Distribution by Scientific Domains
Distribution within Polymers and Materials Science

Kinds of Modulus

  • bending modulus
  • bulk modulus
  • compressive modulus
  • dynamic modulus
  • effective elastic modulus
  • elastic modulus
  • elasticity modulus
  • equilibrium modulus
  • flexural modulus
  • high modulus
  • initial modulus
  • loss modulus
  • plateau modulus
  • shear modulus
  • storage modulus
  • tensile modulus
  • viscoelastic modulus
  • weibull modulus
  • young modulus

  • Terms modified by Modulus

  • modulus algorithm
  • modulus decreased
  • modulus g
  • modulus increase
  • modulus value

  • Selected Abstracts


    ABSTRACT The dynamic shear modulus (elastic and viscous modulus) development of dough during baking was studied. Flooded parallel plate geometry was used to monitor the rheological changes of commercially available canned doughs (bread dough, bun dough and biscuit dough). The normal force exerted on the upper plate by the expanding dough was measured to study the cell-opening event. The dough-baking process was simulated in a rheometer oven. The morphology of baked dough was studied using a scanning electron microscope to elucidate the effect of ingredients and process parameters on the properties of the final baked product. Three stages of modulus development were observed during the baking process: bubble growth and packing, rapid expansion/starch gelatinization and final curing. The cell opening coincided with the sudden rise in modulus caused by starch gelatinization. The rate at which starch gelatinization takes place controls the temperature of the cell opening. The type and concentration of various ingredients have a greater effect on the modulus and on the cell opening than the heating rates. Frequency dependence was observed during baking, but the effect on modulus development diminished at higher frequencies. [source]

    Role of substrate material in failure of crown-like layer structures,

    Jae-Won Kim
    Abstract The role of substrate modulus on critical loads to initiate and propagate radial cracks to failure in curved brittle glass shells on compliant polymeric substrates is investigated. Flat glass disks are used to drive the crack system. This configuration is representative of dental crown structures on dentin support in occlusal contact. Specimens are fabricated by truncating glass tubes and filling with epoxy-based substrate materials, with or without alumina filler for modulus control. Moduli ranging from 3 to 15 GPa are produced in this way. Critical loads for both initiation and propagation to failure increase monotonically with substrate modulus, by a factor of two over the data range. Fracture mechanics relations provide a fit to the data, within the scatter bands. Finite element analysis is used to determine stress distributions pertinent to the observed fracture modes. It is suggested that stiffer substrate materials offer potential for improved crown lifetime in dental practice. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006 [source]

    Shear Modulus of Polycrystalline Rhenium Diboride Determined from Surface Brillouin Spectroscopy

    ADVANCED MATERIALS, Issue 42 2009
    Sergey N. Tkachev
    Surface Brillouin specotroscopy of a densified powder compact of rhenium diboride (see scanning electron microscopy image) results in a determined shear modulus of 223,GPa. This value is comparable to the shear modulus of c-BC2N and provides evidence for the superhard nature of ReB2. [source]

    Processing and mechanical behavior of carbon black graded rubber compounds

    Sandeep S. Ahankari
    Abstract Functionally graded rubber compounds (FGRCs) were prepared by construction based method. The matrix used was natural rubber (NR). Amorphous carbon black (N-330) was used as grading material. The gradation of nanoparticles in a rectangular geometry comprised the variation of particle volume fraction along thickness direction. Its performance was evaluated for structural application through various mechanical and surface properties like tensile strength, modulus, tear strength, elongation at break, hardness, fracture surface by scanning electron microscopy, etc. At the same percentage of nanofiller loading, FGRCs show enhanced properties, i.e., modulus and tear strength (in some grades) compared to uniformly dispersed rubber compounds (UDRCs). Modulus of FGRCs, for a given particular stacking sequence of the layers, increases as much as by 275% compared to UDRCs. The ultimate properties like tensile strength and elongation at break made up for the modulus enhancement that decreases to as minimum as 50 and 80%, respectively. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010 [source]

    Flexural Strength, Elastic Modulus, and pH Profile of Self-etch Resin Luting Cements

    Egle Saskalauskaite DDS
    Abstract Purpose: To determine the flexural strength, modulus of elasticity, and 24-hour pH profile of three self-etching resin luting cements and to obtain comparative data for representative conventional resin and resin-modified glass ionomer luting cements. Materials and Methods: Three self-etching resin luting cements [RelyX Unicem (3M ESPE), Maxcem (Kerr), Embrace Wetbond (Pulpdent)] were tested and compared with two conventional resin cements [RelyX ARC (3M ESPE), Linkmax (GC)] plus two resin-modified glass ionomer luting cements [Fuji Plus (GC), RelyX Luting Plus (3M ESPE)]. Flexural strength and modulus of elasticity were determined using bar-shaped specimens (2 × 2 × 25 mm3) at 24 hours, using an Instron universal testing machine. Setting pH was measured using a flat-surface pH electrode at 0, 2, 5, 15, and 30 minutes and 1, 2, 4, 6, and 24 hours after mixing. Testing was performed under both dual-cured and self-cured conditions for all dual-cure cements. Data analysis included ANOVA and Tukey's test (p < 0.05). Results: The self-etching cements showed similar flexural strength to the conventional resin cements, except for Embrace Wetbond self-cured, which was considerably lower. Modulus of elasticity results were both higher and lower than for conventional resin cements. All photopolymerized conventional and self-etch dual-cure cements showed markedly higher flexural strength and modulus than when solely self-cured. The resin-modified glass ionomer cements were characterized by lower flexural strength and elastic modulus. Self-etching resin cements showed lower initial pH (2.0 to 2.4) than conventional resin cements (4.8 to 5.2) and a wide range of final pH values (3.9 to 7.3) at 24 hours. One self-etching cement (Unicem) revealed a unique pH profile characterized by a more rapid rise in pH to neutrality both when dual-cured (15 minutes) and when auto-cured (1 hour). Conclusions: The self-etching resin cements evaluated in this study displayed disparate properties and cannot be considered a homogeneous group. Flexural strength properties were most uniform and were similar to those of the conventional resin cements, whereas moduli of elasticity showed greater variation. Setting pH profiles differed, depending on the brand and mode of cure, even within the same category of luting cement. All cements with dual-cure capability, both conventional and self-etch, showed significantly superior properties when photopolymerized. [source]

    Morphology and High Modulus of Laminated Ultra-Drawn Polyethylene Films with Biaxial Orientation Prepared by Microwave Heating

    Mami Azuma
    Abstract To improve the poor mechanical properties of uniaxially ultra-drawn films along the transverse direction, lamination of two ultrahigh molecular weight polyethylene/ethylene dimethylaminoethyl methacrylate copolymer blend films was carried out in the rectangular elongation direction by a microwave heating method. The characteristics of the successful laminated films were analyzed theoretically and experimentally. The original orientation of the crystallites for the blend films was maintained perfectly after lamination, and the preferential directions intersected each other. The Young's modulus increased symmetrically with respect to the 45 ° direction. This is the first report concerning a drastic improvement of the Young's modulus in the transverse direction for films ultra-drawn along one direction. [source]

    Effect of Chain Straightening on Plateau Modulus and Entanglement Molecular Weight of Ni-diimine Poly(1-hexene)s

    Zhibin Ye
    Abstract Summary: In this communication, we report the first rheological study on the chain-straightened Ni-diimine poly(1-hexene)s and investigate the unique effect of chain straightening on plateau modulus and entanglement molecular weight of this series of polymers. Two Ni-diimine poly(1-hexene) samples having different levels of chain straightening were prepared with a chain-walking Ni-diimine catalyst, (ArNC(An)C(An)NAr)NiBr2 (An,=,acenaphthene, Ar,=,2,6-(i -Pr)2C6H3) at two different temperatures. Rheological analyses show that the chain-straightened polymers exhibit significantly enhanced plateau modulus and reduced entanglement molecular weight compared to regular poly(1-hexene)s by metallocene catalysis. Such an effect becomes more pronounced with an increase in the level of chain straightening. Loss moduli G,(,) versus reduced angular frequency in a linear, natural logarithm plot for the three polymers at the reference temperature of 100,°C. [source]

    On the Use of the Nanoindentation Unloading Curve to Measure the Young's Modulus of Polymers on a Nanometer Scale

    Davide Tranchida
    Abstract Summary: The nanoindentation test is a fundamental tool to assess the link between morphology and mechanical properties. The preliminary results of a more exhaustive study about the applicability to polymers of the most used procedure to determine elastic modulus by indentation are reported in this short communication. A departure of the experimental conditions from the theoretical assumptions and results that give rise to the Oliver and Pharr analysis is shown to occur under a wide range of experimental conditions, with applied loads and penetration depths covering several orders of magnitude and using different indenter geometries. Unloading curves with exponents significantly larger than 2 are observed in disagreement with the contact mechanics approach used by Oliver and Pharr. An AFM image obtained in non contact mode of an indentation induced by a sharp AFM tip with a maximum applied load of ca 1.2 µN on amorphous PET. [source]

    Synthesis and properties of room temperature curable trimethoxysilane-terminated polyurethane and their dispersions

    Sankaraiah Subramani
    Abstract The purpose of this research is to study the synthesis and characterization of stable aqueous dispersions of externally chain extended polyurethane/urea compositions terminated by hydrolyzable or hydrolyzed trialkoxysilane groups incorporated through secondary amino groups. These dispersions with excellent storage stability are substantially free from organic solvents which cure to water and solvent resistant, tough, scratch resistant, preferably light stable (non-yellowing) silylated polyurethane (SPU) films. The films were characterized by FT-IR, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), tensile strength and water contact angle measurements, nanoindentation, gel content, water and xylene swellability tests. The properties of the films were discussed and correlated in detail by changing length of soft segment, diisocyanates, NCO/OH ratio and chain extender, ethylenediamine (EDA). From the results, it was found that the particle size and viscosity are lower whereas the gel content and thermal stability are higher for SPUs. Modulus, hardness and tensile properties of SPU films are superior compared to EDA-PU film. Higher water contact angle and residual weight percentage of SPU films confirm silylation of PU by [3-(phenylamino)propyl]trimethoxysilane (PAPTMS). Increase in NCO/OH ratios consumes more quantity of PAPTMS which makes PU with superior mechanical properties. Higher PAPTMS content in SPU results in effective crosslinking of the functional silanol groups formed by hydrolysis reaction of trimethoxysilane groups. Overall, SPUs synthesized at 1.4 NCO/OH ratio using Poly-(oxytetramethylene)glycol (PTMG)-2000 and isophorone diisocyanate (or) toluene-2,4-diisocyanate have excellent properties compared to SPUs prepared using PTMG-1000 and at 1.2 and 1.6 NCO/OH ratios. SPUs prepared at 1.6 NCO/OH ratio are brittle due to higher crosslinking density. In addition, the crosslinking density of the films can be modified through silane end-group modification to produce SPUs with a wide range of physical properties. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Synthesis and NMR characterization of 6-Phenyl-6-deoxy-2,3-di- O -methylcellulose,

    Dr Navzer (Nozar) D. Sachinvala
    Abstract Cellulose (1) was converted for the first time to 6-phenyl-6-deoxy-2,3-di- O -methylcellulose (6) in 33% overall yield. Intermediates in the five-step conversion of 1 to­6 were: 6- O -tritylcellulose (2), 6- O -trityl-2,3-di- O -methylcellulose (3), 2,3-di- O -methylcellulose (4); and 6-bromo-6-deoxy-2,3-di- O -methylcellulose (5). Elemental and quantitative carbon-13 analyses were concurrently used to verify and confirm the degrees of substitution in each new polymer. Gel permeation chromotography (GPC) data were generated to monitor the changes in molecular weight (DPw) as the synthesis progressed, and the compound average decrease in cellulose DPw was , 27%. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to characterize the decomposition of all polymers. The degradation temperatures (,°C) and percent char at 500,°C of cellulose derivatives 2 to 6 were 308.6 and 6.3%, 227.6,°C and 9.7%, 273.9,°C and 30.2%, 200.4,°C and 25.6%, and 207.2,°C and 27.0%, respectively. The glass transition temperature (Tg) of­6- O -tritylcellulose by dynamic mechanical analysis (DMA) occurred at 126.7,°C and the modulus (E,, Pa) dropped 8.9 fold in the transition from ,150,°C to,+,180,°C (6.6,×,109 to 7.4,×,108 Pa). Modulus at 20,°C was 3.26,×,109 Pa. Complete proton and carbon-13 chemical shift assignments of the repeating unit of the title polymer were made by a combination of the HMQC and COSY NMR methods. Ultimate non-destructive proof of carbon,carbon bond formation at C6 of the anhydroglucose moiety was established by generating correlations between resonances of CH26 (anhydroglucose) and C1,, H2,, and H6, of the attached aryl ring using the heteronuclear multiple-bond correlation (HMBC) method. In this study, we achieved three major objectives: (a) new methodologies for the chemical modification of cellulose were developed; (b) new cellulose derivatives were designed, prepared and characterized; (c) unequivocal structural proof for carbon,carbon bond formation with cellulose was derived non-destructively by use of one- and two-dimensional NMR methods. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Hochdynamische Materialeigenschaften von Ultrahochleistungsbeton (UHPC)

    Markus Nöldgen Dipl.-Ing.
    Baustoffe; Versuche; Dynamische Einwirkungen Abstract Der vorliegende Bericht liefert einen Beitrag zur Werkstoffbeschreibung von Ultrahochleistungsbetonen unter hochdynamischer Belastung. Grundlage für die Ermittlung der Werkstoffeigenschaften ist eine Hopkinson-Bar Versuchsreihe, die Werte für die dynamische Zugfestigkeit, den dynamischen E-Modul und die dynamische Bruchenergie unter Dehnraten von 102 · s,1 liefert. Ein Vergleich mit den Ergebnissen dieser Parameter für Normalbeton und hochfesten Betonen ermöglicht eine Einordnung des Ultrahochleistungsbetons in etablierte Ansätze und Berechnungsvorschriften und liefert einen Bewertungsansatz für die maßgebenden mechanischen Vorgänge. Unter Einbeziehung der Bruchenergie und der Spannungs-Rissöffnungs-Beziehung für UHPC in das RHT-Betonmodell werden Hydrocode Simulationen durchgeführt, die den Versuch am Hopkinson-Bar adäquat abbilden können. Material Properties of Ultra High Performance Concrete (UHPC) at High Strain Rates The presented paper is a contribution to the material description of Ultra High Performance Concrete (UHPC) under high-speed dynamical loading conditions. Based on a series of Hopkinson-Bar experiments dynamical material parameters such as the Tensile Strength, Young's Modulus and Fracture Energy are derived at high strain rates of 102 · s,1. A comparison with the results of these parameters for normal and high strength concrete leads to a qualitative and quantitative evaluation of UHPC at high strain rates. With the extension of the established RHT material model for UHPC by the material's Fracture Energy and Stress-Crack-Opening-Relation the Hopkinson-Bar experiments are simulated appropriately. [source]

    Effect of Comonomer Ethylene on Plateau Modulus of Crystal-line Ethylene-propylene Random Copolymer with Broad Molecular Weight Distribution

    Ding Jian
    Abstract Ethylene-propylene random copolymer with ultra-high molecular weight (UHPPR) and broad molecular weight distribution (MWD) was prepared with Ziegler-Natta catalyst. The viscoelastic behavior of UHPPR has been investigated by means of oscillatory rheometer at 180, 200 and 220 °C. The loss modulus (G, curves of 180 and 200 °C present a pronounced maximum at 38.10 and 84.70 r/s, respectively. For the first time, this makes it possible to directly determine the plateau modulus () of crystalline ethylene-propylene random copolymer with broad MWD in a certain experimental temperature G,(,) curve. The plateau modulus of UHPPR is 4.51×105 and 3.67×105 Pa at 180 and 200 °C respectively, increasing with random incorporation of comonomer ethylene into the molecular chains and being independent of molecular weight. [source]

    Functional consequences of cartilage degeneration in the equine metacarpophalangeal joint: quantitative assessment of cartilage stiffness

    Summary Reasons for performing study: No quantitative data currently exist on the relationship of the occurrence of cartilage degeneration and changes in site-specific biomechanical properties in the metacarpophalangeal (MCP) joint in the horse. Objectives: To gain insight into the biomechanical consequences of cartilage deterioration at 2 differently loaded sites on the proximal articular surface of the proximal phalanx (P1). Hypothesis: Static and dynamic stiffness of articular cartilage decreases significantly in degenerated cartilage. Methods: Cartilage degeneration index (CDI) values were measured at the lateral dorsal margin (Site 1), lateral central fovea (Site 2) and entire joint surface of P1 (CDIP1) in 30 horses. Group 1 contained joints without (CDIP1 values <25%, n = 22) and Group 2 joints with (CDIP1 values >25%, n = 8) signs of cartilage degeneration. Cartilage thickness at Sites 1 and 2 was measured using ultrasonic and needle-probe techniques. Osteochondral plugs were drilled out from Sites 1 and 2 and subsequently tested biomechanically in indentation geometry. Young's modulus at equilibrium and dynamic modulus were determined. Results: Cartilage thickness values were not significantly different between the 2 groups and sites. Young's modulus at Site 1 was significantly higher in Group 1 than in Group 2; at Site 2, the difference was not significant. Dynamic modulus values were significantly higher in Group 1 than in Group 2 at both sites. Conclusions: Degenerative cartilage changes are clearly related to loss of stiffness of the tissue. Absolute changes in cartilage integrity in terms of CDI are greatest at the joint margin, but concomitant changes are also present at the centre, with a comparable decrease of the biomechanical moduli at the 2 sites. Therefore, significant cartilage degradation at the joint margin not only reflects local deterioration of biomechanical properties, but is also indicative of the functional quality in the centre. Potential relevance: These findings may be important for improving prognostication and developing preventative measures. [source]

    Age-associated changes in viscoelastic properties of the bovine temporomandibular joint disc

    Eiji Tanaka
    To test the hypothesis that compressive properties of the temporomandibular joint (TMJ) disc change with age, we investigated its viscoelastic properties and stress-relaxation behavior under compression. Compressive stress-relaxation tests were performed in different regions of bovine discs of various ages. For each disc, specimens were derived from three different regions (anterior, central, and posterior). For four strain levels (5, 10, 15, and 20%), a stress-relaxation test was conducted over a 5-min period. Values of the instantaneous modulus, E0, appeared to be larger in the anterior than in the posterior region of the disc, irrespective of age. The E0 value increased with age, especially in the central region. Values of the relaxed modulus, ER, also increased significantly with age. There were no regional differences in values of the relaxed modulus. Under stress-relaxation, the relaxation time became longer with age, especially in the posterior region. The results suggest that the compressive properties, instantaneous and relaxed moduli, increase with age, while the relaxation time becomes longer. This implies that the TMJ disc becomes harder with age. Furthermore, the compressive properties of the TMJ disc are region-specific. As a result of the harder disc, it is likely that the TMJ becomes more vulnerable to secondary damage, such as fracture and tissue degradation. [source]

    Dynamic compressive properties of porcine temporomandibular joint disc

    Eiji Tanaka
    This study aimed to evaluate the effect of the strain frequency and amplitude on the compressive properties of the porcine temporomandibular joint disc and to determine the time-dependent changes associated with energy dissipation. Seven discs were used for compressive cycle tests, including various frequencies and magnitudes of compressive strain. Each experiment consisted of 25 cycles of loading and unloading. Hysteresis and the instantaneous and steady moduli were calculated. All specimens showed a clear hysteresis and repeatable stress,strain relationships within 19 cycles. The hysteresis at the initial cycle ranged between 35% and 62%, and gradually decreased in subsequent cycles. The instantaneous modulus became larger when the strain frequency and the strain amplitude increased. The steady modulus was approximately one-third of the instantaneous one. It was concluded that the disc has an energy-dissipating function during dynamic compression. [source]

    Molecular Tailored Histidine-Based Complexing Surfactants: From Micelles to Hydrogels

    Patrick Gizzi
    Abstract Novel histidine-based complexing surfactants, designed as AA-His-EOm -Cn, containing trifunctional moduli (peptidic/hydrophilic/hydrophobic) were synthesized by a modular step-by-step procedure, which allowed easy structural changes, and consequently correlations between their molecular structures and their self-assembling properties could be established. Thus, micelles or hydrogels could be obtained by simply modifying the hydrophobic tail lengths or the junction between the different moduli of the designed compounds. At low pH values, all compounds were surface active in aqueous solutions. At higher pH values, in the range 8,10, micellization took place for decyl compounds (n = 10), whereas hydrogelation occurred for longer chain lengths (n = 12, 14), and this, at very-low concentrations of surfactant (<0.3 wt.-%), could thus act as low molecular weight gelator (LMWG). The driving forces for gel formation were noncovalent intermolecular interactions such as ,-stacking and hydrophobic and hydrogen-bonding interactions.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009) [source]

    Full scale experiments for evaluating theoretical fire wall models

    FIRE AND MATERIALS, Issue 6 2004
    P. Clancy
    Abstract The aim of the research described in this paper was to provide experimental results for the evaluation of theoretical models for predicting the behaviour and time-to-failure of loadbearing and non-loadbearing wood framed walls in fire. References for thermal and mechanical properties of wood and gypsum board are given to provide comprehensive input for the evaluation of theoretical wall models. The scope of the research involved full-scale uninsulated cavity walls with well-controlled clearly known conditions including initial ambient vertical load capacity for benchmarking the reduction in capacity and stiffness, rotational stiffness of supports, eccentricity of vertical load, elastic moduli of wood and gypsum board in compression, stiffness of slip between gypsum board and studs and end stud effects. The experiments were repeated and they demonstrated that the controls led to high consistency in the results despite the inherent large variability of the mechanical properties of wood. The results include temperature distributions, initial vertical load capacity, load-deflection plots and times-to-failure. The results show that the temperatures in the studs are approximately uniform until all the moisture is vaporized. Thermal properties of wood will not vary significantly for consistent density, moisture content and species of wood. The main structural actions that should be modelled for different loading regimes are deduced. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Moduli stabilisation and applications in IIB string theory

    J.P. Conlon
    String compactifications represent the most promising approach towards unifying general relativity with particle physics. However, naive compactifications give rise to massless particles (moduli) which would mediate unobserved long-range forces, and it is therefore necessary to generate a potential for the moduli. In the introductory chapters I review this problem and recall how in IIB compactifications the dilaton and complex structure moduli can be stabilised by 3-form fluxes. There exist very many possible discrete flux choices which motivates the use of statistical techniques to analyse this discretuum of choices. Such approaches generate formulae predicting the distribution of vacua and I describe numerical tests of these formulae on the Calabi-Yau ,4[1,1,2,2,6]. Stabilising the Kähler moduli requires nonperturbative superpotential effects. I review the KKLT construction and explain why this must in general be supplemented with perturbative Kähler corrections. I show how the incorporation of such corrections generically leads to non-supersymmetric minima at exponentially large volumes, giving a detailed account of the,, expansion and its relation to Kähler corrections. I illustrate this with explicit computations for the Calabi-Yau ,4[1,1,1,6,9]. The next part of the article examines phenomenological applications of this construction. I first describe how the magnitude of the soft supersymmetry parameters may be computed. In the large-volume models the gravitino mass and soft terms are volume-suppressed. As we naturally have ,, ,1, this gives a dynamical solution of the hierarchy problem. I also demonstrate the existence of a fine structure in the soft terms, with gaugino masses naturally lighter than the gravitino mass by a factor ln (MP/m3/2). A second section gives a detailed analysis of the relationship of moduli stabilisation to the QCD axions relevant to the strong CP problem, proving a no-go theorem on the compatibility of a QCD axion with supersymmetric moduli stabilisation. I describe how QCD axions can coexist with nonsupersymmetric perturbative stabilisation and how the large-volume models naturally contain axions with decay constants that are phenomenologically allowed and satisfy the appealing relationship fa2 ,MPMsusy. A further section describe how a simple and predictive inflationary model can be built in the context of the above large-volume construction, using the no-scale Kähler potential to avoid the , problem. I finally conclude, summarising the phenomenological scenario and outlining the prospects for future work. [source]

    String theory: exact solutions, marginal deformations and hyperbolic spaces

    D. Orlando
    Abstract This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces. [source]

    On the existence of non-supersymmetric black hole attractors for two-parameter Calabi-Yau's and attractor equations

    P. Kaura
    We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY3(2,128) expressed as a degree-12 hypersurface in WCP4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non-supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C8 which may also be "arithmetic" (in some cases, it is possible to interpret the extremization conditions for the black-hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non-supersymmetric black-hole attractors corresponds to a version of A1 -singularity in the space Image(Z6,R2/Z2 (,R3)) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP5,CP20, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black-hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential. [source]

    Flux vacua statistics for two-parameter Calabi-Yau's

    A. Misra
    Abstract We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau expressed as a hypersurface in WCP4[1,1,2,2,6] by evaluating a suitable integral over the complex-structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. In the process, we evaluate the periods near the conifold locus. We also study (non)supersymmetric solutions near the conifold locus, and show that supersymmetric solutions near the conifold locus do not support fluxes. [source]

    Compactifications on half-flat manifolds,

    S. Gurrieri
    Abstract We review various aspects of compactifications of heterotic and type II supergravities on six dimensional manifolds. In the general framework of non-Kähler compactifications, emphasis is made on a particular class of manifolds with SU(3)-structure named half-flat. We recall how these manifolds appeared in the context of mirror symmetry of type II theories, providing mirror configurations to Calabi-Yau compactifications with NS-NS electric fluxes. In the heterotic sector, they generate a potential for all moduli, and are expected to break the E8 × E8 gauge group down to SO(10) × E8 in 4 dimensions. [source]

    Aspects of stability and phenomenology in type IIA orientifolds with intersecting D6-branes

    T. OttArticle first published online: 14 JAN 200
    Abstract Intersecting branes have been the subject of an elaborate string model building for several years. After a general introduction into string theory, this work introduces in detail the toroidal and -orientifolds. The picture involving D9-branes with B-fluxes is shortly reviewed, but the main discussion employs the T-dual picture of intersecting D6-branes. The derivation of the R-R and NS-NS tadpole cancellation conditions in the conformal field theory is shown in great detail. Various aspects of the open and closed chiral and non-chiral massless spectrum are discussed, involving spacetime anomalies and the generalized Green-Schwarz mechanism. An introduction into possible gauge breaking mechanisms is given, too. Afterwards, both ,, = 1 supersymmetric and non-supersymmetric approaches to low energy model building are treated. Firstly, the problem of complex structure instabilities in toroidal ,R -orientifolds is approached by a -orbifolded model. In particular, a stable non-supersymmetric standard-like model with three fermion generations is discussed. This model features the standard model gauge groups at the same time as having a massless hypercharge, but possessing an additional global B - L symmetry. The electroweak Higgs mechanism and the Yukawa couplings are not realized in the usual way. It is shown that this model descends naturally from a flipped SU(5) GUT model, where the string scale has to be at least of the order of the GUT scale. Secondly, supersymmetric models on the -orbifold are discussed, involving exceptional 3-cycles and the explicit construction of fractional D-branes. A three generation Pati-Salam model is constructed as a particular example, where several brane recombination mechanisms are used, yielding non-flat and non-factorizable branes. This model even can be broken down to a MSSM-like model with a massless hypercharge. Finally, the possibility that unstable closed and open string moduli could have played the role of the inflaton in the evolution of the universe is being explored. In the closed string sector, the important slow-rolling requirement can only be fulfilled for very specific cases, where some moduli are frozen and a special choice of coordinates is taken. In the open string sector, inflation does not seem to be possible at all. [source]

    Mechanical Buckling: Mechanics, Metrology, and Stretchable Electronics

    Dahl-Young Khang
    Abstract Mechanical buckling usually means catastrophic failure in structural mechanics systems. However, controlled buckling of thin films on compliant substrates has been used to advantage in diverse fields such as micro-/nanofabrication, optics, bioengineering, and metrology as well as fundamental mechanics studies. In this Feature Article, a mechanical buckling model is presented, which sprang, in part, from the buckling study of high-quality, single-crystalline nanomaterials. To check the mechanical-buckling phenomenon down to the nano-/molecular scale, well-aligned single-walled carbon nanotube arrays and cross linked carbon-based monolayers are transferred from growth substrate onto elastomeric substrate and then they are buckled into well-defined shapes that are amenable to quantitative analysis. From this nano- or molecular-scale buckling, it is shown that the mechanical moduli of nanoscale materials can easily be determined, even using a model based on continuum mechanics. In addition, buckling phenomena can be utilized for the determination of mechanical moduli of organic functional materials such as poly(3-hexylthiophene) (P3HT) and P3HT/6,6-phenyl-C61 -butyric acid methyl ester (PCBM) composite, which are widely used for organic transistors and organic photovoltaics. The results provide useful information for the realization of flexible and/or stretchable organic electronics. Finally, the fabrication and applications of "wavy, stretchable" single-crystal Si electronics on elastomeric substrates are demonstrated. [source]

    Three-dimensional models of elastostatic deformation in heterogeneous media, with applications to the Eastern California Shear Zone

    Sylvain Barbot
    SUMMARY We present a semi-analytic iterative procedure for evaluating the 3-D deformation due to faults in an arbitrarily heterogeneous elastic half-space. Spatially variable elastic properties are modelled with equivalent body forces and equivalent surface traction in a ,homogenized' elastic medium. The displacement field is obtained in the Fourier domain using a semi-analytic Green function. We apply this model to investigate the response of 3-D compliant zones (CZ) around major crustal faults to coseismic stressing by nearby earthquakes. We constrain the two elastic moduli, as well as the geometry of the fault zones by comparing the model predictions to Synthetic Aperture Radar inferferometric (InSAR) data. Our results confirm that the CZ models for the Rodman, Calico and Pinto Mountain faults in the Eastern California Shear Zone (ECSZ) can explain the coseismic InSAR data from both the Landers and the Hector Mine earthquakes. For the Pinto Mountain fault zone, InSAR data suggest a 50 per cent reduction in effective shear modulus and no significant change in Poisson's ratio compared to the ambient crust. The large wavelength of coseismic line-of-sight displacements around the Pinto Mountain fault requires a fairly wide (,1.9 km) CZ extending to a depth of at least 9 km. Best fit for the Calico CZ, north of Galway Dry Lake, is obtained for a 4 km deep structure, with a 60 per cent reduction in shear modulus, with no change in Poisson's ratio. We find that the required effective rigidity of the Calico fault zone south of Galway Dry Lake is not as low as that of the northern segment, suggesting along-strike variations of effective elastic moduli within the same fault zone. The ECSZ InSAR data is best explained by CZ models with reduction in both shear and bulk moduli. These observations suggest pervasive and widespread damage around active crustal faults. [source]

    Seismic singularities at upper-mantle phase transitions: a site percolation model

    Felix J. Herrmann
    SUMMARY Mineralogical phase transitions are usually invoked to account for the sharpness of globally observed upper-mantle seismic discontinuities. We propose a percolation-based model for the elastic properties of the phase mixture in the coexistence regions associated with these transitions. The major consequence of the model is that the elastic moduli (but not the density) display a singularity at the percolation threshold of the high-pressure phase. This model not only explains the sharp but continuous change in seismic velocities across the phase transition, but also predicts its abruptness and scale invariance, which are characterized by a non-integral scale exponent. Using the receiver-function approach and new, powerful signal-processing techniques, we quantitatively determine the singularity exponent from recordings of converted seismic waves at two Australian stations (CAN and WRAB). Using the estimated values, we construct velocity,depth profiles across the singularities and verify that the calculated converted waveforms match the observations under CAN. Finally, we point out a series of additional predictions that may provide new insights into the physics and fine structure of the upper-mantle transition zone. [source]

    Elastic properties of dry clay mineral aggregates, suspensions and sandstones

    Tiziana Vanorio
    SUMMARY The presence of clay minerals can alter the elastic behaviour of rocks significantly. Although clay minerals are common in sedimentary formations and seismic measurements are our main tools for studying subsurface lithologies, measurements of elastic properties of clay minerals have proven difficult. Theoretical values for the bulk modulus of clay are reported between 20 and 50 GPa. The only published experimental measurement of Young's modulus in a clay mineral using atomic force acoustic microscopy (AFAM) gave a much lower value of 6.2 GPa. This study has concentrated on using independent experimental methods to measure the elastic moduli of clay minerals as functions of pressure and saturation. First, ultrasonic P - and S -wave velocities were measured as functions of hydrostatic pressure in cold-pressed clay aggregates with porosity and grain density ranging from 4 to 43 per cent and 2.13 to 2.83 g cm,3, respectively. In the second experiment, P - and S -wave velocities in clay powders were measured under uniaxial stresses compaction. In the third experiment, P -wave velocity and attenuation in a kaolinite,water suspension with clay concentrations between 0 and 60 per cent were measured at ambient conditions. Our elastic moduli measurements of kaolinite, montmorillonite and smectite are consistent for all experiments and with reported AFAM measurements on a nanometre scale. The bulk modulus values of the solid clay phase (Ks) lie between 6 and 12 GPa and shear (,s) modulus values vary between 4 and 6 GPa. A comparison is made between the accuracy of velocity prediction in shaley sandstones and clay,water and clay,sand mixtures using the values measured in this study and those from theoretical models. Using Ks= 12 GPa and ,s= 6 GPa from this study, the models give a much better prediction both of experimental velocity reduction due to increase in clay content in sandstones and velocity measurements in a kaolinite,water suspension. [source]

    Ultrasonic velocities of North Sea chalk samples: influence of porosity, fluid content and texture

    Birte Røgen
    ABSTRACT We have studied 56 unfractured chalk samples of the Upper Cretaceous Tor Formation of the Dan, South Arne and Gorm Fields, Danish North Sea. The samples have porosities of between 14% and 45% and calcite content of over 95%. The ultrasonic compressional- and shear-wave velocities (VP and VS) for dry and water-saturated samples were measured at up to 75 bar confining hydrostatic pressure corresponding to effective stress in the reservoir. The porosity is the main control of the ultrasonic velocities and therefore of the elastic moduli. The elastic moduli are slightly higher for samples from the South Arne Field than from the Dan Field for identical porosities. This difference may be due to textural differences between the chalk at the two locations because we observe that large grains (i.e. filled microfossils and fossil fragments) that occur more frequently in samples from the Dan Field have a porosity-reducing effect and that samples rich in large grains have a relatively low porosity for a given P-wave modulus. The clay content in the samples is low and is mainly represented by either kaolinite or smectite; samples with smectite have a lower P-wave modulus than samples with kaolinite at equal porosity. We find that ultrasonic VP and VS of dry chalk samples can be satisfactorily estimated with Gassmann's relationships from data for water-saturated samples. A pronounced difference between the VP/VS ratios for dry and water-saturated chalk samples indicates promising results for seismic amplitude-versus-offset analyses. [source]

    Effective elastic properties of randomly fractured soils: 3D numerical experiments

    Erik H. Saenger
    ABSTRACT This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so-called rotated staggered finite-difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non-intersecting thin penny-shaped dry cracks, the numerical simulations of P- and S-wave velocities are in good agreement with the predictions of the self-consistent approximation. We observe similar results for fluid-filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non-intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective-medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. [source]

    Effects of pore aspect ratios on velocity prediction from well-log data

    Jun Yan
    ABSTRACT We develop a semi-empirical model which combines the theoretical model of Xu and White and the empirical formula of Han, Nur and Morgan in sand,clay environments. This new model may be used for petrophysical interpretation of P- and S-wave velocities. In particular, we are able to obtain an independent estimation of aspect ratios based on log data and seismic velocity, and also the relationship between velocities and other reservoir parameters (e.g. porosity and clay content), thus providing a prediction of shear-wave velocity. To achieve this, we first use Kuster and Toksöz's theory to derive bulk and shear moduli in a sand,clay mixture. Secondly, Xu and White's model is combined with an artificial neural network to invert the depth-dependent variation of pore aspect ratios. Finally these aspect ratio results are linked to the empirical formula of Han, Nur and Morgan, using a multiple regression algorithm for petrophysical interpretation. Tests on field data from a North Sea reservoir show that this semi-empirical model provides simple but satisfactory results for the prediction of shear-wave velocities and the estimation of reservoir parameters. [source]