in one-dimensional nonlinear chains, testbed for understanding the thermal properties of nanotubes and nanowires., Comment: 4 figures, supplemental material with 3 figures

Starting from the action-angle variables and using a standard asymptotic expansion, here we present a new derivation of the Wave Kinetic Equation for resonant process of the type $2\leftrightarrow 2$. Despite not offering new physical results and despite not being more rigorous than others, our procedure has the merit of being straightforward; it allows for a direct control of the random phase and random amplitude hypothesis of the initial wave field. We show that the Wave Kinetic Equation can be derived assuming only initial random phases. The random amplitude approximation has to be taken only at the end, after taking the weak nonlinearity and large box limits. This is because the $\delta$-function over frequencies contains the amplitude-dependent nonlinear correction which should be dropped before the random amplitude approximation applies. If $\epsilon$ is the small parameter in front of the anharmonic part of the Hamiltonian, the time scale associated with the Wave Kinetic equation is shown to be $1/\epsilon^2$. We give evidence that random phase and amplitude hypotheses persist up to a time of the order $1/\epsilon$.

A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatio-temporal wave field configurations, which can be defined using the mathematical framework of Large Deviation Theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves that originate from a simple linear superposition mechanism (in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by making the unknown model parameters random with given statistics. Here this approach is used in concert with tools from large deviation theory (LDT) and optimal control to estimate the probability that some observables in a dynamical system go above a large threshold after some time, given the prior statistical information about the system's parameters and/or its initial conditions. Specifically, it is established under which conditions such extreme events occur in a predictable way, as the minimizer of the LDT action functional. It is also shown how this minimization can be numerically performed in an efficient way using tools from optimal control. These findings are illustrated on the examples of a rod with random elasticity pulled by a time-dependent force, and the nonlinear Schr\"odinger equation (NLSE) with random initial conditions.