Time Scale Of Deformation Research Articles

Parametric instability in long optical cavities and suppression by dynamic transverse mode frequency modulation

Three mode parametric instability has been predicted in Advanced gravitational wave detectors. Here we present the first observation of this phenomenon in a large scale suspended optical cavity designed to be comparable to those of advanced gravitational wave detectors. Our results show that previous modelling assumptions that transverse optical modes are stable in frequency except for frequency drifts on a thermal deformation time scale is unlikely to be valid for suspended mass optical cavities. We demonstrate that mirror figure errors cause a dependence of transverse mode offset frequency on spot position. Combined with low frequency residual motion of suspended mirrors, this leads to transverse mode frequency modulation which suppresses the effective parametric gain. We show that this gain suppression mechanism can be enhanced by laser spot dithering or fast thermal modulation. Using Advanced LIGO test mass data and thermal modelling we show that gain suppression factors of 10-20 could be achieved for individual modes, sufficient to greatly ameliorate the parametric instability problem.

Modeling of Non-Equilibrium Homogeneous Turbulence in Rapidly Compressed Flows

The response of homogeneous turbulence to rapid mean-flow compression in idealized internal combustion engines and rapid compression machines is examined using a hierarchy of closure models for the Reynolds stress anisotropy. This hierarchy is based on a Reynolds stress anisotropy transport equation that is modeled from the exact transport equation for the anisotropy. The hierarchy of models includes a recently-developed non-equilibrium model, which is shown to be in good agreement with more computationally-complex fully differential models. Using this hierarchical approach, the flow physics addressed by each closure is identified and closure accuracy is shown to depend on the degree to which non-equilibrium turbulent flow effects are captured. We examine the evolution of the turbulence kinetic energy, Reynolds stresses, and anisotropy as a function of the degree of non-equilibrium in the flow, which is parameterized by the ratio of characteristic turbulence and mean-flow deformation time scales. By comparing model results to results obtained from rapid distortion theory and higher level closures, prescriptions are provided for the applicability of different closure models based on the magnitude of the non-equilibrium parameter. The theoretical analysis is complemented by comparisons of simulation results with previously established direct numerical simulations for a one-dimensional compression. Finally, we connect these prescriptions with experimental measurements of turbulent and mean-flow time scales for internal combustion engines operating at realistic conditions.

The influence of cooling, crystallisation and re-melting on the interpretation of geodetic signals in volcanic systems

Deformation of volcanic edifices is typically attributed to the movement of magma within the volcanic plumbing system, but a wide range of magmatic processes are capable of producing significant volume variations and may also produce deformation. In order to understand the evolution of magmatic systems prior to eruption and correctly interpret monitoring signals, it is necessary to quantify the patterns and timescales of surface deformation that processes such as crystallisation, degassing and expansion of the hydrothermal system can produce. We show how the combination of petrology and thermal modelling can be applied to geodetic observations to identify the processes occurring in a magmatic reservoir during volcanic unrest. Thermal modelling and petrology were used to determine the timescales and volumetric variations associated with cooling, crystallisation and gas exsolution. These calculations can be performed rapidly and highlight the most likely processes responsible for the variation of a set of monitoring parameters. We then consider the magnitude and timescales of deformation produced by other processes occurring within the vicinity of an active magma system. We apply these models to a time series of geodetic data spanning the period between the 1997 and 2008 eruptions of Okmok volcano, Aleutians, examining scenarios involving crystallisation, degassing and remelting of the crystallising shallow magmatic body and including a viscoelastic shell or hydrothermal system. The geodetic observations are consistent with the injection of a water-saturated basalt, followed by minor crystallisation and degassing. Other scenarios are not compatible either with the magnitude or rate of the deformation signals.

Critical Scales Govern the Mechanical Fragmentation Mechanisms of Biomolecular Assemblies

Fragmentation mechanisms of peptide assemblies under shock deformation are studied using molecular dynamics simulations and are found to depend strongly on the relative magnitude of the shock front radius to the fibril length and the ratio of the impact energy to the fibril cohesive energy. The competition between size scaling of curvature and impact energy leads to a mechanism change at a critical impact velocity, developing a stark contrast in the size scaling of fragmentation at low and high strain rates. We show that the fragmentation mechanisms can be classified on the basis of the length and time scales of deformation and relaxation to provide new insight into experimental observations.

Nanoparticle agglomeration in an evaporating levitated droplet for different acoustic amplitudes

Radiatively heated levitated functional droplets with nanosilica suspensions exhibit three distinct stages namely pure evaporation, agglomeration, and finally structure formation. The temporal history of the droplet surface temperature shows two inflection points. One inflection point corresponds to a local maximum and demarcates the end of transient heating of the droplet and domination of vaporization. The second inflection point is a local minimum and indicates slowing down of the evaporation rate due to surface accumulation of nanoparticles. Morphology and final precipitation structures of levitated droplets are due to competing mechanisms of particle agglomeration, evaporation, and shape deformation. In this work, we provide a detailed analysis for each process and propose two important timescales for evaporation and agglomeration that determine the final diameter of the structure formed. It is seen that both agglomeration and evaporation timescales are similar functions of acoustic amplitude (sound pressure level), droplet size, viscosity, and density. However, we show that while the agglomeration timescale decreases with initial particle concentration, the evaporation timescale shows the opposite trend. The final normalized diameter can be shown to be dependent solely on the ratio of agglomeration to evaporation timescales for all concentrations and acoustic amplitudes. The structures also exhibit various aspect ratios (bowls, rings, spheroids) which depend on the ratio of the deformation timescale (tdef) and the agglomeration timescale (tg). For tdef<tg, a sharp peak in aspect ratio is seen at low concentrations of nanosilica which separates high aspect ratio structures like rings from the low aspect ratio structures like bowls and spheroids.

Deformation experiments of bubble‐ and crystal‐bearing magmas: Rheological and microstructural analysis

Simple shear deformation experiments on three‐phase, hydrous, haplogranitic magmas, composed of quartz crystals (24–65 vol.%), CO2‐rich gas bubbles (9–12 vol.%) and melt in different proportions, were performed with a Paterson‐type rock deformation apparatus. Strain rates from 5 · 10−6 s−1 to 4 · 10−3 s−1 were applied at temperatures between 723 and 1023 K and at pressure of 200 MPa. The results show that the three‐phase suspension rheology is strongly strain rate dependent (non‐Newtonian behavior). Two non‐Newtonian regimes were observed: shear thinning (viscosity decreases with increasing strain rate) and shear thickening (viscosity increases with increasing strain rate). Shear thinning occurs in crystal‐rich magmas (55–65 vol.% crystals; 9–10 vol.% bubbles) as a result of crystal size reduction and shear zoning. Shear thickening prevails in dilute suspensions (24 vol.% crystals; 12 vol.% bubbles), where bubble coalescence and outgassing dominate. At intermediate crystallinity (44 vol.% crystals; 12 vol.% bubbles) both shear thickening and thinning occur. Based on the microstructural observations using synchrotron radiation X‐ray tomographic microscopy, bubbles can develop two different shapes: oblate at low temperature (<873 K) and prolate at high temperature (>873 K). These differences in shape are caused by different conditions of flow: unsteady flow, where the relaxation time of the bubbles is much longer than the timescale of deformation (oblate shapes); steady flow, where bubbles are in their equilibrium deformation state (prolate shapes). Three‐phase magmas are characterized by a rheological behavior that is substantially different with respect to suspensions containing only crystals or only gas bubbles.

Distinguishing and Correlating Multiple Phases of Metamorphism across Multiply Deformed Regions Using the Axes of Inclusion Trails in Porphyroblasts

Abstract:Successions of FIAs (foliation inflection/intersection axes preserved within porphyroblasts) provide a relative time scale for deformation and metamorphism. In‐situ dating of monazite grains preserved as inclusions within garnet and staurolite porphyroblasts within the foliations defining each FIA from such successions provides a rigorous approach to grouping ages that formed over extended periods of deformation and metamorphism. Matching age and FIA progressions confirms the suitability of this approach plus provides access to lengthy histories that cannot otherwise be determined. Tectonism in the Big Thompson region of the Colorado Rocky Mountains, USA began about a SW‐NE trending axis defined by FIA set 1 at around 1761 ± 13 Ma. Subsequent periods of tectonism occurred around 1712 ± 25 and 1672 ± 21 Ma about W‐E and NW‐SE trending FIAs 2 and 3, respectively. Tectonism in the Balcooma Metamorphic Group NW of Greenvale in NE Queensland, Australia began around 470 Ma with the growth of garnet porphyroblasts about a W‐E trending axis defined by FIA set 1. No monazite grains were preserved as inclusions in this mineral phase but they were in subsequently grown staurolite. Tectonism then occurred around 443.2±3.8, 424 ± 4 and 408.9 ± 8.9 Ma about NNW‐SSE, SSW‐NNE and W‐E trending FIAs 2, 3 and 4, respectively. This test of a FIA based approach to monazite dating in tectonic regimes in different parts of the world and with dramatically different ages suggests it can be used in all orogens containing porphyroblasts preserving inclusion trails.

Molecular Dynamics Study of Rotating Nanodroplets: Finite-size Effects and Nonequilibrium Deformation

Noneqiuilibrium dynamics of rotating droplets are studied by molecular dynamics simulations. Small deviations from the theoretical prediction are observed when the size of a droplet is small, and the deviations become smaller as the size of the droplet increases. The characteristic timescale of the deformation is observed, and we find (i) the deformation timescale is almost independent of the rotating velocity with for small frequency and (ii) the deformation timescale becomes shorter as temperature increases. A simple model is proposed to explain the deformation dynamics of droplets.

Kinetics and mechanism of antigorite dehydration: Implications for subduction zone seismicity

Properties of serpentine minerals are thought to influence the occurrence and location of intermediate‐depth seismicity in subduction zones, which is often characterized by two dipping planes separated by ∼30 km defining a double seismic zone. The seismicity of the lower plane is believed to be provoked by the dehydration of serpentine since the experimentally determined stability limit for antigorite matches hypocenter locations. This requires that the fluid produced by dehydration is released much faster than the typical time scale of ductile deformation mechanisms. Here we measured the kinetics of antigorite dehydration in situ at high pressure and high temperature by time‐resolved synchrotron X‐ray diffraction in a closed system. Antigorite dehydrates in two steps. During step 1 it partially breaks down into olivine and a hydrous phyllosilicate closely related to the 10 A phase. The modal abundance of the intermediate assemblage is described by 66 wt % antigorite, 19 wt % olivine, 12 wt % 10 A phase. During step 2 at higher temperature, the remaining antigorite and the 10 A phase fully dehydrate. From the analysis of reaction progress data, we determined that the major release of aqueous fluid occurs during step 2 at a fast rate of 10−4 mfluid 3 mrock −3 s−1. This exceeds by orders of magnitude the typical time scale of deformation by ductile mechanisms of any mineral or rock in the subducting slab or in the overlying mantle wedge. These results suggest that the fast dehydration of antigorite may well trigger the seismicity of the lower plane of the double seismic zone.

The Shapes of Splash-Form Tektites: Their Geometrical Analysis, Classification and Mechanics of Formation

Splash-form tektites are found with a wide range of sizes and in an intriguing array of shapes ranging from spheres to flat discs to dumbbells. Despite the considerable interest that exists in tektites, there has been relatively little effort to develop rational shape descriptors and to understand the origin of their shapes based on basic physics. Tektites represent a natural laboratory experiment that can be analyzed to better understand the physics of rotating fluid drops. In this paper, we propose a classification scheme based on the axial ratios of ellipsoids, and we analyze the frequency of tektite shapes using a database of over 1,000 measured tektites. We show that the shape distribution for tektites from Thailand and Vietnam are very similar and that the most common tektites are moderately deformed discs but there exist also a significant number of moderately deformed dumbbells, and we argue that this distribution comes about because fluid drops first deform as oblate forms and then undergo a non-axisymmetric instability to become prolate. We also find that the largest tektites are most likely to be weakly deformed oblate objects while the most strongly deformed and most highly prolate forms are considerably smaller. A numerical model for the evolution of an axisymmetric fluid drop, such as a tektite in its molten early stage, is presented which demonstrates that drops that deform relatively slowly over a longer period of time are likely to develop central thinning while those that deform more rapidly are more likely to retain the shape of an ellipsoid. For the numerical parameters used the characteristic time scale for deformation was less than 1 s.

Correlation between stick-slip frictional sliding and charge transfer

A decade ago, Budakian and Putterman (Phys. Rev. Lett., {\bf 85}, 1000 (2000)) ascribed friction to the formation of bonds arising from contact charging when a gold tip of a surface force apparatus was dragged on polymethylmethacrylate surface. We propose a stick-slip model that captures the observed correlation between stick-slip events and charge transfer, and the lack of dependence of the scale factor connecting the force jumps and charge transfer on normal load. Here, stick-slip dynamics arises as a competition between the visco-elastic and plastic deformation time scales and that due to the pull speed with contact charging playing a minor role. Our model provides an alternate basis for explaining most experimental results without ascribing friction to contact charging.

Cation Diffusion Kinetics in Aluminosilicate Garnets and Geological Applications

The compositional properties of garnet probably preserve the most extensive records of the pressure-temperature-time ( P - T - t ) history of metamorphic rocks. There are a number of cation-exchange and discontinuous reactions involving garnet that have been extensively used to decipher the P - T conditions or P - T paths of the host rocks as these were buried and exhumed (e.g., Ganguly and Saxena 1987; Spear 1993). However, as metamorphic garnets commonly show compositional zoning, the choice of composition within a zoned garnet to retrieve peak metamorphic conditions requires consideration of its diffusion kinetic properties (Dasgupta et al. 2004, 2009), as does the issue of whether the peak condition is at all preserved in the compositional property of a garnet of a given grain size (e.g., Spear 1991; Ganguly and Tirone 1999; Tirone and Ganguly 2010). Diffusion kinetic modeling of the major-element compositional zonings of garnets leads to important constraints on the time scales of metamorphic processes such as heating and cooling rates (e.g., Florence and Spear 1993; Ganguly et al. 2000; Faryad and Chakraborty 2005; Augue and Baxter 2007), from which one may infer the burial and exhumation rates, respectively (e.g., Ganguly et al. 2000; Faryad and Chakraborty 2005), and time scales of deformation (Camacho et al. 2009). In addition, the presence of garnet in the source region of a basaltic magma imparts a characteristic signature, often referred to as the “garnet signature,” to its rare earth element (REE) pattern. In addition to providing an important constraint on the depth of the source region of a basaltic magma, since garnet is stable below ~50 km depth in the Earth’s interior (e.g., Saxena and Eriksson 1983), the REE pattern of basaltic magma with “garnet signature” is often used to infer …

Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

We explore the utility of strain-controlled large amplitude oscillatory shear (LAOS) deformation for identifying and characterizing apparent yield stress responses in elastoviscoplastic materials. Our approach emphasizes the visual representation of the LAOS stress response within the framework of Lissajous curves with strain, strain rate, and stress as the coordinate axes, in conjunction with quantitative analysis of the corresponding limit cycle behavior. This approach enables us to explore how the material properties characterizing the yielding response depend on both strain amplitude and frequency of deformation. Canonical constitutive models (including the purely viscous Carreau model and the elastic Bingham model) are used to illustrate the characteristic features of pseudoplastic and elastoplastic material responses under large amplitude oscillatory shear. A new parameter, the perfect plastic dissipation ratio, is introduced for uniquely identifying plastic behavior. Experimental results are presented for two complex fluids, a pseudoplastic shear-thinning xanthan gum solution and an elastoviscoplastic invert-emulsion drilling fluid. The LAOS test protocols and the associated material measures provide a rheological fingerprint of the yielding behavior of a complex fluid that can be compactly represented within the domain of a Pipkin diagram defined by the amplitude and timescale of deformation.

Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed two-dimensional spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation time scale and an inertial time scale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation is proposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles not only in terms of kinematics but also in terms of forces.

Dynamic simulation of emulsion formation in a high pressure homogenizer

A simulation model for emulsification in high pressure homogenization (HPH), based on a population balance approach, is developed assuming it to be controlled by three simultaneous processes; fragmentation, coalescence and adsorption of a macromolecular emulsifier. The aim is to investigate the implications of adding a set of models together; studying the effects of dynamics, size effects and process interactions. For fragmentation, turbulent inertial and turbulent viscous forces are included using a dynamic model based on the Weber and Capillary number. It was extended to include a deformation time scale. The rate of adsorption and coalescence is assumed to be controlled by the collision rate of macromolecular stabilizer and bare interface, modeled using convective and diffusive transport in turbulent flow. By comparing simulation results to general trends found in the literature, it can be concluded that the models can reproduce the general HPH process well. By dividing the active region of emulsification in the homogenizing valve into discrete steps, the dynamic process could also be examined, indicating the homogenization process being composed of three stages with coalescence predominantly found in the last one.

Time-dependent strain localization in viscous media with state-dependent viscosity

The temporal evolution of viscous rheologies with dependence on an additional state variable is examined. A localization measure is introduced that quantifies the change in the degree of localization in time. Three sample rheologies are analyzed in detail, each representative of a larger class of rheologies: (1) a grain-size dependent viscosity with grain growth and diminution, (2) shear heating with temperature-dependence according to the Arrhenius law, and (3) shear heating with temperature dependence in the Frank-Kamenetzky approximation. All three rheologies display stages of temporal increase and decrease of localization, depending on the initial conditions. This localization behavior is not discernible in plots of strain rate versus strain at constant driving stress which are the typical output of creep experiments. The grain-size dependence of olivine leads to effectively non-Newtonian behavior with a stress exponent of about 5. If the laws describing the grain-size evolution are applicable to the mantle, then the lower mantle and those parts of the upper mantle that are dominated by diffusion creep thus have a stronger stress-dependence than the depth range governed by dislocation creep, provided that the timescale of deformation is greater than 1 0 5 – 1 0 6 years.

Modelling interactions between fold–thrust belt deformation, foreland flexure and surface mass transport

ABSTRACTInteractions between fold and thrust belt deformation, foreland flexure and surface mass transport are investigated using a newly developed mathematical model incorporating fully dynamic coupling between mechanics and surface processes. The mechanical model is two dimensional (plane strain) and includes an elasto‐visco‐plastic rheology. The evolving model is flexurally compensated using an elastic beam formulation. Erosion and deposition at the surface are treated in a simple manner using a linear diffusion equation. The model is solved with the finite element method using a Lagrangian scheme with marker particles. Because the model is particle based, it enables straightforward tracking of stratigraphy and exhumation paths and it can sustain very large strain. It is thus ideally suited to study deformation, erosion and sedimentation in fold–thrust belts and foreland basins.The model is used to investigate how fold–thrust deformation and foreland basin development is influenced by the non‐dimensional parameter , which can be interpreted as the ratio of the deformation time scale to the time scale for surface processes. Large values of imply that the rate of surface mass transport is significantly greater than the rate of deformation. When , the rates of surface processes are so slow that one observes a classic propagating fold–thrust belt with well‐developed wedge top basins and a largely underfilled foreland flexural depression. Increasing causes (1) deposition to shift progressively from the wedge top into the foredeep, which deepens and may eventually become filled, (2) widespread exhumation of the fold–thrust belt, (3) reduced rates of frontal thrust propagation and possible attainment of a steady‐state orogen width and (4) change in the style and dynamics of deformation. Together, these effects indicate that erosion and sedimentation, rather than passively responding to tectonics, play an active and dynamic role in the development of fold–thrust belts and foreland basins. Results demonstrate that regional differences in the relative rates of surface processes (e.g. because of different climatic settings) may lead to fold–thrust belts and foreland basins with markedly different characteristics. Results also imply that variations in the efficiency of surface processes through time (e.g., because of climate change or the emergence of orogens above sea level) may cause major temporal changes in orogen and basin dynamics.

Dynamic Surface Activity of Phenylalanine Glycerol−Ether Surfactant Solutions Measured by a Differential Maximum Bubble Pressure Tensiometer

A refined differential maximum bubble pressure tensiometer was used for measuring the dynamic surface tension at various concentrations of a nonconventional surfactant, a member of a new homologous series of phenylalanine glycerol-ether amphiphiles, with 10 carbon atoms to the hydrophobic alkyl chain (C(10)-PhGE). The effective bubble formation frequency for the examined surfactant concentrations was varied from 2 bubbles per second to 1 bubble per 20 s. The variation of equilibrium surface tension with concentration as well as the critical micelle concentration were determined by a Wilhelmy plate technique. Comparisons between dynamic and equilibrium surface tension values demonstrate that, under the employed surface deformation rates, the equilibrium surface tension is a misleading indicator of surface activity. This is also supported by simple surface rheology considerations. Results based on a diffusion-controlled kinetic analysis provide further evidence on the strong dependence of surface activity on the particular time scale of deformation.

Time scales of deformation and exhumation in extensional detachment systems determined by high-spatial resolution in situ UV-laser 40Ar/ 39Ar dating

Once dated with adequate precision, intra grain recrystallization microstructures in deformed minerals provide valuable information about the tectonic and kinematic history of shear zones and entire orogens. We present combined in situ UV-laser 40Ar/ 39Ar geochronology and stable isotope data to decipher the relationships between intra grain recrystallization microstructures and 40Ar/ 39Ar ages in muscovite fish from extensional mylonite of the Porsgrunn–Kristiansand Shear Zone, Southern Norway. Texturally controlled UV-laser 40Ar/ 39Ar dating of isotopically and compositionally distinct cores, rims, and tips of muscovite fish resolves intra grain age variations on the micrometer scale. Twenty-eight in situ UV-laser 40Ar/ 39Ar analyses from two muscovite cores yield a weighted mean age of 891.2 ± 2.9 Ma, interpreted to date synkinematic neocrystallization of muscovite. The integrated 880.2 ± 2.8 Ma ( n = 30 analyses) weighted mean age of rims and tips is in good agreement with observed recrystallization relationships which suggest that rims and tips of the muscovite fish record the final increments of the ductile deformation history. Diffusion considerations based on published argon diffusion rates and peak temperature estimates from oxygen isotope thermometry show that the 40Ar/ 39Ar ages are unlikely to be disturbed during cooling. The 11.0 ± 4.0 my core-to-rim age difference together with the stable isotope data are consistent with protracted ductile deformation, extensional detachment faulting, and meteoric fluid infiltration occurring over this time interval. This approach combining X-ray element mapping, stable isotope geochemistry, and in situ UV-laser 40Ar/ 39Ar dating allows well-characterized microstructures to be analyzed with high precision and permits direct determination of the time scales of deformation in crustal-scale shear zones.

Formation of bands and ridges on Europa by cyclic deformation: Insights from analogue wax experiments

We perform a set of analogue wax experiments aimed at understanding the processes and conditions that lead to lineament formation on Europa. We heat a layer of wax from below and cool it from above so that a solid layer of wax forms above a molten layer, simulating either the liquid ocean or the actively convecting part of the ice shell. The solid layer of wax is then deformed periodically, simulating the cyclic strain caused by tides or by the satellite's nonsynchronous rotation. We find that the formation and morphology of lineaments that develop in the solid wax layer are governed by two main dimensionless parameters: Ψ, the ratio of the cooling timescale for the solid layer to the deformation timescale, and the dilation quotient γ, which is defined as the magnitude of net extension during one cycle of deformation divided by the amplitude of the periodic deformation. For Ψ ∼ 1, features form that qualitatively resemble bands and ridge complexes on Europa. We conclude that diurnal tides may be responsible for the formation of bands on Europa if the conducting layer of ice is a few hundred meters thick and is underlain by a convecting layer of ice. Features resembling double ridges can form if the ice shell has a thickness of a few kilometers and periodic strains are caused by Europa's nonsynchronous rotation.