Showing papers on "Slab published in 2003"

P wave tomography of the mantle under the Alpine-Mediterranean area

Abstract: [1] We study the upper mantle P wave velocity structure below the Euro-Mediterranean area, down to 1000 km depth, by seismic travel time tomography. We invert summary residuals constructed with both regional and teleseismic first arrival data reported by the International Seismological Centre (ISC) (1964–1995), introducing some alternative strategies in the travel time tomographic approach and a new scheme to correct teleseismic data for global mantle structure. Our high-resolution model PM0.5 is parameterized with three-dimensional (3-D) linear splines on a grid of nodes with 0.5° spacing in both horizontal directions and 50 km vertical spacing. We obtain about 26% root-mean-square (RMS) reduction of residuals by inversion in addition to roughly 31% reduction after summary rays formation and selection. Sensitivity analyses are performed through several test inversions to explore the resolution characteristics of the model at different spatial scales. The distribution of large-scale fast anomalies suggests that two different stages of a convection process presently coexist in very close regions. The mantle dynamics of western central Europe is dominated by blockage of subducted slabs at the 660 km discontinuity and ponding of seismically fast material in the transition zone. Contrarily, in the eastern Mediterranean, fast velocity material sinks into the lower mantle, suggesting that the flow of the cold downwelling here is not blocked by the 660 km discontinuity. On a smaller scale, the existence of tears in the subducted slab (lithospheric detachment) all along both margins of the Adriatic plate, as proposed by some authors, is not supported by our tomographic images.

Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency

Abstract: Here, we analyze the transverse-magnetic (TM) wave interaction with a pair of slabs, one being an epsilon-negative (ENG) layer in which the real part of permittivity is assumed to be negative while its permeability has positive real part, and the other being a mu-negative (MNG) layer that has the real part of its permeability negative but its permittivity has positive real part. Although the wave interaction with each slab by itself has predictable features, we show that the juxtaposition and pairing of such ENG and MNG slabs may, under certain conditions, lead to some unusual features, such as resonance, complete tunneling, zero reflection and transparency. The field distributions inside and outside such paired slabs are analyzed, and the Poynting vector distributions in such structures are studied. Using equivalent transmission-line models, we obtain the conditions for the resonance, complete tunneling and transparency, and we justify and explain the field behavior in these resonant paired structures. Salient features of the tunneling conditions, such as the roles of material parameters, slab thicknesses, dissipation, and angle of incidence are discussed. The analogy and correspondence between the ENG-MNG pair and the pair of a slab of conventional material juxtaposed with a "double-negative" medium is also discussed. Finally, a conceptual idea for a potential application of such a "matched" lossless ENG-MNG pair in "ideal" image displacement and image reconstruction is proposed.

Limitations on subdiffraction imaging with a negative refractive index slab

Abstract: A planar slab of material, for which both the permittivity and permeability have the values of −1, can bring not only the propagating fields associated with a source to a focus, but can also refocus the nonpropagating near fields, thereby achieving resolution beyond the diffraction limit. We study the sensitivity of this subwavelength focus to the slab material properties and periodicity, and note the connection to slab surface plasmon modes. We conclude that significant subwavelength resolution is achievable with a single negative index slab, but only over a restrictive range of parameters.

Heat-transfer and solidification model of continuous slab casting: CON1D

Abstract: A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.

How Laramide-Age Hydration of North American Lithosphere by the Farallon Slab Controlled Subsequent Activity in the Western United States

Abstract: Starting with the Laramide orogeny and continuing through the Cenozoic, the U.S. Cordilleran orogen is unusual for its width, nature of uplift, and style of tectonic and magmatic activity. We present teleseismic tomography evidence for a thickness of modified North America lithosphere ≥200 km beneath Colorado and >100 km beneath New Mexico. Existing explanations for uplift or magmatism cannot accommodate lithosphere this thick. Imaged mantle structure is low in seismic velocity roughly beneath the Rocky Mountains of Colorado and New Mexico, and high in velocity to the east and west, beneath the tectonically intact Great Plains and Colorado Plateau. Structure internal to the low-velocity volume has a NE grain suggestive of influence by inherited Precambrian sutures. We conclude that the high-velocity upper mantle is Precambrian lithosphere, and the lowvelocity volume is partially molten Precambrian North America mantle. We suggest, as others have, that the Farallon slab was in contact with the lithosphere beneath most of the western U.S. during the Laramide orogeny. We further suggest that slab de-watering under the increasingly cool conditions of slab contact with North America hydrated the base of the continental lithosphere, causing a steady regional uplift of the western U.S. during the Laramide orogeny. Imaged low-velocity upper mantle is attributed to hydration-induced lithospheric melting beneath much of the southern Rocky Mountains. Laramide-age magmatic ascent heated and weakened the lithosphere, which in turn allowed horizontal shortening to occur in the mantle beneath the region of Laramide thrusting in the southern Rocky Mountains. Subsequent Farallon slab removal resulted in additional uplift through unloading. It also triggered vigorous magmatism, especially where asthenosphere made contact with the hydrated and relatively thin and fertile lithosphere of what now is the Basin and Range. This mantle now is dry, depleted of basaltic components, hot, buoyant, and weak.

Subduction and the depth of convection in the Mediterranean mantle

Abstract: [1] We tie together geological data, paleotectonic reconstruction, plate motion, and tomographic analysis to unravel the history of subduction and back arc extension of the eastern and central Mediterranean. In these two regions, extensional processes started contemporaneously, around 30 Myr ago, but with marked differences. In the eastern region, the Aegean basin opened slowly (∼1 cm/yr) behind a shallow dipping slab (40–45°). The corresponding high-velocity anomaly extends inside the upper mantle and can be also followed in the midmantle down to a depth of at least 1500 km. Its descent into the midmantle initiated most probably during the Late Cretaceous, and the trench moved northeastward, following the path of the Eurasian plate and under the persistent push of the African plate. Conversely, in the central Mediterranean region, subduction initiated later, and the motion of the subducting slab is confined to the upper mantle, causing punctuated and rapid episodes of back arc extension (Provencal and Tyrrhenian basins) behind a slab that dips steeply (75°). We explore the causes that control how the slab subducted and interacted with the lower, more viscous part of the mantle.

Dynamics of retreating slabs : 2. Insights from three-dimensional laboratory experiments

Abstract: [1] A laboratory analogue of a three-layer linear viscous slab-upper mantle-lower mantle system is established in a silicone putty, honey and crystallized honey tank experiment. The same setup as in the numerical investigation (part 1) is used. We focus on the interaction of the slab with the induced passive mantle flow by widely varying the mantle volume flux boundary conditions. In our numerical experiments the lateral volume flux was set to zero. In interpreting the results relative to the real Earth, the base of the box is taken as the bottom of the mantle convection system, while the lateral boundaries may be associated with the presence of other nearby slabs. Dynamic force equilibrium, assessed on the basis of an analytical review of forces, is described for four different phases: (1) the subduction initiation instability, (2) the accelerating dynamic free fall phase of the slab, (3) the dynamic interaction with the 660-km discontinuity, and (4) a final phase of steady state trench retreat. Phase 3 is an important feature not observed in the numerical experiments. This highly dynamic phase of interrupted trench retreat can therefore be attributed to boundary conditions on mantle volume flux. On the basis of integration constants of force equilibrium in phases 2 and 4 we identify two different classes of volume flux: one in which the lateral boundary can be considered open and the other class where it is “closed.” Closed boundary condition cases are obtained if any of the lateral box boundaries are 600 km away from the slab. Assuming a one-to-one relation between trench retreat and back arc spreading, enigmatic observations of episodic opening of back arc basins can be explained by our experimental observations.

Double seismic zone and dehydration embrittlement of the subducting slab

Abstract: [1] Dehydration embrittlement of metamorphosed oceanic crust and mantle in the subducting slab may be responsible for the occurrence of intermediate-depth earthquakes. We explore the possibility that this hypothesis can explain the morphology of the double seismic zones observed in northeast Japan, southwest Japan, northeast Taiwan, northern Chile, Cape Mendocino, and eastern Aleutians. We calculate transient temperature structures of slabs based on geologically estimated subduction histories of these regions. We then determine dehydration loci of metamorphosed oceanic crust and serpentinized mantle using experimentally derived phase diagrams. The depth range of the dehydration loci of metamorphosed oceanic crust and serpentine is dependent on slab age. The dehydration loci of serpentine produce a double-layered structure. Because the upper dehydration loci of serpentine are mostly located in the wedge mantle above the slab, we regard the upper plane seismicity representing dehydration embrittlement in the oceanic crust, and we fix the slab geometry so that the upper plane seismicity is just below the upper surface of the slab. We find that the lower plane seismicity is located at the lower dehydration loci of serpentine, which indicates that the morphology of the double seismic zones is consistent with the dehydration embrittlement.

Negative Lateral Shift of a Light Beam Transmitted through a Dielectric Slab and Interaction of Boundary Effects

Abstract: It is found that when a light beam travels through a slab of optically denser dielectric medium in air, the lateral shift of the transmitted beam can be negative. This is a novel phenomenon that is reversed in comparison with the geometrical optic prediction according to Snell's law of refraction. A Gaussian-shaped beam is analyzed in the paraxial approximation, and a comparison with numerical simulations is made. Finally, an explanation for the negativity of the lateral shift is suggested, in terms of the interaction of boundary effects of the slab's two interfaces with air.

Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability

Abstract: The guidance conditions of modes with both real and imaginary transverse wave numbers inside a dielectric slab with negative permittivity and permeability are solved. We show that for real transverse wave numbers, cutoffs exist for all modes, unlike in conventional media where the first even mode is always propagating. In addition, we also show that guided modes exist for imaginary transverse wave numbers, with the power concentrated at the interfaces instead of having maxima inside the slab. A graphical method of determining the imaginary transverse wave numbers of the guided modes is introduced which clearly identifies the different conditions of propagation depending on the properties of the slab. In particular, propagation of guided waves inside less dense negative media is shown to be possible.

Dubious case for slab melting in the Northern volcanic zone of the Andes

Abstract: It was first suggested by R.W. Kay that adakites may represent melts of subducted slab: since then, the term adakite has become synonymous with slab melts based on their unusual geochemical signature. This contribution, using the Northern volcanic zone of the Andes as an example, aims (1) to expose the weakness in simply associating a geochemical signature with a genetic mechanism and (2) to underline the importance of using several integrated lines of evidence in assessing the viability of slab melting. We conclude that although slab melting probably occurs in some arcs, regional geochemical trends in the Northern volcanic zone and their relationship to the subduction-zone architecture are not indicative of slab melting and can be accounted for by normal arc magmatic processes acting on wedge-derived basaltic magmas.

Evaluation of lensing in photonic crystal slabs exhibiting negative refraction

Abstract: We systematically investigate lensing of electromagnetic waves by a negative refractive-index material slab constructed from a two-dimensional photonic crystal with properly designed equifrequency-surface configuration [Luo et al., Phys. Rev. B 65, 201104 (2002)]. We find that a point source placed in the vicinity of the slab can form a good-quality image in the opposite side of the slab. However, the image is strongly confined in the near-field region of the slab and gradually degrades and disappears when moved beyond the near-field domain. In addition, the image-slab distance has little dependence on the source-slab distance and the slab thickness. On the other hand, the image can also form by a slab with a positive effective refractive index. We have analyzed the equifrequency-surface contour configuration of this photonic crystal and found that the overall imaging properties of this photonic crystal slab are dominantly governed by the self-collimation effect and complex near-field wave scattering effect, rather than by the all-angle negative-refraction effect.

Multiscale dynamics of the Tonga—Kermadec subduction zone

Abstract: Our understanding of mantle convection and the motion of plates depends intimately on our understanding of the viscosity structure of the mantle. While geoid and gravity observations have provided fundamental constraints on the radial viscosity structure of the mantle, the influence of short-wavelength variations in viscosity is still poorly understood. We present 2-D and 3-D finite-element models of mantle flow, including strong lateral viscosity variations and local sources of buoyancy, owing to both thermal and compositional effects. We first use generic 2-D models of a subduction zone to investigate how different observations depend on various aspects of the viscosity structure, in particular, the slab and lower-mantle viscosity and the presence of a low-viscosity region in the mantle wedge above the slab. We find that: (1) the strain rate provides a strong constraint on the absolute viscosity of the slab (10^(23) Pa s); (2) stress orientation within the slab is sensitive to the relative viscosity of the slab, lower mantle and the wedge; and (3) the stress state and topography of the overriding plate depend on the wedge viscosity and local sources of buoyancy. In particular, the state of stress in the overriding plate changes from compression to extension with the addition of a low-viscosity wedge. We then use observations of strain rate, stress orientation, dynamic topography and the geoid for the Tonga–Kermadec subduction zone as simultaneous constraints on the viscosity and buoyancy in a 3-D regional dynamic model. Together these observations are used to develop a self-consistent model of the viscosity and buoyancy by taking advantage of the sensitivity of each observation to different aspects of the dynamics, over a broad range of length-scales. The presence of a low-viscosity wedge makes it possible to match observations of shallow dynamic topography and horizontal extension within the backarc, and down-dip compression in the shallow portion of the slab. These results suggest that a low-viscosity wedge plays an important role in controlling the presence of backarc spreading. However, for a model with a low-viscosity and low-density region that provides a good fit to the observed topography, we find that a reduction of the slab density by a factor of 1.3 relative to the reference density model, is required to match the observed geoid. These results suggest that compensation of the slab by dynamic topography may be a much smaller effect at short to intermediate wavelengths than predicted by long-wavelength modelling of the geoid.

Far-field display

Abstract: A flat-panel projection display comprises a transparent slab and integral area grating, a transparent rod with rectangular cross-section and integral linear grating, arranged along the edge of the slab, and a small video projector. The projector is arranged to direct a virtual image into the end of the rod, directly or via mirrors, the light travelling along the rod via total internal reflection. The linear grating diverts the light into the plane of the slab, and the area grating projects it out of the slab towards a viewer, so that the viewer sees an image at infinity.

Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes

Abstract: The effects of truncated cone air holes on propagation losses from line defect waveguides in two-dimensional (2D) photonic crystal (PC) slabs are investigated. It is shown that coupling between TE-like waveguide modes and TM-like slab modes due to out-of-plane structural asymmetries can result in large propagation losses. It is also shown that coupling, and therefore propagation loss, does not occur in a frequency range where wave vectors of TE-like waveguide modes do not match projections of those of TM-like slab modes. The results are thought to be applicable to other structures exhibiting out-of-plane asymmetries, such as 2D PC slabs attached to silicon on insulator substrates.

Kinematic soil-structure interaction from strong motion recordings

Abstract: Earthquake strong motion recordings from 29 sites with instrumented structures and free-field accelerographs are used to evaluate variations between foundation-level and free-field ground motions. The focus of the paper is on buildings with surface and shallowly embedded foundations. The foundation/free-field ground motion variations are quantified in terms of frequency-dependent transmissibility function amplitude uHu. Procedures are developed to fit to uHu analytical models for base slab averaging for the assumed conditions of a rigid base slab and a vertically propagating, incoherent incident wave field characterized by ground motion incoherence parameter k. The limiting assumptions of the model are not strictly satisfied for actual structures, and the results of the identification are apparent k values ~denoted k a) that reflect not only incoherence effects, but also possible foundation flexibility and wave inclination effects. Nonetheless, a good correlation is found between k a values and soil shear wave velocity for sites with stiff foundation systems. Based on these results, recommendations are made for modifying free-field ground motions to estimate base slab motions for use in response analyses of buildings.

Geochemical confirmation of the Kula-Farallon slab window beneath the Pacific Northwest in Eocene time

Abstract: Plate tectonic models indicate subduction of the Kula-Farallon spreading ridge, and thus imply formation of the Kula-Farallon slab window, beneath western North America from Late Cretaceous to middle Eocene time. Seafloor magnetic anomalies, however, pro- vide few constraints on the configuration of the subducted ridge and the location of the slab window. We use geochemical data from Eocene igneous rocks to provide an estimate of the slab window's position at 50 Ma. Contouring of the trace element ratios K 2O/SiO2, Rb/Zr, and Ta/Ce for lavas of the Eocene Challis-Kamloops volcanic belt demonstrates a southward trend toward enriched geochemical character. This trend is consistent with a Pacific Northwest position for the slab window; this is supported by the presence of adak- ites (slab melts) near the Canada-United States border, and by ca. 51 Ma forearc intru- sions and volcanic rocks on Vancouver Island that are regarded as products of ridge subduction. A new reconstruction of the slab window's geometry over time indicates that its chemically defined position is kinematically viable.

A Transient Simulation and Dynamic Spray Cooling Control Model for Continuous Steel Casting

Abstract: A two-dimensional heat-transfer model for transient simulation and control of a continuous steel slab caster is presented. Slab temperature and solidification are computed by the model as a function of time-varying casting speed, secondary spray cooling water flow rates and temperature, slab thickness, steel chemistry, and pouring and ambient temperatures. Typically, the solidification path, temperature-solid fraction relationship, is prescribed. However, if these data are not available, a microsegregation solidification model that approximates the effects of steel chemistry and cooling rate is incorporated in the caster model. Measured slab surface temperatures recorded from an operating caster are compared with predictions from the transient model. These demonstrate that the model typically can predict the temperature response at the slab surface within 30 °C. Results of several simulations are given to demonstrate the effects of changing casting conditions on the slab thermal profile, end of liquid pool, and solidification end point. A control methodology and algorithm suitable for online control of a continuous casting machine is described, and the ability to control the surface temperature profile by dynamically adjusting secondary spray cooling flow rates is demonstrated by simulation. Results from a preliminary version of the model that is capable of running in real time are presented and are compared with the slower, but more realistic, version of the model.

Trace element partitioning between mantle wedge peridotite and hydrous MgO-rich melt

Abstract: Magmas erupted at convergent margins consist of components from both mantle wedge and subducted slab. In an effort to quantify the relative contributions of these sources, we have determined 19 trace element partition coefficients ( D values) for orthopyroxene and clinopyroxene, in equilibrium with spinel and hydrous high-MgO melt under conditions appropriate to melting in the mantle wedge, i.e., 1.3 GPa, 1245 °C, and f O 2 of NNO + 1. All trace elements are more incompatible in clinopyroxene during hydrous melting than during anhydrous melting of fertile and depleted peridotite. Orthopyroxene D values are relatively insensitive to pressure, temperature, and phase composition. The new D values are used to calculate the trace-element composition of the mantle wedge, which produced primitive South Sandwich Islands and St. Vincent (Lesser Antilles) arc basalts. Both sources correspond to previously depleted mantle that has been enriched in LILEs and LREEs by slab-derived fluids. In the case of the South Sandwich Islands, the calculated source is in very close agreement with dredged fore-arc lherzolites. Our partitioning data confirm that hydrous melting of wedge peridotite itself cannot produce the characteristic enrichments of LILEs over REEs and HFSEs. Our estimates of the slab component in South Sandwich Islands and St. Vincent are consistent with estimates from other arcs, derived by alternative methods.

On Planewave Remittances and Goos–Hänchen Shifts of Planar Slabs with Negative Real Permittivity and Permeability

Abstract: Two results about the planewave response of an isotropic, dielectric-magnetic, homogeneous, planar slab are deduced when the real parts of both the permittivity and the permeability are altered from positive to negative. First, the reflection and the transmission coefficients suffer phase reversals without change in their respective magnitudes. Second, the Goos–Hanchen shifts experienced by beams on total reflection reverse their directions.

Evidence for slab melt/mantle reaction: Petrogenesis of Early Cretaceous and Eocene high-Mg andesites from Kitakami Mountains, Japan

Abstract: Abstract Lower Cretaceous and Eocene igneous rocks in the Kitakami Mountains, northeast Japan, attract special interest because of the occurrence of adakitic rocks. In addition, high-Mg andesites (HMAs) were discovered from the Lower Cretaceous dike rocks and from the Eocene Jodogahama rhyolitic rocks in the Kitakami Mountains. Lower Cretaceous HMAs occur as several small dikes (less than 5 m thick, rarely up to 70 m) from Ubaishi, Gongen, Shizugawa, Numazu, and Oshika, southern Kitakami Mountains, intrude slightly older than the Lower Cretaceous plutonic rocks. Among these HMAs, the HMA dike from Gongen, characteristically contains ultramafic inclusions. Eocene HMA, a small intrusive mass (observed maximum diameter is 300 m) consisting of aphyric andesite and olivine andesite, occurs only in Matsuhashi, Iwaizumi, northern Kitakami Mountains. The Eocene HMA is associated with hornblende rhyolite belonging to the Eocene Jodogahama rhyolitic rocks. The Lower Cretaceous and Eocene HMAs show similar petrochemical characteristics to those of Cenozoic adakite (high LREE/HREE ratios and Sr contents, low Y and HREE contents) except higher Cr, Ni, and Mg contents. In addition, the Eocene HMAs and the ultramafic inclusions in the Lower Cretaceous HMAs show less radiogenic Nd–Sr isotopic characteristics than those from the adakitic granites in Kitakami, and similar to those of the Cenozoic adakite. On the other hand, the Miocene Setouchi HMAs in southwestern Japan are characterized by lower Sr/Y ratios, less fractionated REE patterns, weak negative Eu anomalies, and more radiogenic Nd–Sr isotopic characteristics than those of Cenozoic adakite. The ultramafic inclusions from Gongen have clinopyroxene characterized by high Sr concentrations and high LREE/HREE ratios. These clinopyroxenes are considered to be crystallized during interaction of slab derived adakitic melt with overlying mantle peridotite. The olivine phenocrysts of the Eocene HMA show extremely high NiO contents (maximum 0.58 wt.%), which may be an evidence for slab melt/mantle reaction. Concludingly, the petrochemical features of HMA magmas in Kitakami can be explained by reaction of slab derived adakitic melt with overlying mantle peridotite to equilibrate with mantle olivine. The difference between the chemical compositions of the Kitakami and Setouchi HMAs can be explained by the difference in compositions of initial slab melt resulted from the difference in depth of slab melting.

Modeling Membrane Action of Concrete Slabs in Composite Buildings in Fire. I: Theoretical Development

Abstract: A nonlinear layered finite element procedure for predicting the structural response of reinforced concrete slabs subjected to fire is described. The proposed procedure is based on Mindlin/Reissner (thick plate) theory, and both geometric and material nonlinearities are taken into account. The complications of structural behavior in fire conditions, such as thermal expansion, cracking or crushing, and change of material properties with temperature are modeled. In this study a total Lagrangian approach is adopted throughout, in which displacements are referred to the original configuration and small strains are assumed. A numerical example, in which a rectangular reinforced concrete slab is modeled at elevated temperatures, is presented. The influences of different thermal expansion characteristics, tensile membrane action, and differential temperature distributions across the thickness of the slab are investigated. It is evident that the nonlinear layered procedure proposed in this paper can properly model...

Oblique frozen modes in periodic layered media.

Abstract: We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode with the amplitude diverging linearly with the distance from the slab boundary. Remarkably, the slab reflectivity in such a situation can be very low, which means an almost 100% conversion of the incident light into the axially frozen mode with the electromagnetic energy density exceeding that of the incident wave by several orders of magnitude. The effect can be realized at any desirable frequency, including optical and UV frequency range. The only essential physical requirement is the presence of dielectric layers with proper oblique orientation of the anisotropy axes. Some practical aspects of this phenomenon are considered.

Size effect law and fracture mechanics of the triggering of dry snow slab avalanches

Abstract: (1) A size effect law for fracture triggering in dry snow slabs of high enough length-to- thickness ratio is formulated, based on simplified one-dimensional analysis by equivalent linear elastic fracture mechanics. Viscoelastic effects during fracture are neglected. The derived law, which is analogous to Bazant's energetic size effect law developed for concrete and later for sea ice, fiber composites, rocks, and ceramics, is shown to agree with two-dimensional finite element analysis of mode II cohesive crack model with a finite residual shear stress. Fitting the proposed size effect law to fracture data for various slab thicknesses permits identifying the material fracture parameters. The value of preexisting shear stress in a thin weak zone of finite length is shown to have significant effect. There exists a certain critical snow depth, depending on the preexisting stress value, below which the size effect disappears. Practical applications require considering that the material properties (particularly the mode II fracture toughness or fracture energy) at the snow slab base are not constant but depend strongly on the slab thickness. This means that one must distinguish the material size effect from the structural size effect, and the combined size effect law must be obtained by introducing into the structural size effect law dependence of its parameters on snow thickness. The thickness dependence of these parameters can be obtained by matching the combined law to avalanche observations. Matching Perla's field data on 116 avalanches suggests that the mode II fracture toughness is approximately proportional to 1.8 power of snow thickness. INDEX TERMS: 1827 Hydrology: Glaciology (1863); 1863 Hydrology: Snow and ice (1827); 3210 Mathematical Geophysics: Modeling; 3220 Mathematical Geophysics: Nonlinear dynamics; 8020 Structural Geology: Mechanics; KEYWORDS: snow, avalanches, scaling, size effect, fracture mechanics

Dynamics of retreating slabs: 1. Insights from two-dimensional numerical experiments

Abstract: from the effects of mantle flux (part 2). Therefore, in this paper, we apply forces to the slab using simple analytical functions related to buoyancy and viscous forces in order to isolate the role of rheology on slab dynamics. We analyze parameters for simplified elastic, viscous, and nonlinear viscoelastoplastic single-layer models of slabs and compare them with a stratified thermomechanical viscoelastoplastic slab embedded in a thermal solution. The near-surface behavior of slabs is summarized by assessing the amplitude and wavelength of forebulge uplift for each rheology. In the complete thermomechanical solutions, vastly contrasting styles of slab dynamics and force balance are observed at top and bottom bends. However, we find that slab subduction can be modeled using simplified rheologies characterized by a narrow range of selected benchmark parameters. The best fit linear viscosity ranges between 5 � 10 22 Pa s and 5 � 10 23 Pa s. The closeness of the numerical solution to nature can be characterized by a Deborah number >0.5, indicating that elasticity is an important ingredient in subduction. INDEX TERMS: 8120 Tectonophysics: Dynamics of lithosphere and mantle—general; 8159 Tectonophysics: Rheology—crust and lithosphere; 8160 Tectonophysics: Rheology—general; KEYWORDS: subduction, numerical models, lithospheric rheology