Orders Of Magnitude Research Articles

Reversible primes

AbstractFor an ‐bit positive integer written in binary as where , , , let us define the digital reversal of . Also let . With a sieve argument, we obtain an upper bound of the expected order of magnitude for the number of such that and are prime. We also prove that for sufficiently large , where denotes the number of prime factors counted with multiplicity of and is an absolute constant. Finally, we provide an asymptotic formula for the number of ‐bit integers such that and are both squarefree. Our method leads us to provide various estimates for the exponential sum

Patterns, Transport, and Anisotropy of Salt Fingers in Shear

Abstract Through an expansive series of simulations, we investigate the effects of spatially uniform shear on the transport, structure, and dynamics of salt fingers. The simulations reveal that shear adversely affects the heat and salt fluxes of the system, reducing them by up to an order of magnitude. We characterize this in detail across a broad range of Richardson numbers and density ratios. We demonstrate that the density ratio is strongly related to the amount of shear required to disrupt fingers, with larger density ratio systems being more susceptible to disruption. An empirical relationship is proposed that captures this behavior that could be implemented into global ocean models. The results of these simulations accurately reproduce the microstructure measurements from North Atlantic Tracer Release Experiment (NATRE) observations. This work suggests that typical salt finger fluxes in the ocean will likely be a factor of 2–3 less than predicted by models not taking the effects of shear on double-diffusive systems into account. Significance Statement The purpose of this work is to measure how large-scale (>1 m) motion affects specific small-scale (∼1 cm) mixing in the ocean. We approach this topic using simulations of meter-scale boxes of fluid containing both temperature and salt concentration with an applied background flow. We measure how this background flow changes the mixing of temperature and salt as the strength of the applied flow increases. We find that current estimates may overpredict mixing at this scale throughout the World Ocean by about a factor of 2–3, on average. This could have consequences for estimates of climate in addition to heat, salt, nutrient, and pollutant transport.

Phase-encoding of loosely bound soliton molecules

Dissipative soliton molecules (DSMs) are of great interest for studying the complexity of nonlinear optical problems as they can map with the matter molecules for making interdisciplinary analogies. In contrast to strongly bound DSMs that have a short time separation between the bound solitons, the complex dynamics and underlying binding mechanism of loosely bound soliton molecules (LBSMs) with orders of magnitude longer time separation remain open questions. To this end, here, we explore real-time spectroscopy using a dispersive temporal interferometer (DTI) to visualize the dynamics of LBSMs in a mode-locked fiber laser and unveil their underlying phase-evolving mechanism. The DTI enables fringe-resolved spectroscopy in real time of the LBSM’s evolution by creating duplicates of the LBSM that results in a much closer time separation between the individual solitons of the LBSM. The real-time evolution of the LBSM’s phase exhibits a diverging sliding landscape, which is theoretically and experimentally proved to be closely associated with gain dynamics. Based on the understanding of its phase dynamics, we finally demonstrate programmable phase-encoding modulation of the LBSM through gain control. These efforts not only shed light on understanding the mechanism of long-range interactions in LBSMs but also provide an alternative approach for all-optical information processing.

Research on Pulsar Time Steered Atomic Time Algorithm Based on DPLL

In today’s society, there is a wide demand for high-precision and high-stability time service in the fields of electric power, communication, transportation and finance. At present, the time standard in various countries is mainly based on atomic clocks, but the frequency drift of atomic clocks will affect the long-term stability performance. Compared with atomic clocks, millisecond pulsars have better long-term stability and can complement with the excellent short-term stability of atomic clocks. In order to improve the long-term stability of the atomic timescale, and then improve the timing accuracy, this paper proposes an algorithm for steering the atomic clock ensemble (ACE) by ensemble pulsar time (EPT) based on digital phase locked loop (DPLL). First, the ACE and EPT are generated by the ALGOS algorithm, then the ACE is steered by EPT based on DPLL to calibrate the long-term frequency drift of the atomic clock, so that the generated steered atomic time follows both the short-term stability characteristics of ACE and the long-term stability characteristics of EPT, and finally, the steered atomic time is used to calibrate the local cesium clock. The experimental results show that the long-term stability of atomic time after steering is improved by 2 orders of magnitude compared with that before steering, and the daily drift of a local cesium clock after calibration is less than 9.47 ns in 3 yr, 3 orders of magnitude higher than that before calibration on accuracy.

Constant Fraction Discriminator for NA62 experiment at CERN

A new Constant Fraction Discriminator with additionalTime over Threshold measurement capabilities will be presented.It operates in a wide dynamic range of 1:150, with an excellent timeresolution of better than 70 psover one order of magnitude of the input signals.It is highly customizable for different signal shapes and thresholds,using remotely-programmableparameters for Detector Control System commands.Two outputs, each in the Nuclear Instrumentation Module and Low VoltageDifferentialSignaling standards,provide a precise signal arrival time and Time over Thresholdinformation with programmable thresholds.The technical specification and performance measured with cosmic rays and in thehigh-intensity NA62 experiment will be reported.

The rheological response of magma to nanolitisation

Viscosity exerts a fundamental control on magmatic kinetics and dynamics, controlling magma ascent, eruptive style, and the emplacement of lava. Nanolites – crystals smaller than a micron – are thought to affect magma viscosity, but the underlying mechanisms for this remain unclear. Here, we use a cylinder compression creep technique to measure the viscosity of supercooled silicate liquids with different amounts of iron (0–20 wt% FeOtot) as a function of temperature, applied shear stress, and time. Sample viscosity was independent on the applied shear stresses, and as expected, melt viscosity decreases as temperature is increased, but only until a critical temperature where a time-dependent increase in viscosity occurs for samples contaning 6.0 wt% FeOtot or more. The magnitude of this increase is controlled by the melt iron content. At constant temperature, these changes are substantial and can reach up to three orders of magnitude for the sample with the most iron. Using transmission electron microscopy, X-ray diffraction, and viscosity modelling, we conclude that this viscosity increase is caused by the formation of nanolites. By using scaling approaches to test suspension effects with and without crystal aggregation, we conclude that the nanolites have only a minimal direct physical effect on the observed viscosity change. Rather, our models show that it is the chemical shift in the groundmass silicate melt composition associated with non-stoichiometric crystallisation that dominates the observed viscosity increase. These findings suggest that iron-rich silicates may encounter chemical viscosity jumps once certain elements are removed from the melt phase to form nanolites. Our work demonstrates an underlying mechanism for the role played by nanolites in viscosity changes of magmas.

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters.

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve. We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve. Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers. Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

Sound diffraction by knife-edges of finite length: Integral solution, dimensionless parameters, and explicit formulas.

Sound diffraction by knife-edges of finite length is considered in the frequency domain. An approximate analytical solution in integral form is derived from a previously published time domain solution. Unlike the well-established finite length diffraction solution by Svensson et al. [Acta Acust. Acust. 95(3) 568-572 (2009)], the presented solution contains no singularities and both solutions agree, except very close to the diffracting edge. It is shown that finite length diffraction can be studied based on two dimensionless parameters: one expressing the receiver's proximity to the shadow boundary and one associated with the edge length. Depending on the dimensionless parameters, a given edge can be considered a short edge, an infinitely long edge or an edge of medium length, each case with different characteristics. Furthermore, a nomograph and the corresponding database are presented. They provide the normalized diffracted field for any source/receiver location, any source frequency, and any edge length. Also, easy to compute explicit mathematical expressions are presented to approximate the analytical integral solution. These expressions, along with the database method, accelerate diffraction calculations by order of magnitude compared to the presented integral solution or the Svensson solution. Finally, predictions from all proposed methods agree reasonably well with experimental data.

Physical-layer key distribution using synchronous complex dynamics of DBR semiconductor lasers

Common-signal-induced synchronization of semiconductor lasers with optical feedback inspired a promising physical-layer key distribution with information-theoretic security and potential in high rate. A significant challenge is the requirement to shorten the synchronization recovery time for increasing the key rate without sacrificing the operation parameter space for security. Here, open-loop synchronization of wavelength-tunable multi-section distributed Bragg reflector lasers is proposed as a solution for physical-layer key distribution. Experiments show that the synchronization is sensitive to two operation parameters, i.e., currents of grating section and phase section. Furthermore, fast wavelength-shift keying synchronization can be achieved by direct modulation on one of the two currents. The synchronization recovery time is shortened by one order of magnitude compared to close-loop synchronization. An experimental implementation is demonstrated with a final key rate of 5.98 Mbit/s over 160 km optical fiber distance. It is thus believed that fast-tunable multi-section semiconductor lasers open a new avenue for a high-rate physical-layer key distribution using laser synchronization.

Testing Cosmic-Ray Propagation Scenarios with AMS-02 and Voyager Data

AMS-02 on board the International Space Station provides precise measurements of cosmic rays (CR) near Earth, while Voyager measures CRs in the local interstellar medium, beyond the effects of solar modulation. Based on these data, we test and revise various CR propagation scenarios under standard assumptions: pure diffusion, diffusion with convection, diffusion with reacceleration, and diffusion with reacceleration and convection. We report on the scenarios’ performance against CR measurements, aiming to limit the number of model parameters as much as possible. For each scenario, we find parameters that are able to reproduce Voyager and AMS-02 data for the entire energy band for all the CR species tested. Above several GV, we observe a similar injection spectral index for He and C, with He harder than H. Some scenarios previously disfavored are now reconsidered. For example, contrary to usual assumptions, we find that the pure diffusion scenario does not need an upturn in the diffusion coefficient at low energy, while it needs the same number of low-energy breaks in the injection spectrum as diffusive-reacceleration scenarios. We show that scenarios differ in modeled spectra of one order of magnitude for positrons at ∼1 GeV and of a factor of 2 for antiprotons at several GV. The force-field approximation describes well the AMS-02 and Voyager spectra analyzed, except antiprotons. We confirm the ∼10 GeV excess in the antiproton spectrum for all scenarios. Also, for all scenarios, the resulting modulation should be stronger for positrons than for nuclei, with reacceleration models requiring much larger modulation.

A Massively Parallel Spatially Resolved Stochastic Cluster Dynamics Method for Simulations of Irradiated Materials

The spatially resolved stochastic cluster dynamics (SRSCD) method is one of the most important methods for simulating the time-evolution of spatially correlated microstructures in irradiated materials. It is a kinetic Monte Carlo-based method for stochastically evolving integer-valued populations of defects within multi finite volume elements according to reaction rates. However, the increasing spatial scale and complexity of the simulated systems have exceeded the capabilities of serial SRSCD. To extend SRSCD to simulate large-scale complex systems, we propose a massively parallel SRSCD method in this paper and implement the program named MISA-SLSCD. It contains four contributions: (1) a dynamic Defect-Reaction Tree data structure to efficiently store and update millions of defect species and reactions; (2) a double-grouping search strategy to speed up the search for defects and reactions; (3) an adaptive synchronous algorithm to balance the accuracy and efficiency of simulations; and (4) an on-demand communication strategy to eliminate communication redundancy. A series of numerical simulation results show that our method has high accuracy in simulating damage accumulation in irradiated materials and obtains a good performance of over 90% parallel efficiency on 32,000 CPU cores with a 32 million-volume-element system. Program summaryProgram Title: MISA-SLSCDCPC Library link to program files:https://doi.org/10.17632/ctmn5f5bzk.1Code Ocean capsule:https://codeocean.com/capsule/8351487Licensing provisions: BSD 3-clauseProgramming language: Fortran90Nature of problem: Behaviours of defects in irradiated materials are typically space-dependent long-term dynamical processes, and spanning multiple orders of magnitude in space (∼nm to m) and time (∼ μs to years). The SRSCD method is an important method for simulating the time-evolution of spatially correlated microstructures in irradiated materials. However, the increasing spatial scale and complexity of the simulated systems have exceeded the capabilities of serial and existing parallel versions. It is necessary to develop new massively parallel method and program to extend SRSCD to simulate large-scale complex systems.Solution method: To extend SRSCD to simulate large-scale complex systems, we propose a massively parallel SRSCD method in this paper and implement the program named MISA-SLSCD. It contains: (1) a dynamic Defect-Reaction Tree data structure to efficiently store and update millions of defect species and reactions; (2) a double-grouping search strategy to speed up the search for defects and reactions; (3) an adaptive synchronous algorithm to balance the accuracy and efficiency of simulations; and (4) an on-demand communication strategy to eliminate communication redundancy.

Architecture Augmentation for Performance Predictor via Graph Isomorphism.

Neural architecture search (NAS) can automatically design architectures for deep neural networks (DNNs) and has become one of the hottest research topics in the current machine learning community. However, NAS is often computationally expensive because a large number of DNNs require to be trained for obtaining performance during the search process. Performance predictors can greatly alleviate the prohibitive cost of NAS by directly predicting the performance of DNNs. However, building satisfactory performance predictors highly depends on enough trained DNN architectures, which are difficult to obtain due to the high computational cost. To solve this critical issue, we propose an effective DNN architecture augmentation method named graph isomorphism-based architecture augmentation method (GIAug) in this article. Specifically, we first propose a mechanism based on graph isomorphism, which has the merit of efficiently generating a factorial of n (i.e., n) diverse annotated architectures upon a single architecture having n nodes. In addition, we also design a generic method to encode the architectures into the form suitable to most prediction models. As a result, GIAug can be flexibly utilized by various existing performance predictors-based NAS algorithms. We perform extensive experiments on CIFAR-10 and ImageNet benchmark datasets on small-, medium-and large-scale search space. The experiments show that GIAug can significantly enhance the performance of the state-of-the-art peer predictors. In addition, GIAug can save three magnitude order of computation cost at most on ImageNet yet with similar performance when compared with state-of-the-art NAS algorithms.

Observation of single-molecule Raman spectroscopy enabled by synergic electromagnetic and chemical enhancement

There has been a long fundamental pursuit to enhance and levitate the Raman scattering signal intensity of molecule by a huge number of ~ 14–15 orders of magnitude, to the level comparable with the molecule fluorescence intensity and truly entering the regime of single-molecule Raman spectroscopy. In this work we report unambiguous observation of single-molecule Raman spectroscopy via synergic action of electromagnetic and chemical enhancement for rhodamine B (RhB) molecule absorbed within the plasmonic nanogap formed by gold nanoparticle sitting on the two-dimensional (2D) monolayer WS2 and 2 nm SiO2 coated gold thin film. Raman spectroscopy down to an extremely dilute value of 10–18 mol/L can still be clearly visible, and the statistical enhancement factor could reach 16 orders of magnitude compared with the reference detection sample of silicon plate. The electromagnetic enhancement comes from local surface plasmon resonance induced at the nanogap, which could reach ~ 10–11 orders of magnitude, while the chemical enhancement comes from monolayer WS2 2D material, which could reach 4–5 orders of magnitudes. This synergic route of Raman enhancement devices could open up a new frontier of single molecule science, allowing detection, identification, and monitor of single molecules and their spatial–temporal evolution under various internal and external stimuli.

Метод оперативной корректуры спутниковой гидрометеорологической информации в районе плавания судна с помощью подспутниковых измерений

The problem of assessing the state of the sea surface by combining satellite and ship measurements is considered. Information about the strength and direction of the wind at the sea surface is important to ensure safe navigation and planning of vessel transit routes. It is of key importance for weather forecasting and excitement. Wind data is traditionally obtained from passing ships and buoys. Ship data covers only limited areas of the World Ocean and is received unevenly, buoy data is highly sparse, which makes it impossible to obtain an adequate picture of the distribution of atmospheric currents. The use of remote sensing satellites has made it possible to increase the density of measurements of wind speed and direction by orders of magnitude, and the relevance of the data obtained. However, satellite measurements can be distorted. In particular, the influence of atmospheric precipitation (rain) can give a two-fold error in measuring wind speed. Strong and weak winds also create problems: in strong winds, the measured data underestimate the true wind speed, in weak winds they overestimate. A method for correcting satellite data on wind speed and direction is proposed. The essence of the method is to use subsatellite ship measurements in conjunction with satellite information. Knowing the weather data measured locally (from the ship), it is possible to calculate regression parameters for correcting satellite data. By applying regressions with calculated parameters to satellite images in the water area, it is possible to obtain more accurate weather data in the area of the vessel's route. The results of calculations based on real satellite and on-board data in the waters of the Sea of Okhotsk are presented. A polynomial of the second degree is taken as a regression function. It is shown that the correction using subsatellite ship measurements more accurately characterizes the wave than the data directly received from the satellite.

Addressing Die Displacement in Lithography Processes for Advanced Packaging Applications

To perpetuate Moore’s Law, semiconductor manufacturers are adopting advanced packaging technology as the mainstream solution. As a result, today, fan-out wafer level packaging is a key enabler of two- and three-dimensional packaging solutions. Among the manufacturing challenges, die displacement in lithography processes has been widely discussed, but a total solution is yet to come. In this study, we demonstrate die-by-die and global wafer alignment strategies available on-board the Kulicke & Soffa LITEQ 500 projection stepper. The versatility of a die-by-die alignment strategy allows for working with reconstituted wafers without resorting to an external metrology tool. The die displacement residuals can be reduced by three orders of magnitude, typically, from 100um to 100nm. The evaluation of overlay accuracy by implementing a die-by-die and global wafer alignment strategy indicates comparable performances. Considering high volume manufacturing, advanced process control of overlay is also capable of applying to a batch of wafers.

Global impacts of aviation on air quality evaluated at high resolution

Abstract. Aviation emissions cause global changes in air quality which have been estimated to result in ∼ 58 000 premature mortalities per year, but this number varies by an order of magnitude between studies. The causes of this uncertainty include differences in the assessment of ozone exposure impacts and in how air quality changes are simulated, as well as the possibility that low-resolution (∼ 400 km) global models may overestimate impacts compared to finer-resolution (∼ 50 km) regional models. We use the GEOS-Chem High-Performance chemistry-transport model at a 50 km global resolution, an order of magnitude finer than recent assessments of the same scope, to quantify the air quality impacts of aviation with a single internally consistent global approach. We find that aviation emissions in 2015 resulted in 21 200 (95 % confidence interval due to health response uncertainty: 19 400–22 900) premature mortalities due to particulate matter exposure and 53 100 (36 000–69 900) due to ozone exposure. Compared to a prior estimate of 6800 ozone-related premature mortalities for 2006 our central estimate is increased by 5.6 times due to the use of updated epidemiological data, which includes the effects of ozone exposure during winter, and by 1.3 times due to increased aviation fuel burn. The use of fine (50 km) resolution increases the estimated impacts on both ozone and particulate-matter-related mortality by a further 20 % compared to coarse-resolution (400 km) global simulation, but an intermediate resolution (100 km) is sufficient to capture 98 % of impacts. This is in part due to the role of aviation-attributable ozone, which is long-lived enough to mix through the Northern Hemisphere and exposure to which causes 2.5 times as much health impact as aviation-attributable PM2.5. This work shows that the air quality impacts of civil aviation emissions are dominated by the hemisphere-scale response of tropospheric ozone to aviation NOx rather than local changes and that simulations at ∼ 100 km resolution provide similar results to those at a 2 times finer spatial scale. However, the overall quantification of health impacts is sensitive to assumptions regarding the response of human health to exposure, and additional research is needed to reduce uncertainty in the physical response of the atmosphere to aviation emissions.

Spectroscopic Properties of Cobalt Ions in Ca3(VO4)2 Crystals Doped via Thermal Diffusion and During Synthesis

The spectroscopic properties of cobalt ions in Ca3(VO4)2 crystals doped via thermal diffusion and during synthesis are investigated. The diffusion doped crystal shows the potential for higher cobalt doping while maintaining its high initial optical quality. The redistribution of several absorption and fluorescence lines intensities with cobalt concentration is attributed to the formation of Co2+ optical centers with sufficiently different local environments. The fluorescence decay times of Co2+ optical centers are measured to differ by an order of magnitude (95 and 13 μs) and are attributed to centrosymmetric M1 and low symmetry M2 types of Co2+ optical centers, possibly corresponding to Ca(4) and Ca(1) positions of Ca3(VO4)2 crystal, respectively. Nonlinear transmission of Co2+ M2 centers is measured, and efficient absorption cross‐sections of 1.4 × 10−19 and 2.4 × 10−19 cm2 are evaluated at 1300 and 1500 nm, respectively. The narrow fluorescence line of cobalt ions peaking at about 1170 nm, detected in both Ca3(VO4)2 crystals doped via thermal diffusion and during synthesis, is attributed to Co ions in a trivalent state.

Secondary organic aerosol formed by Euro 5 gasoline vehicle emissions: chemical composition and gas-to-particle phase partitioning

Abstract. In this study we investigated the photo-oxidation of Euro 5 gasoline vehicle emissions during cold urban, hot urban and motorway Artemis cycles. The experiments were conducted in an environmental chamber with average OH concentrations ranging between 6.6 × 105–2.3 × 106 molec. cm−3, relative humidity (RH) between 40 %–55 % and temperatures between 22–26 °C. A proton-transfer-reaction time-of-flight mass spectrometer (PTR-ToF-MS) and the CHemical Analysis of aeRosol ON-line (CHARON) inlet coupled with a PTR-ToF-MS were used for the gas- and particle-phase measurements respectively. This is the first time that the CHARON inlet has been used for the identification of the secondary organic aerosol (SOA) produced from vehicle emissions. The secondary organic gas-phase products ranged between C1 and C9 with one to four atoms of oxygen and were mainly composed of small oxygenated C1–C3 species. The SOA formed contained compounds from C1 to C14, having one to six atoms of oxygen, and the products' distribution was centered at C5. Organonitrites and organonitrates contributed 6 %–7 % of the SOA concentration. Relatively high concentrations of ammonium nitrate (35–160 µg m−3) were formed. The nitrate fraction related to organic nitrate compounds was 0.12–0.20, while ammonium linked to organic ammonium compounds was estimated only during one experiment, reaching a fraction of 0.19. The SOA produced exhibited log C∗ values between 2 and 5. Comparing our results to theoretical estimations for saturation concentrations, we observed differences of 1–3 orders of magnitude, indicating that additional parameters such as RH, particulate water content, aerosol hygroscopicity, and possible reactions in the particulate phase may affect the gas-to-particle partitioning.

The Sonora Substellar Atmosphere Models. IV. Elf Owl: Atmospheric Mixing and Chemical Disequilibrium with Varying Metallicity and C/O Ratios

Disequilibrium chemistry due to vertical mixing in the atmospheres of many brown dwarfs and giant exoplanets is well established. Atmosphere models for these objects typically parameterize mixing with the highly uncertain K zz diffusion parameter. The role of mixing in altering the abundances of C-N-O-bearing molecules has mostly been explored for atmospheres with a solar composition. However, atmospheric metallicity and the C/O ratio also impact atmospheric chemistry. Therefore, we present the Sonora Elf Owl grid of self-consistent cloud-free 1D radiative-convective equilibrium model atmospheres for JWST observations, which includes a variation in K zz across several orders of magnitude and also encompasses subsolar to supersolar metallicities and C/O ratios. We find that the impact of K zz on the T(P) profile and spectra is a strong function of both T eff and metallicity. For metal-poor objects, K zz has large impacts on the atmosphere at significantly higher T eff than in metal-rich atmospheres, where the impact of K zz is seen to occur at lower T eff. We identify significant spectral degeneracies between varying K zz and metallicity in multiple wavelength windows, in particular, at 3–5 μm. We use the Sonora Elf Owl atmospheric grid to fit the observed spectra of a sample of nine early to late T-type objects from T eff = 550–1150 K. We find evidence for very inefficient vertical mixing in these objects, with inferred K zz values lying in the range between ∼101 and 104 cm2 s−1. Using self-consistent models, we find that this slow vertical mixing is due to the observations, which probe mixing in the deep detached radiative zone in these atmospheres.

Friction of a driven chain: role of momentum conservation, Goldstone and radiation modes

We analytically study friction and dissipation of a driven bead in a 1D harmonic chain, and analyze the role of internal damping mechanism as well as chain length. Specifically, we investigate Dissipative Particle Dynamics and Langevin Dynamics, as paradigmatic examples that do and do not display translational symmetry, with distinct results: For identical parameters, the friction forces can differ by many orders of magnitude. For slow driving, a Goldstone mode traverses the entire system, resulting in friction of the driven bead that grows arbitrarily large (Langevin) or gets arbitrarily small (Dissipative Particle Dynamics) with system size. For a long chain, the friction for DPD is shown to be bound, while it shows a singularity (i.e. can be arbitrarily large) for Langevin damping. For long underdamped chains, a radiation mode is recovered in either case, with friction independent of damping mechanism. For medium length chains, the chain shows the expected resonant behavior. At the resonance, friction is non-analytic in damping parameter γ, depending on it as γ −1. Generally, no zero frequency bulk friction coefficient can be determined, as the limits of small frequency and infinite chain length do not commute, and we discuss the regimes where ‘simple’ macroscopic friction occurs.