Shallow Wedge Research Articles

Phase separation in a wedge: exact results.

The exact theory of phase separation in a two-dimensional wedge is derived from the properties of the order parameter and boundary condition changing operators in field theory. For a shallow wedge we determine the passage probability for an interface with endpoints on the boundary. For generic opening angles we exhibit the fundamental origin of the filling transition condition and of the property known as wedge covariance.

Some basic contact problems in couple stress elasticity

Indentation tests have long been a standard method for material characterization due to the fact that they provide an easy, inexpensive, non-destructive and objective method of evaluating basic properties from small volumes of materials. As the contact scales in such experiments reduce progressively (micro to nano-scales) the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. In the present study, we derive general solutions for three basic two-dimensional (2D) plane-strain contact problems within the framework of the generalized continuum theory of couple-stress elasticity. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling microstructured materials. By using this theory, we initially study the problem of the indentation of a deformable elastic half-plane by a flat punch, then by a cylindrical indentor, and finally by a shallow wedge indentor. Our approach is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that it is inadequate to analyze indentation problems in microstructured materials employing only classical contact mechanics.

Iron isotopic evidence for convective resurfacing of recycled arc-front mantle beneath back-arc basins

[1] Geophysical observations suggest sub-arc convective flow transports melt-exhausted and metasomatized wedge mantle into deeper mantle regions. Reciprocally, asthenospheric, fertile mantle may supply back-arc ridges distal to the trench by shallow, lateral mantle ingress, insinuating initial wedge mantle depletion in its back-arc region. Here we show that light Fe isotope compositions of the Central Lau Spreading Centre located in the Lau back-arc basin on the farside of the Tonga-Kermadec arc are indicative for derivation from a modified arc-front mantle with elemental and Nd-isotopic memory of former slab fluid addition. We propose that this shallow wedge material has been transported from the sub-arc mantle to the back-arc either convectively or in a buoyant diapir. This implies that melt-depleted mantle in subduction zones is, at least in parts, recycled in a resurfacing loop. This can explain the depletion in back-arc regions, and the progressively depleted nature of island arc sources in maturing arc systems.

Sedimentology and foreland basin paleogeography during Taiwan arc continent collision

The Western foreland basin in Taiwan originated through the oblique collision between the Luzon volcanic arc and the Asian passive margin. Crustal flexure adjacent to the growing orogenic load created a subsiding foreland basin. The sedimentary record reveals progressively changing sedimentary environments influenced by the orogen approaching from the East. Based on sedimentary facies distribution at five key stratigraphic horizons, paleogeographic maps were constructed. The maps highlight the complicated basin-wide dynamics of sediment dispersal within an evolving foreland basin.The basin physiography changed very little from the middle Miocene (∼12.5Ma) to the late Pliocene (∼3Ma). The transition from a passive margin to foreland basin setting in the late Pliocene (∼3Ma), during deposition of the mud-dominated Chinshui Shale, is dominantly marked by a deepening and widening of the main depositional basin. These finer grained Taiwan derived sediments clearly indicate increased subsidence, though water depths remain relatively shallow, and sedimentation associated with the approach of the growing orogen to the East.In the late Pleistocene as the shallow marine wedge ahead of the growing orogen propagated southward, the proximal parts of the basin evolved into a wedge-top setting introducing deformation and sedimentation in the distal basin. Despite high Pleistocene to modern erosion/sedimentation rates, shallow marine facies persist, as the basin remains open to the South and longitudinal transport is sufficient to prevent it from becoming overfilled or even fully terrestrial.Our paleoenvironmental and paleogeographical reconstructions constrain southward propagation rates in the range of 5–20km/Myr from 2Ma to 0.5Ma, and 106–120km/Myr between late Pleistocene and present (0.5–0Ma). The initial rates are not synchronous with the migration of the sediment depocenters highlighting the complexity of sediment distribution and accumulation in evolving foreland basins.

Effects of tilt moment on the contact stresses for a wedge under sliding condition

The contact stresses between a tilted, shallow wedge and half-plane, under frictional sliding condition, are investigated analytically. The closed-form of contact law itself, together with the contact tractions and the size of the contact segments are explicitly found. The effects of tilt moment, material property, geometry variation and the applied loads on the contact pressure distributions are investigated. By making use of the Muskhelishvili’s potential function and the Plemelj formulae, the analytically derived contact pressure is the same as that obtained based on the singular integral equations. The result is verified by comparing with that in the literature. The in-plane stress field is evaluated from the standpoint of fatigue. It is shown that the Muskhelishvili’s potential function and the Plemelj formulae can be also used to solve this type of contact problem. This study is helpful for understanding the mechanism of frictional sliding contact problem with singular point and designing better high precision instruments and devices.

Turbulent mixing in a strongly forced salt wedge estuary

Turbulent mixing of salt is examined in a shallow salt wedge estuary with strong fluvial and tidal forcing. A numerical model of the Merrimack River estuary is used to quantify turbulent stress, shear production, and buoyancy flux. Little mixing occurs during flood tides despite strong velocities because bottom boundary layer turbulence is dislocated from stratification elevated in the water column. During ebbs, bottom salinity fronts form at a series of bathymetric transitions. At the fronts, near‐bottom velocity and shear stress are low, but shear, stress, and buoyancy flux are elevated at the pycnocline. Internal shear layers provide the dominant source of mixing during the early ebb. Later in the ebb, the pycnocline broadens and moves down such that boundary layer turbulence dominates mixing. Mixing occurs primarily during ebbs, with internal shear mixing accounting for about 50% of the total buoyancy flux. Both the relative contribution of internal shear mixing and the mixing efficiency increase with discharge, with bulk mixing efficiencies between 0.02 and 0.07. Buoyancy fluxes in the estuary increase with discharge up to about 400 m3 s−1 above which a majority of the mixing occurs offshore. Observed buoyancy fluxes were more consistent with the k‐ɛ turbulence closure than the Mellor‐Yamada closure, and more total mixing occurred in the estuary with k‐ɛ. Calculated buoyancy fluxes were sensitive to horizontal grid resolution, as a lower resolution grid yielded less integrated buoyancy flux in the estuary and exported lower salinity water but likely had greater numerical mixing.

Constraints on upper mantle anisotropy surrounding the Cocos slab from SK(K)S splitting

SKS and SKKS splitting observations are used to constrain the pattern of mantle flow in the Central American subduction zone beneath Costa Rica and Nicaragua. After removing the effects of shallow wedge anisotropy on SK(K)S waveforms, a best fitting model of anisotropy beneath the Cocos Plate and in the deeper mantle wedge is determined. Fast polarization directions and model symmetry axis orientations in both regions (as well as the shallow wedge) are dominated by roughly arc‐parallel azimuths and, therefore, are not consistent with sublithospheric mantle flow entrained by the subducting Cocos Plate or simple two‐dimensional corner flow in the wedge. In conjunction with geochemical data and local S splitting tomography, the SK(K)S splitting observations and anisotropy models are consistent with flow to the WNW within the mantle wedge on the Caribbean side of the Cocos Plate, possibly drawn through a slab window beneath Panama and southern Costa Rica. Anisotropy in the Pacific mantle beneath the Cocos Plate is also best explained by flow with a component that is roughly parallel to the strike of the slab, although the absolute direction of this flow is not uniquely constrained.

Structure, variability, and salt flux in a strongly forced salt wedge estuary

The tidally varying circulation, stratification, and salt flux mechanisms are investigated in a shallow salt wedge estuary where fluvial and tidal velocities are large and the steady baroclinic circulation is comparatively weak. The study integrates field observations and numerical simulations of the Merrimack River estuary. At moderate to high discharge the estuary is short and highly stratified, while at lower discharges it shifts to a longer, more weakly stratified estuary; the transition occurs when the length of the salinity intrusion is similar to the tidal excursion. The Merrimack is highly variable at tidal time scales owing to the advection and mixing of a bottom salinity front. Salt flux is predominantly due to tidal processes rather than steady baroclinic or bathymetric shear. Tidal pumping is important near the mouth, but inside the estuary salt flux is due to tidal asymmetries in the elevation and thickness of the halocline that depend on the tidal amplitude and river discharge. Conditions in the Merrimack, including the salinity intrusion length and stratification, vary more with event to seasonal shifts in river discharge than with spring‐neap changes in tidal amplitude. An unstructured grid hydrodynamic model is used to simulate conditions in the Merrimack and model results are compared quantitatively against field observations. The model achieves a high skill against time series of water level, salinity, and velocity and captures the spatial structures of salinity, velocity, and salt flux observed in along‐ and across‐estuary transects. High model skills depend on accurate and well‐resolved grid bathymetry and low background vertical and horizontal diffusivities.

Multistage metamorphism of orogenic garnet–lherzolite from Zhimafang, Sulu UHP terrane, E. China: Implications for mantle wedge convection during progressive oceanic and continental subduction

Seven stages of mineral assemblage were recognized in the Zhimafang orogenic garnet lherzolite from the Sulu ultrahigh-pressure (UHP) metamorphic terrane of eastern China, which suggest that it experienced progressive mantle wedge convection during subduction of previous oceanic and subsequent continental slabs. M 1 is recorded by inclusions of high-Mg olivine, high-Mg–Al–Cr–Ca orthopyroxene and high-Mg clinopyroxene in the high Ca–Cr cores of the garnet porphyroclasts, suggesting that the Zhimafang peridotite was probably a garnet lherzolite originated from a deep and hot mantle wedge above the previously subducted oceanic slab. M 2 is represented by inclusions of high-Mg–Al chromite, high-Mg olivine and high-Mg orthopyroxene in the low-Cr mantles of the garnet porphyroclasts and core of the matrix garnet, suggesting that the rock was convected to shallow and hot mantle wedge, and was transformed to refractory spinel harzburgite or spinel dunite due to high degree of decompressional partial melting. M 3 is manifested by the origin of metasomatic clinopyroxene and orthopyroxene porphyroblasts with inclusions of high-Fe chromite, tremolitic or edenitic amphibole, phlogopite, barite and pyrite, indicating that the rock was convected to shallow, cold and wet corner of the mantle wedge, and was transformed to a fertile amphibole-bearing spinel lherzolite during continental subduction. The lherzolites was subsequently transformed to high-pressure (HP) amphibole-bearing garnet lherzolite ( M 4) and UHP garnet lherzolite ( M 5), indicating its convection to deep mantle wedge. Finally, the UHP garnet–lherzolite exhumed to the Earth’s surface, together with the UHP terrane, and subsequently retrograded to amphibole-bearing garnet lherzolite ( M 6) and chlorite-amphibole-bearing spinel lherzolite ( M 7). Detailed analyses of reaction textures and mineral compositions revealed several stages of metasomatism related to oceanic and continental subduction and exhumation.

Deformation and fault activity in space and time in high-resolution numerical models of doubly vergent thrust wedges

A discrete-element model is used to investigate the manner in which deformation and fault activity change in space and time during the development of a doubly vergent thrust wedge in the upper crust. Deformation is a result of shortening at a subduction slot in the base of the model, a configuration which produces a dynamic backstop within the cohesionless, frictional cover material. A series of experiments with differing basal (decollement) friction are performed. The distinct manners in which thrust wedges grow, and the variability of fault development and activity in space and time, are then examined. Both predicted large-scale wedge geometries and individual fault-fold structures are similar to those observed in sandbox models, and show the complex manner in which shortening is accommodated and localized during the development of the thrust wedge. When compared to a sandbox model with similar boundary conditions, model results are strikingly similar. In all cases, deformation initiates above the subduction slot with the formation of an axial zone; the wedge is then developed by displacement on a retro-wedge thrust and propagation of deformation into the pro-wedge region. Models with low coefficients of basal friction typically develop wide, shallow wedges with distributed, spaced deformation and rather symmetric, box-like structures; whereas those with high coefficients of basal friction develop narrower, steeper wedges, consisting of a series of stacked, pro-wedge thrust sheets, and a high-displacement retro-wedge thrust. In general, fault initiation and linkage is extremely complex in our models, with several smaller faults operating until linkage occurs to form a major through-going structure. Of particular interest is the observation that many of the faults do not develop at the basal decollement and propagate upwards through the cover but rather initiate at high levels in the cover and propagate/link downwards with other, deeper structures. Results also indicate the utility of the discrete-element approach in modelling large-displacement, complex deformation of geological materials.

Unsteady natural convection in a reservoir induced by constant surface cooling

This article concerns numerical simulations of unsteady natural convection induced by constant cooling at the water surface of a reservoir. Numerical computations reveal the occurrence of sinking cold water plumes soon after the initiation of cooling. These sinking plumes are responsible for an initial mixing over the local water depth, resulting later in a distinct horizontal temperature gradient with the water temperature decreasing toward the shallow region due to the presence of a sloping boundary. Simulations also show that the relatively higher cooling rate in the shallow water causes a cold water current flowing downwards along the sloping bottom and penetrating into the deeper regions. After a sufficient time a quasi-steady state is attained and at the end two main fluid layers are developed: a relatively stable undercurrent, and a very unstable return flow just below the water surface. Numerical results for different Grashof numbers are discussed. Understanding of the flow mechanisms pertinent to this flow is important for predicting the transport of nutrients and pollutants across the reservoir. References G. M. Horsch, H. G. Stefan, Convective circulation in littoral water due to surface cooling, Limnol. Oceanogr., 33, 1998, 1068--1083. C. Lei, J. C. Patterson, Unsteady natural convection in a triangular enclosure induced by surface cooling, Int. J. Heat and Fluid Flow, 26, 2005, 307--321. C. Lei, J. C. Patterson, A direct three-dimensional simulation of radiation-induced natural convection in a shallow wedge, Int. J. Heat and Mass Transfer, 46, 2003, 1183--1197. doi:10.1016/S0017-9310(02)00401-5 C. Lei, J. C. Patterson, Natural convection induced by diurnal heating and cooling in a reservoir with slowly varying topography, JSME International Journal, Series B: Fluids and Thermal Engineering, 49(3), 2006, 605--615. doi:10.1299/jsmeb.49.605 E. E. Adams, S. A. Wells, Field measurements on side arms of Lake Anna Va, J.Hydraulic Eng., 110, 1984, 773--793. S. G. Monismith, J. Imberger, M. L. Morison, Convective motions in the sidearm of a small reservoir, Limnol. Oceanogr., 35(8), 1990, 1676--1702. D. E. Farrow, J. C. Patterson, On the response of a reservoir sidearm to diurnal heating and cooling, J. Fluid Mech., 246, 1993, 143--161. doi:10.1017/S0022112093000072 D. Farrow, Periodically forced natural convection over slowly varying topography, J. Fluid Mech., 508, 2004, 1--21. doi:10.1017/S002211200400847X FLUENT 6.2 User's guide, Fluent Inc., Lebanon, 2005. H. K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics: the Finite Volume method, Longman Scientific and Technical, 1995. T. P. Bednarz, C. Lei, J. C. Patterson, An experimental study of unsteady natural convection in a reservoir model cooled from the water surface, Experimental Thermal and Fluid Science, in press, 2007. doi:10.1016/j.expthermflusci.2007.10.007

Analytical solution for contact problem between a tilted wedge and half-plane under partial slip condition

Elastic contact problem of a tilted shallow wedge with a half-plane is considered. The problem is solved analytically in either full slip or partial slip conditions. Closed-form expression is given for the Muskhelishvili’s potential function of the contact. In the partial slip condition, the locations of the stick and slip zones were given explicitly in terms of the applied external loads and coefficient of friction. The results have been compared with finite elements modelling results.

Determination of potential function for uncoupled-plane contact problems

In this paper, the elastic contact problem of an asymmetrical shallow wedge with a half-plane is considered. The potential function of the contact problem has been obtained through a simple approach. This approach simplifies the routine method of determination of potential functions in elastic contact problems. Then this approach was utilized to solve the aforementioned geometry under frictionless and frictional condition. Utilization of the new relation not only simplifies the procedure of solving contact problems but also is very helpful for fretting fatigue studies.

Geochemistry of adakites from Neoarchaean active continental margin of Shimoga schist belt, Western Dharwar Craton, India: Implications for the genesis of TTG

Adakites are identified for the first time from a Neoarchaean active continental margin (ACM) preserved in the eastern part of the Shimoga schist belt, near Ranibennur, Western Dharwar Craton, India. These adakites consists mainly of quartz, plagioclase and minor amphiboles and are interlayered with the turbidites. They exhibit typical adakitic low Y (8.35–14.70 ppm) and Yb (0.85–1.47 ppm), may be classified as high SiO 2 and low Mg#, Ni and Cr type adakites. Other constituents such as Na 2O, K 2O, Nb, Zr, LREE and HREE and their ratios such as Na 2O/K 2O, Zr/Sm, Nb/La, (La/Yb) n , (Gd/Yb) n and Th/U also closely resemble with the high silica adakites (HSA) of Martin et al. [Martin, H., Smithies, R.H., Rapp, R., Moyen, J.-F., Champion, D., 2005. An overview of adakite, tonalite–trondhjemite–granodiorite (TTG), and sanukitoid: relationships and some implications for crustal evolution. Lithos 79, 1–24]. Sr/Y values are moderate, generally lower than the high Sr–low silica Cenozoic adakites, but within the range of Archaean adakites. The negative Nb, Ta, and Ti anomalies characteristic of Cenozoic adakites are found in Ranibennur adakites also. Zr/Zr* and Hf/Hf* ratios are also similar to HSA. These adakites further depict compositional similarities with Meso and Neoarchaean tonalite–trondhjemite–granodiorites (TTGs). Such types of adakites have been experimentally generated by the partial melting of hydrous basalts, that are similar to adakitic glass veins (low MgO, CaO, Cr and Ni) found in peridotite xenoliths of Kamchatka arc [Xiong, X.L., Xia, B., Xu, J.F., Niu, H.C., Xiao, W.S., 2006. Na depletion in modern adakites via melt/rock reaction within the sub-arc mantle. Chem. Geol. 229, 273–292]. Since Archaean had higher geothermal regime, subduction of the basaltic slab was most probably shallow and significant mantle wedge was not available to react with adakitic melt. Hence Archaean adakites in general, and particularly from Ranibennur are relatively depleted in the peridotiitic mantle wedge components. Their identification from an Archaean ACM and their compositional similarities with the Paleo-Meso Archaean TTGs suggest the possibility of identical origin, i.e. the melting of a shallow hydrous basaltic slab. This mechanism during Archaean was widespread and rapid, resulted in faster continental crustal growth during the early history of the Earth. Identification of Archaean adakites in association with island arc turbidites from a greenstone belt sequence supports the rapid subduction mechanism for the crustal growth that coincides with 2.7 Ga peak (episode) of almost all geological processes.

Late Quaternary (marine isotope stages 6-1) seismic sequence stratigraphic evolution of the Otago continental shelf, New Zealand

A proposed chronostratigraphic model for the Late Quaternary evolution of the Otago continental shelf, New Zealand, includes fluvially incised sequence boundaries eroded during marine isotope stages 2, 4 and 6, bounding three sequences subdivided into lowstand, transgressive and highstand/regressive systems tracts. Datable material is limited to the uppermost 1 m of the sequence, and consequently the model is based on correlation of new high-resolution seismic reflection data (Geopulse™) to a compilation of independent global sea-level curves. A second chronostratigraphic model that lacks a stage 4 sequence boundary and distinct stage 3 highstand/forced regressive deposit is discounted because its subsidence-corrected paleoshoreline depths do not match lowstands in the eustatic curves or temporally constrained sequences at other far-field locations. In the preferred chronostratigraphic model, sea-level lowstands during stages 2, 4 and 6 reached maximum depths of 126–131 m, 101–111 m and 116–135 m, respectively, producing sequence boundaries, landward-pinching deltaic wedges on the outer Otago shelf, and submarine canyon incision. Lowstand paleoshoreline depths have been corrected for subsidence from thermal cooling, sediment compaction and loading, but may be erroneously deep owing to erosion of paleoshoreline indicators. Clastic, shallow marine wedges and back-barrier valley-fill deposits accumulated during the stage 6–5, 4–3 and 2–1 marine transgressions. Contrary to the traditional sequence stratigraphic model, deltaic and strandline units deposited during highstand through falling sea level (stages 5–4, 3–2, 1) volumetrically dominate Otago Late Quaternary sequences. Discrete units and minor marine erosion surfaces within the transgressive and regressive systems tract deposits are interpreted as strong evidence for seventh- (∼ 20 ka) or higher-order sea-level fluctuations influencing sedimentation on the Otago shelf.

Sedimentary response to a tectonically induced sea‐level fall in a shallow back‐arc basin: the Mulichinco Formation (Lower Cretaceous), Neuquén Basin, Argentina

AbstractThis study examines the sedimentary response to a tectonically driven relative sea‐level fall that occurred in the Neuquén Basin, west‐central Argentina, during the late Early Valanginian (Early Cretaceous). At this time the basin lay behind the emergent Andean magmatic arc to the west. Following the relative sea‐level fall, sedimentation was limited to the central part of the Neuquén Basin, with the deposition of a predominantly clastic, continental to shallow marine wedge on top of basinal black shales. This lowstand wedge is called the Mulichinco Formation and consists of a third‐order sequence that lasted about 2 Myr and contains high frequency lowstand, transgressive, and highstand deposits. Significant variations in facies, depositional architecture, and internal organization of the sequence occur along depositional strike. These variations are attributed mainly to tectonic and topographic controls upon sediment flux, basin gradient, fault tilting, and shifting of the depocentre through time. These controls were ultimately related to asymmetrically distributed tectonic activity that was greater towards the magmatic arc in the west. The superposition of fluvial deposits directly upon offshore facies provides unequivocal evidence for a sequence boundary at the base of the Mulichinco Formation. However, the Mulichinco sequence boundary is marked by shallow, low erosional relief and widespread fluvial deposition. The surface lacks prominent valleys traditionally associated with sequence boundaries. This non‐erosive sequence boundary geometry is attributed to the ramp‐type geometry of the basin and/or rapid uplift that limited stratigraphic adjustment to base‐level fall. Significant along‐strike facies changes and a low‐relief sequence boundary are attributes that may be common in tectonically active, semi‐enclosed basins (e.g. shallow back‐arc basins, foreland basins).

The tilted shallow wedge problem

The problem of indentation of a half-plane by a titled, shallow wedge, under frictionless conditions, is studied, using half-plane theory. The contact law itself, together with the pressure distribution and internal state of stress are found. Particular attention is then given to the nature of the pressure and state of stress at the apex, and an asymptotic form appropriate to all angular features within contacts, and therefore of widespread application, is introduced.

Variability in flow and temperatures within mantle subduction zones

A series of laboratory experiments is used to model three‐dimensional aspects of flow in subduction zones, and the consequent temperature variations in the slab and overlying mantle wedge. The effects of longitudinal, rollback and slab‐steepening components of motions are considered, along with different thicknesses of the over‐riding lithosphere. The results show that the style of plate sinking influences the evolution of subduction zones, both in terms of the speed, orientation and temperature of flow in the overlying wedge and in terms of the temperatures at the surface of the descending slab. In the simplest case of longitudinal sinking, without rollback motion, velocities in the mantle wedge are 30–40% of the downdip plate speed. Return flow paths in the shallow mantle wedge are nearly horizontal for slow slab speeds and steepen with higher slab speeds, and there is no mass flux around the edges of a slab segment (of finite width). Rollback subduction leads to flow both around and beneath the sinking slab, with larger velocities in the wedge (up to 150% of the slab speed) and flow focused toward the center of the plate segment. Rollback subduction, in which either the trench migrates or the plate steepens with time, induces shallow and steep wedge return flow trajectories, respectively. The thermal evolution of the plate is strongly influenced by sinking style and rate: highest temperatures are along the edges of the slab for longitudinal sinking, but along the centerline of the slab segment for rollback motion. Slab surface temperatures, when scaled to the mantle, are higher than those given by previous two‐dimensional numerical models, and are consistent with recent observational and experimental data on melt compositions.

Three-dimensional wedge filling in ordered and disordered systems

We investigate interfacial structural and fluctuation effects occurring at continuous fillingtransitions in 3D wedge geometries. We show that fluctuation-induced wedgecovariance relations that have been reported recently for 2D filling and wetting havemean-field or classical analogues that apply to higher-dimensional systems. Classicalwedge covariance emerges from analysis of filling in shallow wedges based on asimple interfacial Hamiltonian model and is supported by detailed numericalinvestigations of filling within a more microscopic Landau-like density functionaltheory. Evidence is presented that classical wedge covariance is also obeyed forfilling in more acute wedges in the asymptotic critical regime. For sufficientlyshort-ranged forces mean-field predictions for the filling critical exponents andcovariance are destroyed by pseudo-one-dimensional interfacial fluctuations. Weargue that in this filling fluctuation regime the critical exponents describing thedivergence of length scales are related to values of the interfacial wandering exponentζ(d) defined for planar interfaces in (bulk) two-dimensional(d = 2) andthree-dimensional (d = 3) systems. For the interfacial height , with θ the contactangle and α the wedgetilt angle, we find βw = ζ(2)/2(1−ζ(3)). For pure systems (thermal disorder) we recover the known resultβw = 1/4 predicted by interfacial Hamiltonian studies whilst for random-bond disorder we predictthe universal critical exponent even in the presence of dispersion forces. We revisit the transfer matrix theory ofthree-dimensional filling based on an effective interfacial Hamiltonian model and discussthe interplay between breather, tilt and torsional interfacial fluctuations. We show that thecoupling of the modes allows the problem to be mapped onto a quantum mechanicalproblem as conjectured by previous authors. The form of the interfacial height probabilitydistribution function predicted by the transfer matrix approach is shown to be consistentwith scaling and thermodynamic requirements for distances close to and far from the wedgebottom respectively.

Thermal‐contraction‐crack networks as evidence for late‐Pleistocene permafrost in Inner Mongolia, China

AbstractNumerous wedges on the Ordos Plateau show typical characteristics of periglacial sand wedges that enable them to be distinguished from desiccation cracks in clayey illuviation soil horizons. The sand wedges are organized in two generations of polygonal networks. The older generation is a large‐scale network with a diameter of 8 to 9 m and wedge depths up to more than 2 m. The younger generation has a mean diameter of 3 to 4 m and is formed within the large networks. It consists of shallow (0.6 to 1 m deep) but relatively wide wedges. In contrast to the typical sand wedges that form within continuous permafrost, the shallow wedges formed probably as ‘ground wedges’ by seasonal freezing. Ice wedges and cryoturbations developed only rarely, and exclusively in the most humid areas. Thermal‐contraction cracking occurred mainly between 26 and 20 ka BP, indicating mean annual temperatures at least 13°C lower than present. Before and after that period mean annual temperatures were at least 7 to 8.5° lower than today. The presence of these periglacial phenomena show that the southern limit of continuous permafrost in Inner Mongolia occurred south of 38°N during the Last Glacial Maximum. Copyright © 2004 John Wiley & Sons, Ltd.