Classical Belt Research Articles

Rotational Study of 5:3 and 7:4 Resonant Objects within the Main Classical Trans-Neptunian Belt

The 5:3 and 7:4 mean motion resonances of Neptune are at 42.3 and 43.7 au, respectively, and overlap with objects in the classical trans-Neptunian belt (Kuiper Belt). We report the complete/partial lightcurves of 13 and 14 trans-Neptunian objects (TNOs) in the 5:3 and 7:4 resonances, respectively. We report a most likely contact binary in the 7:4 resonance, 2013 FR28, with a periodicity of 13.97 ± 0.04 hr and a lightcurve amplitude of 0.94 ± 0.02 mag. With a V-/U-shaped lightcurve, 2013 FR28 has one of the largest well-sampled TNO amplitudes observed with ground-based observations, comparable to the well-determined contact binary 2001 QG298. 2013 FR28 has a mass ratio q ∼ 1 with a density ρ ∼ 1 g cm−3. We find several objects with large amplitudes and classify 2004 SC60, 2006 CJ69, and 2013 BN82 as likely contact binaries and 2001 QF331, 2003 YW179, and 2015 FP345 as likely elongated objects. We observe the 17:9 resonant or classical object 2003 SP317 that we classify as a likely contact binary. A lower estimate of 10%–50% and 20%–55% for the fraction of (nearly) equal-sized contact binaries is calculated in the 5:3 and 7:4 resonances, respectively. Surface colors of 2004 SC60, 2013 BN82, 2014 OL394, and 2015 FP345 have been obtained. Including these colors with ones from the literature reveals that elongated objects and contact binaries share the same ultrared surface color, except Manwë–Thorondor and 2004 SC60. Not only are the colors of the 7:4 and 5:3 TNOs similar to the cold classicals, but we demonstrate that the rotational properties of the 5:3 and 7:4 resonants are similar to those of the cold classicals, inferring a clear link between these subpopulations.

Col-OSSOS: The Distribution of Surface Classes in Neptune's Resonances

The distribution of surface classes of resonant trans-Neptunian objects (TNOs) provides constraints on the protoplanetesimal disk and giant planet migration. To better understand the surfaces of TNOs, the Colours of the Outer Solar System Origins Survey acquired multiband photometry of 102 TNOs and found that the surfaces of TNOs can be well described by two surface classifications: BrightIR and FaintIR. These classifications both include optically red members and are differentiated predominantly based on whether their near-infrared spectral slope is similar to their optical spectral slope. The vast majority of cold classical TNOs, with dynamically quiescent orbits, have the FaintIR surface classification, and we infer that TNOs in other dynamical classifications with FaintIR surfaces share a common origin with the cold classical TNOs. Comparison between the resonant populations and the possible parent populations of cold classical and dynamically excited TNOs reveal that the 3:2 has minimal contributions from the FaintIR class, which could be explained by the ν 8 secular resonance clearing the region near the 3:2 before any sweeping capture occurred. Conversely, the fraction of FaintIR objects in the 4:3 resonance, 2:1 resonance, and the resonances within the cold classical belt suggest that the FaintIR surface formed in the protoplanetary disk between ≳34.6 and ≲47 au, though the outer bound depends on the degree of resonance sweeping during migration. The presence and absence of the FaintIR surfaces in Neptune’s resonances provides critical constraints for the history of Neptune’s migration, the evolution of the ν 8, and the surface class distribution in the initial planetesimal disk.

Sliding bifurcations of a two DOF self-excited SD oscillator with Coulomb friction

In this study, on the basis of the SD (smooth and discontinuous) oscillator, we analyze the sliding bifurcations of a two DOF self-excited system driven by the classical conveyor belt friction. In order to elaborate the nonsmooth model named the self-excited SD oscillator, we model the friction of the conveyor belt of this system as Coulomb friction. Switching surfaces and sliding regions of this nonsmooth system are obtained based on the Filippov theory. The numerical simulations are performed to present the various scenarios of sliding bifurcation and chaotic attractors in the system. The results of this study give us an opportunity to understand clearly the bifurcation mechanism of the rich nonlinear frictional dynamics in machinery field.

Collisional evolution of the trans-Neptunian region in an early dynamical instability scenario

ABSTRACT Any early or late dynamical instability in the outer Solar system should have left their footprint on the trans-Neptunian object (TNO) populations. Here, we study the collisional and dynamical evolution of such populations numerically by an updated version of ALICANDEP, which suitably takes into account the onset of an early dynamical instability. Key parameters for collisional and dynamical evolution are chosen to match results with current observables. The new model (ALICANDEP-22) considers an original region located between 22 and 30 au, containing 20–30 M⊕ from which bodies are either dynamically ejected from the region or implanted into the current plutinos and hot classical trans-Neptunian belt. An in situ population of objects is also present since the beginning, corresponding to the current cold-classical population. Collisional and dynamical evolution is allowed starting from initial conditions accounting for streaming instability models and observational constraints. ALICANDEP-22 successfully reproduces observational constraints as well as the shape of the size-frequency distribution expected for the Trojan population. The model concludes that Arrokoth is likely a primordial body but cannot be conclusive on the origin of comet 67P/Churyumov–Gerasimenko. The current presence of bodies larger than Pluto in the outer TNO population – waiting to be discovered – is compatible with the initial distributions that allow the model to match current constraints.

TECHNICAL AND ECONOMIC SUBSTANTIATION OF THE PROCESS OF SEMI-FLUIDISATION TREATMENT OF FRUIT AND BERRY PRODUCTS

The search for effective patterns for implementing the semi-fluidisation process for freezing and partial freezing of fruit and berry products under the condition of minimising energy consumption and high productivity of the process constitutes the relevance of the research. The purpose of the study is to develop energy-efficient and reliable technological solutions for the implementation of vibro-wave refrigeration processing of fruit and berry products based on the development of a vibration transport and technological fluidisation machine; determination of power and energy characteristics of the semi-fluidisation process; substantiation of rational speed modes of raw material movement in the processing zone. Based on a comparative analysis of the design and technological characteristics of wave, conveyor and vibration machines, the main trends in their development were substantiated; the main power and energy parameters of the developed oscillatory system were determined. A comparative analysis of the technological schemes of semi-fluidisation using the transport movement of products by belt and vibrating wave conveyor was carried out, which allowed substantiating the effectiveness of the use of the corresponding drive mechanisms of the studied machine. Graph-analytical analysis of the speed and energy parameters of the studied semi-fluidisation process on the basis of the obtained theoretical and experimental data allowed to verify the adequacy of the developed mathematical model and to substantiate the main parameters of the operating mode of the technological load advancement along the processing zone. The conducted research using the developed experimental model and the classical belt conveyor showed an increase in the speed of transportation of raw materials by almost 2 times with a decrease in energy consumption for the process by 1.4 times for the vibro-wave scheme. In the developed vibrating transport-technological semi-fluidisation machine, the vibration effect provides a decrease in technological resistance in the mass of products, significantly reducing the force effect on it, as a result of the generated travelling wave on the surface of the load-carrying body, the movement of the processed material along the belt and continuous mixing or renewal of product layers are provided. The practical value of the study includes the use of a combined scheme for creating a fluidised layer of products due to the oscillation of the belt and bubbling with the flow of coolant; the use of the belt wave to create the movement of products in the production area

Dynamical Implantation of Blue Binaries in the Cold Classical Kuiper Belt

Abstract Colors and binarity provide important constraints on the Kuiper Belt formation. The cold classical objects at radial distance r = 42–47 au from the Sun are predominantly very red (spectral slope s > 17%) and often exist as equal-size binaries (∼30% observed binary fraction). This has been taken as evidence for the in situ formation of cold classicals. Interestingly, a small fraction (∼10%) of cold classicals is less red with s < 17%, and these “blue” bodies are often found in wide binaries. Here we study the dynamical implantation of blue binaries from r < 42 au. We find that they can be implanted into the cold classical belt from a wide range of initial radial distances, but the survival of the widest blue binaries—2001 QW322 and 2003 UN284—implies formation at r > 30 au. This would be consistent with the hypothesized less-red to very-red transition at 30 < r < 40 au. For any reasonable choice of parameters (Neptune’s migration history, initial disk profile, etc.), however, our model predicts a predominance of blue singles, rather than blue binaries, which contradicts existing observations. We suggest that wide blue binaries formed in situ at r = 42–47 au and their color reflects early formation in a protoplanetary gas disk. The predominantly VR colors of cold classicals may be related to the production of methanol and other hydrocarbons during the late stages of the disk, when the temperature at 45 au dropped to ≃20 K and carbon monoxide was hydrogenated.

Onset of the anorogenic alkaline magmatism in the Nigerian Younger Granite province: Constraints from the Daura and Dutse complexes

The Younger Granite province of Niger and Nigeria exemplifies a classical anorogenic alkaline ring granite belt with southward age migration from ca. 470 Ma to 140 Ma. However, the precise age transition from the older Nigerien Younger Granite (NrYG) to the younger Nigerian Younger Granite (NaYG) is poorly constrained. The Daura and Dutse complexes, located at the northernmost tip of the NaYG province, represent a temporal and spatial link between the NrYG and NaYG provinces. The Daura complex is composed of amphibole syenite and biotite granite, while the Dutse complex consists of fayalite syenite and arfvedsonite aegirine granite. Similar to other alkaline rocks of the NrYG and NaYG provinces, the Daura and Dutse samples all chemically show typical A1-type granite features, such as high alkalis (K2O + N2O = 8.33–11.27 wt%.), Ga/Al ratios, Zr + Nb + Ce + Y contents (527–2345 ppm) and FeOt/(FeOt+MgO) ratios (0.03–0.70) as well as elevated HFSEs. The NdHf and Pb isotopic systematics show that all the syenite-granites yield εNd (t) = −2.9 to +1.5, ɛHf (t) = −3.8 to +16.7, and 206Pb/204Pb = 17.818 to 19.555, suggestive of magmas derived from a slightly depleted mantle source with OIB imprints. A reduced to slightly oxidized redox state is invoked for the parental melt based on estimations from mineral chemistry. The Daura amphibole syenite is composed of >60% alkali feldspar, show high Eu/Eu* (>1), Ba/Zr (>3.5) values and cumulate textures, resembling an alkali feldspar cumulate rock. The other alkaline granitic rocks were likely generated from variable fractional crystallization of the residual melt with distinct crustal contaminations. Zircon UPb dating reveal that the Daura amphibole syenite and biotite granite were emplaced at 324 ± 1 Ma and 321 ± 3 Ma, respectively, whereas the Dutse granitoids showed episodic intrusive periods of ca. 264 Ma and 232 Ma. All these results predate other anorogenic alkaline complexes of the NaYG and update the oldest age (ca. 214 Ma in previous references) recorded in the alkaline granite province. To the north, it connects well with ages from the Zinder complex (~330 Ma) in the southernmost NrYG province, reflecting a significant link between the NrYG and NaYG provinces. From a broad view, a linear age migration from north to south in the Niger-Nigeria Younger Granite province remains well preserved, although temporal and spatial intervals exist in local region. This emplacement pattern can be traced to the periodic and repeated reactivation of lithospheric shear zones and transcurrent faults.

OSSOS Finds an Exponential Cutoff in the Size Distribution of the Cold Classical Kuiper Belt

Abstract The cold main classical Kuiper Belt consists of the nonresonant small solar system bodies with low orbital inclinations and orbital semimajor axes between 42.4 and 47.7 au. These objects likely formed in situ, and the population has experienced minimal collisional modification since formation. Using the Outer Solar System Origins Survey ensemble sample and characterization, combined with constraints from deeper surveys and supported by evidence from the Minor Planet Center catalog and the Deep Ecliptic Survey, we determine the absolute magnitude H r distribution of the cold classical belt from H r ≃ 5 to 12 (roughly diameters of 400–20 km). We conclude that the cold population’s H r distribution exhibits an exponential cutoff at large sizes. Exponential cutoffs at large sizes are not a natural outcome of pairwise particle accretion, but exponentially tapered power-law size distributions are a feature of numerical simulations of planetesimal formation via a streaming instability. Our observation of an exponential cutoff agrees with previous observational inferences that no large objects (D ≳ 400 km) exist in the cold population. We note that the asymptotic slope of the H r distribution is consistent with α ∼ 0.4. This asymptotic slope is also found in streaming instability modeling of planetesimal formation and is thus not necessarily associated with achieving collisional equilibrium. Studies of the trans-Neptunian region are providing the parameters that will enable future streaming-instability studies to determine the initial conditions of planetesimal formation in the ≈45 au region of the Sun’s protoplanetary disk.

Evolution of primordial Kuiper belt binaries through a giant planet instability

ABSTRACT The non-resonant Kuiper belt objects between the 3:2 and 2:1 Neptunian mean motion resonances can be largely divided between a cold classical belt (CCB) and a hot classical belt (HCB). A notable difference between these two subpopulations is the prevalence of widely spaced, equal-mass binaries in the CCB, and a much smaller but non-zero number in the HCB. The primary reason for this difference in binary rate remains unclear. Here using N-body simulations we examine whether close encounters with the giant planets during an early outer Solar system instability may have disrupted primordial Kuiper belt binaries that existed within the primordial Kuiper belt before they attained HCB orbits. We find that such encounters are very effective at disrupting binaries down to separations of ∼ 1% of their Hill radius' (as measured in the modern Kuiper belt), potentially explaining the paucity of widely spaced, equal mass binaries in the modern HCB. Moreover, we find that the widest binaries observed in the modern HCB are quite unlikely to survive planetary encounters, but these same planetary encounters can widen a small subset of tighter binaries to give rise to the small population of very wide binaries seen in today's HCB.

OSSOS. XXI. Collision Probabilities in the Edgeworth–Kuiper Belt

Abstract Here, we present results on the intrinsic collision probabilities, P I , and range of collision speeds, V I , as a function of the heliocentric distance, r, in the trans-Neptunian region. The collision speed is one of the parameters that serves as a proxy for a collisional outcome (e.g., disruption and scattering of fragments, or formation of a crater, as both processes are related to the impact energy). We utilize an improved and debiased model of the trans-Neptunian object (TNO) region from the “Outer Solar System Origins Survey” (OSSOS). It provides a well-defined model of TNO orbital distribution, based on multiple opposition observations of more than 1000 bodies. We compute collisional probabilities for the OSSOS models of the main classical, resonant, detached+outer, and scattering TNO populations. The intrinsic collision probabilities and collision speeds are computed using Öpik’s approach, as revised and modified by Wetherill for noncircular and inclined orbits. The calculations are carried out for each of the dynamical TNO groups, allowing for inter-population collisions as well as collisions within each TNO population, resulting in 28 combinations in total. Our results indicate that collisions in the trans-Neptunian region are possible over a wide range in (r, V I ) phase space. Although collisions are calculated to happen within r ∼ 20–200 au and V I ∼ 0.1 km s−1 to as high as V I ∼ 9 km s−1, most of the collisions are likely to happen at low relative velocities V I < 1 km s−1 and are dominated by the main classical belt.

Dynamical Classification of Trans-Neptunian Objects Detected by the Dark Energy Survey

Abstract The outer solar system contains a large number of small bodies (known as trans-Neptunian objects or TNOs) that exhibit diverse types of dynamical behavior. The classification of bodies in this distant region into dynamical classes—subpopulations that experience similar orbital evolution—aids in our understanding of the structure and formation of the solar system. In this work, we propose an updated dynamical classification scheme for the outer solar system. This approach includes the construction of a new (automated) method for identifying mean motion resonances. We apply this algorithm to the current data set of TNOs observed by the Dark Energy Survey (DES) and present a working classification for all of the DES TNOs detected to date. Our classification scheme yields 1 inner centaur, 19 outer centaurs, 21 scattering disk objects, 47 detached TNOs, 48 securely resonant objects, 7 resonant candidates, and 97 classical belt objects. Among the scattering and detached objects, we detect 8 TNOs with semimajor axes greater than 150 au.

Comparison of Detailed Belt - Cylinder Interaction Model with Classical Belt Friction Formula

Abstract This paper deals with a comparison of the classical belt friction formula, also called Euler-Eytelwein equation, with a detailed belt-cylinder interaction model. The belt friction is a typical pedagogical problem where the usage of equilibrium conditions is shown, but also have a practical usage, e.g. a heavy ship anchor pulling or a belt brake. The presented belt-cylinder interaction model is based on the absolute nodal coordinate formulation of beam finite elements with the consideration of nonlinear contact forces between a beam and a rigid cylinder.

OSSOS. XIII. Fossilized Resonant Dropouts Tentatively Confirm Neptune’s Migration Was Grainy and Slow

Abstract The migration of Neptune’s resonances through the proto–Kuiper Belt has been imprinted in the distribution of small bodies in the outer solar system. Here we analyze five published Neptune migration models in detail, focusing on the high pericenter distance (high-q) trans-Neptunian objects (TNOs) near Neptune’s 5:2 and 3:1 mean-motion resonances because they have large resonant populations, are outside the main classical belt, and are relatively isolated from other strong resonances. We compare the observationally biased output from these dynamical models with the detected TNOs from the Outer Solar System Origins Survey (OSSOS) via its Survey Simulator. All four of the new OSSOS detections of high-q nonresonant TNOs are on the sunward side of the 5:2 and 3:1 resonances. We show that even after accounting for observation biases, this asymmetric distribution cannot be drawn from a uniform distribution of TNOs at 2σ confidence. As shown by previous work, our analysis here tentatively confirms that the dynamical model that uses grainy slow Neptune migration provides the best match to the real high-q TNO orbital data. However, due to extreme observational biases, we have very few high-q TNO discoveries with which to statistically constrain the models. Thus, this analysis provides a framework for future comparison between the output from detailed, dynamically classified Neptune migration simulations and the TNO discoveries from future well-characterized surveys. We show that a deeper survey (to a limiting r-magnitude of 26.0) with a similar survey area to OSSOS could statistically distinguish between these five Neptune migration models.

BEYOND THE KUIPER BELT EDGE: NEW HIGH PERIHELION TRANS-NEPTUNIAN OBJECTS WITH MODERATE SEMIMAJOR AXES AND ECCENTRICITIES

ABSTRACT We are conducting a survey for distant solar system objects beyond the Kuiper Belt edge (∼50 au) with new wide-field cameras on the Subaru and CTIO telescopes. We are interested in the orbits of objects that are decoupled from the giant planet region to understand the structure of the outer solar system, including whether a massive planet exists beyond a few hundred astronomical units as first reported in 2014 by Trujillo & Sheppard. In addition to discovering extreme trans-Neptunian objects detailed elsewhere, we found several objects with high perihelia (q > 40 au) that differ from the extreme and inner Oort cloud objects due to their moderate semimajor axes (50 < a < 100 au) and eccentricities (e ≲ 0.3). Newly discovered objects 2014 FZ71 and 2015 FJ345 have the third and fourth highest perihelia known after Sedna and 2012 VP113, yet their orbits are not nearly as eccentric or distant. We found several of these high-perihelion but moderate orbit objects and observe that they are mostly near Neptune mean motion resonances (MMRs) and have significant inclinations (i > 20°). These moderate objects likely obtained their unusual orbits through combined interactions with Neptune’s MMRs and the Kozai resonance, similar to the origin scenarios for 2004 XR190. We also find the distant 2008 ST291 has likely been modified by the MMR+KR mechanism through the 6:1 Neptune resonance. We discuss these moderately eccentric distant objects along with some other interesting low inclination outer classical belt objects like 2012 FH84 discovered in our ongoing survey.

The Debiased Kuiper Belt: Our Solar System as a Debris Disk

AbstractThe dust measured in debris disks traces the position of planetesimal belts. In our Solar System, we are also able to measure the largest planetesimals directly and can extrapolate down to make an estimate of the dust. The zodiacal dust from the asteroid belt is better constrained than the only rudimentary measurements of Kuiper belt dust. Dust models will thus be based on the current orbital distribution of the larger bodies which provide the collisional source. The orbital distribution of many Kuiper belt objects is strongly affected by dynamical interactions with Neptune, and the structure cannot be understood without taking this into account. We present the debiased Kuiper belt as measured by the Canada-France Ecliptic Plane Survey (CFEPS). This model includes the absolute populations for objects with diameters >100 km, measured orbital distributions, and size distributions of the components of the Kuiper belt: the classical belt (hot, stirred, and kernel components), the scattering disk, the detached objects, and the resonant objects (1:1, 5:4, 4:3, 3:2 including Kozai subcomponent, 5:3, 7:4, 2:1, 7:3, 5:2, 3:1, and 5:1). Because a large fraction of known debris disks are consistent with dust at Kuiper belt distances from the host stars, the CFEPS Kuiper belt model provides an excellent starting point for a debris disk model, as the dynamical interactions with planets interior to the disk are well-understood and can be precisely modelled using orbital integrations.

THE COLOR DIFFERENCES OF KUIPER BELT OBJECTS IN RESONANCE WITH NEPTUNE

(Abridged) New optical colors of 58 objects in mean motion resonances with Neptune show the various resonant populations have significantly different color distributions. The 5:3 and 7:4 resonances have semi-major axes near the middle of the main Kuiper Belt and both are dominated by ultra-red material. The 5:3 and 7:4 resonances have statistically the same color distribution as the low inclination "cold" classical belt. The inner 4:3 and distant 5:2 resonances have objects with mostly moderately red colors, similar to the scattered and detached disk populations. The 2:1 resonance, which is near the outer edge of the main Kuiper Belt, has a large range of colors with similar numbers of moderately red and ultra-red objects at all inclinations. The inner 3:2 resonance, like the outer 2:1, has a large range of objects from neutral to ultra-red. The Neptune Trojans (1:1 resonance) are only slightly red, similar to the Jupiter Trojans. The inner 5:4 resonance only has four objects with measured colors but shows equal numbers of ultra-red and moderately red objects. The 9:5, 12:5, 7:3, 3:1 and 11:3 resonances do not have reliable color distribution statistics, though it appears noteworthy that all three of the measured 3:1 objects have only moderately red colors, similar to the 4:3 and 5:2 resonances. The different color distributions are likely a result from the disruption of the primordial Kuiper Belt from the scattering and migration of the giant planets. The few low inclination objects known in the outer 2:1 and 5:2 resonances are mostly only moderately red. This suggests if the 2:1 and 5:2 have a cold low inclination component, the objects likely had a significantly different origin than the ultra-red dominated cold components of the cold classical belt and 5:3 and 7:4 resonances.

The Umbria-Marche Apennines as a Double Orogen: Observations and hypotheses

The Umbria-Marche Apennines, an arc-shaped fold and thrust belt with eastward convexity and vergence, form the external part of the Northern Apennines. In the middle 1980s, the Umbria-Marche Apennines were interpreted by some as a classical thin-skinned foldthrust belt, with thrust sheets emplaced in an in-sequence, piggyback mode, from the interior to the exterior of the orogen, over a main, basal detachment in the Triassic evaporites. In the mechanics of this kind of edifice, the folds and thrusts would develop within a prism or tapered wedge, bounded at the base by an undeformed basement with a regional monocline dipping toward the hinterland, and at the top by a topographic and structural slope generally dipping toward the foreland. Other authors saw the Umbria-Marche Apennines as a more complex orogen, with basement involvement, possible tectonic inversions, and out-of-sequence thrusts. In the present paper, the geometry, structure, and tectono-sedimentary evolution of the Umbria-Marche Apennines are compared with the classical thin-skinned model. We suggest that this fold-thrust belt can be divided longitudinally into two sectors. The eastern part of the chain, comprising the high Mesozoic carbonate anticlinal ridges of the axial zone together with the Marche external folds, fits the classical model well, but the western part, comprising the Umbrian Pre-Apennines, shows striking differences. The boundary between the eastern and western parts of the Umbria-Marche Apennines is here termed the Scheggia-Foligno Line (SFL). East of this line, the Eastern Umbria-Marche Apennines show an eastward taper between the undeformed basement, dipping gently west, and an upper surface in which both topographic and structural elevation decrease toward the east. West of the Scheggia-Foligno Line, by contrast, seismic reflection profiles and subsurface data show basement involvement in the thrusting at shallow depths, while both the topographic and structural elevations are anomalously low compared to the more easterly parts of the chain. There is also a notable discontinuity in foredeep-basin evolution at the Scheggia-Foligno Line, with welldeveloped foredeep basins in the Umbrian Pre-Apennines and the external Marche belt (the Marnoso-arenacea and Marche Plio-Pleistocene, respectively), whereas only thrust-top basins developed in the axial zone, during the Tortonian-Messinian interval. Various mechanisms, not all mutually exclusive, might be invoked to explain the discontinuity at the Scheggia-Foligno Line. These possible explanations include causes of local character, linked to the sedimentary and tectonic evolution of the region, involving episodic departures from steady-state conditions, interrupting the regular growth of the accretionary wedge. However, it also possible that the Western and Eastern Umbria-Marche Apennines represent completely different orogenic systems, with different causes possibly with the former related to Corsica-Adria collision and the latter due to slab rollback of Adriatic lithosphere. In either case, this study demonstrates the complexity of evolution of the Northern Apennines, with adjacent zones showing abrupt variations in their history and style of deformation, which are difficult to incorporate in a single, unified geodynamic model.

Collisional evolution of trans-Neptunian object populations in a Nice model environment

Almost 20 years of observations of the trans-Neptunian region have shed light on the overall dynamical structure of the trans-Neptunian object (TNO) populations and absolute magnitude distributions. The TNO region can be inserted in the global frame of the dynamical evolution of the giant planets, as described by the Nice model. Any reliable collisional evolution model should account for dynamical effects and should produce results that meet the constraints imposed by current observables. With this aim, we have developed a code package [Asteroid-LIke Collisional ANd Dynamical Evolution Package (alicandep)], which is a collisional evolution code that includes statistical elimination of objects by dynamical effects within the frame of a disc migrating and gradually dynamically exciting, as well as the dynamical migration of objects between regions. Moreover, we included the possibility to distinguish between dynamically cold and hot bodies in the main classical belt and to keep track of primordial bodies in the whole region. Finally, we performed a large number of numerical simulations varying physical parameters, boundary and initial conditions, in order to match the current observables and the dynamical conditions of the Nice model. Our results are in agreement with those observables and can explain the flattened size distributions in the 30–100 km size range. This allows us to constrain the original mass of the belt (not less than 50 M⊕), which is compatible with initial shallow size distributions below 100 km. alicandep also finds an extremely high probability for the existence of at least one more large (>1700 km) object yet to be discovered in the outer belt. This model supports the reliability of the Nice model, and it can be a suitable tool to statistically study many features of the trans-Neptunian region.

NEPTUNE ON TIPTOES: DYNAMICAL HISTORIES THAT PRESERVE THE COLD CLASSICAL KUIPER BELT

The current dynamical structure of the Kuiper belt was shaped by the orbital evolution of the giant planets, especially Neptune, during the era following planet formation, when the giant planets may have undergone planet-planet scattering and/or planetesimal-driven migration. Numerical simulations of this process, while reproducing many properties of the belt, fail to generate the high inclinations and eccentricities observed for some objects while maintaining the observed dynamically "cold" population. We present the first of a three-part parameter study of how different dynamical histories of Neptune sculpt the planetesimal disk. Here we identify which dynamical histories allow an in situ planetesimal disk to remain dynamically cold, becoming today's cold Kuiper belt population. We find that if Neptune undergoes a period of elevated eccentricity and/or inclination, it secularly excites the eccentricities and inclinations of the planetesimal disk. We demonstrate that there are several well-defined regimes for this secular excitation, depending on the relative timescales of Neptune's migration, the damping of Neptune's orbital inclination and/or eccentricity, and the secular evolution of the planetesimals. We model this secular excitation analytically in each regime, allowing for a thorough exploration of parameter space. Neptune's eccentricity and inclination can remain high for a limited amount of time without disrupting the cold classical belt. In the regime of slow damping and slow migration, if Neptune is located (for example) at 20 AU, then its eccentricity must stay below 0.18 and its inclination below 6{\deg}.

Rolling contact between a rubber ring and rigid cylinders: Mechanics of rubber belts

We revisit the classical creep theory for a belt drive system as a rolling contact problem between a rubber ring and rigid cylinders to evaluate the effects of linear viscoelasticity and large strain of the belt on the system in a steady state. We first construct the general theory of belt mechanics for a multi-pulley system by dimensional reduction from 3D extensible, unshearable rod. We then develop the belt mechanics for a linear viscoelastic belt and show that the effect of retardation time can be involved in the effective friction coefficient: the classical Euler's belt formula can be recovered. Next, we assume that the belt is a neo-Hookean material and examine the effect of large strain of the belt on the contact pressure distribution. We compare the theory with the results by finite element analysis and show that the theory provides good quality.