Bulk Deformations Research Articles

D-brane superpotentials and RG flows on the quintic

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.

Effect of bulk deformation on rubber adhesion

In general, rubber friction is divided into two parts; the bulk hysteresis and the contact adhesive term. These two contributions are regarded to be independent of each other, but this is only a simplified assumption. If the adhesive force is solely a function of the surface free energy, it has been assumed that this adhesive force per unit area should be constant during any bulk (surface) deformation. The surface free energy is a function of both internal energy and entropy, and so it should change if the internal energy and/or entropy are changing due to any bulk deformation. In order to ascertain the effect of the bulk deformation on rubber adhesion, this effect on the surface free energy of two rubber compounds filled with various loading fractions of carbon black, natural rubber (NR) and styrene butadiene rubber (SBR) was studied. The surface free energy was determined from measured contact angles on rubber samples at constant applied strain. It was found that the surface free energy increases significantly upon applying a deformation. However, with increasing the carbon black loading fraction the surface tension increase becomes less pronounced. The effect of the surface free energy on the surface damage generated by scratch tests was also discussed. It was found that roll debris formation occurs only in the case of the rubber compounds whose apparent surface free energy increases greatly after applying large bulk deformations.

Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A-infinity relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

Guest–host encapsulation of microporous zeolites in ordered mesoporous materials by molecular simulations

The present work provides the first study of ordered mesoporous materials SBA-15 coated with microporous zeolites ZSM-5 using molecular simulations. Several model structures with characteristics such as periodic arrangement of mesopores, randomly arranged micropores, surface hydroxyls and bulk deformations of SBA-15 were used. Cartesian coordinates of ZSM-5 unit lattice were obtained from the literature and the 100 face of H-ZSM-5 unit cell was then placed on the surface of SBA-15 and the entire structure was equilibrated to obtain final configuration. The resulting structure was characterized using simulated small angle and wide angle X-ray diffraction, Connolly surface area (to compare BET area), accessible pore volume for nitrogen molecules (to compare with t-plot volume of micro and mesopores) and methane adsorption at 303 K. The orientation of ZSM-5 on the SBA-15 had no effect on the surface area, pore volume or adsorption capacity. In order to find out if the addition of microporous ZSM-5 should increase the total methane adsorption capacity due to addition of micropores, we studied adsorption on bare and coated SBA-15. However, total adsorption capacity was found to decrease, while the number of methane molecules adsorbed per unit cell of the SBA-15 structure increased. An existing experimental method (J. Am. Chem. Soc., 2004, 126, 14324) of the synthesizing hybrid ZSM-5/SBA-15 structure was studied using accessible micropore volume (by t-plot). It was found that the procedure made all the micropores inaccessible. A modification of the method or use of other host materials is suggested to use the benefits of narrow micropore distribution in ZSM-5.

Insight into the physics of foam densification via numerical simulation

Foamed materials are increasingly finding application in engineering systems on account of their unique properties. The basic mechanics which gives rise to these properties is well established, they are the result of collapsing the foam microstructure. Despite a basic understanding, the relationship between the details of foam microstructure and foam bulk response is generally unknown. With continued advances in computational power, many researchers have turned to numerical simulation to gain insight into the relationship between foam microstructure and bulk properties. However, numerical simulation of foam microscale deformation is a very challenging computational task and, to date, simulations over the full range of bulk deformations in which these materials operate have not been reported. Here a particle technique is demonstrated to be well-suited for this computational challenge, permitting simulation of the compression of foam microstructures to full densification. Computations on idealized foam microstructures are in agreement with engineering guidelines and various experimental results. Dependencies on degree of microstructure regularity and material properties are demonstrated. A surprising amount of porosity is found in fully-densified foams. The presence of residual porosity can strongly influence dynamic material response and hence needs to be accounted for in bulk (average) constitutive models of these materials.

Modes of detachment at the inclusion–matrix interface

With the help of a 2D theoretical model, this paper analyses the modes of matrix detachment around a circular–elliptical rigid inclusion under pure and simple shear bulk deformations. Three modes of matrix detachment are possible: Mode 1—the matrix is displaced normal to the inclusion boundary, forming fissures at the interface; Mode 2—the matrix slips along the inclusion boundary without any separation; Mode 3—the detachment occurs by a combination of Modes 1 and 2. In order to determine the onset of detachment at any point on the coherent inclusion–matrix interface, the tensile and shear stresses were derived at that point, and compared with imposed critical values. Numerical simulations based on the theoretical model reveal that the three modes occur systematically along the inclusion–matrix interface, the geometrical dispositions of which depend on the aspect ratio ( R) and orientation ( φ) of the inclusion. In the case of circular inclusions, Mode 1 and Mode 2 domains are separated by a Mode 3 domain and the disposition shows an internal symmetry. On the other hand, it is asymmetrical when the inclusions are elliptical and oriented oblique to the bulk extension direction in pure shear and to the shear direction in simple shear. In simple shear, Mode 2 detachment with synthetic slip occurs dominantly when φ is less than 45° and greater than 135°. The results obtained from numerical models are complemented with observations in physical experiments. The paper also determines theoretically the critical stresses for detachment to occur as a function of R for different φ values, revealing that for a given mechanical strength of the inclusion–matrix interface, a particular mode of detachment can take place only when the aspect ratio crosses a threshold value.

The time-dependent bulk response of Poly (Methyl Methacrylate)

The dynamic bulk compliance of Poly (Methyl Methacrylate) (PMMA) hasbeen determined at atmospheric pressure over a wide range oftemperatures and frequencies, following a new examination of the bulkresponse of Poly (Vinyl Acetate) (PVAc) at different pressures. Theoverall bulk behavior of the current measurements of PVAc agrees fairlywell with those reported by Deng and Knauss (1997) at atmosphericpressure, but a discrepancy in primarily the frequency response of thestorage compliance is accredited to a difference in the moisturecontents of the specimens. In PMMA, strong evidence of effects ofphysical aging on the volumetric behavior is observed and a carefulprescription of thermal history was thus necessary to obtain consistentresults. The master curves for the bulk compliance are generated bymeans of the time-temperature superposition principle. A comparison ofthe bulk and shear response shows that the extent of the transitionranges for the two material functions are comparable. Further comparisonof the shift factors for bulk and shear responses supports the idea thatdifferent molecular mechanisms contribute to shear and bulkdeformations. Another key observation regards the time-temperaturesuperposition principle when applied to bulk compliance data of PMMA.The shifting procedure appears to lead to consistent results for temperatures below 92°, however its validity may have to be questionedfor higher temperatures. This failure is tentatively attributed to thepresence of primary (α) and secondary (β) relaxation mechanisms with the latter possibly playing a dominant role in controlling the bulk deformations in the lower temperature range.

Measurement of the Deformation and Adhesion of Rough Solids in Contact

A contact mechanics approach is used to study the impact of deformations on the adhesion between microscopically rough gold and molecularly smooth mica. The surface forces apparatus was used to directly measure deformations at the interface and in the bulk, while also controlling applied loads. Surface forces and applied loads act to deform gold asperities in an unrecoverable fashion. Concurrent bulk deformations, namely the nominal area of contact, are also nonreversible. Using Johnson−Kendall−Roberts theory to interpret these findings illustrates how adhesion between the bodies effectively increases with increasing load. Correlating this phenomenon to deformations at the interface details how adhesion varies when multiple metallic asperities contact and deform under external stress. Moreover, observed hysteresis is explained.

Density functional approach to study the elastic constants of biaxial nematic liquid crystals

A density functional theory for bulk and surface elastic constants of biaxial nematic liquid crystals is developed. It is based on a functional Taylor expansion of the free energy of a distorted biaxial nematic with respect to the one-particle distribution function. Detailed microscopic expressions for the biaxial elastic constants of bulk and surface deformations are derived by expanding further the distribution functions into symmetry-adapted Wigner matrices. The final expressions depend on generalized orientational order parameters characterizing the biaxial nematic and on expansion coefficients of the direct pair correlation function. The case where the expansions are truncated at the lowest nontrivial order with respect to the momentum index of the Wigner matrices is analyzed in detail. It gives only six distinct, nonzero bulk elastic constants. The mixed elastic constants, which measure distortions of more than one director, vanish within this approximation. As in the uniaxial case, a splay-bend degeneracy for all directors is apparent. The theory is next applied to the biaxial nematic phase recently studied by Biscarini et al. [Phys. Rev. Lett. 75, 1803 (1995)] providing numerical estimates of biaxial elastic constants for the case of thermodynamically stable biaxial ordering. It is shown that the values of the elastic constants connected with secondary directors are much lower than those associated with the primary one.

Viscoelastic effective rheologies for modelling wave propagation in porous media

Biot's poroelastic differential equations are modified for including matrix–fluid interaction mechanisms. The description is phenomenological and assumes a solid–fluid relaxation function coupling coefficient. The model satisfies basic physical properties such as, for instance, that P‐wave velocities at low frequencies are lower than those predicted by Biot's theory. In many cases, the results obtained with the Biot (two‐phase) modelling are equal to those obtained with single‐phase elastic modelling, mainly at seismic frequencies. However, a correct equivalence is obtained with a viscoelastic rheology, which requires one relaxation peak for each Biot (P and S) mechanism. The standard viscoelastic model, which generalizes compressibility and shear modulus to relaxation functions, is not appropriate for modelling the Biot complex moduli, since Biot's attenuation is of a kinetic nature (i.e. it is not related to bulk deformations). The problem is solved by associating relaxation functions with each wave modulus. The equivalence between the two modelling approaches is investigated for a homogeneous water‐filled sandstone and a periodically layered poroelastic medium, alternately filled with gas and water. The simulations indicate that, in the homogeneous case, particle velocities in the solid skeleton, caused by a source applied to the matrix, are equivalent to viscoelastic particle velocities. In a finely layered medium, viscoelastic modelling is not, in principle, equivalent to porous modelling, due to substantial mode conversion from fast wave to slow static mode. However, this effect, caused by local fluid‐flow motion, can be simulated by including an additional relaxation mechanism similar to the squirt‐flow.

The Temperature and Frequency Dependence of the Bulk Compliance of Poly(Vinyl Acetate). A Re-Examination

Measurements are described and analyzed for the determination of thedynamic bulk compliance for Poly(vinyl acetate) [PVAc] as a function offrequency and temperature at atmospheric pressure to generate a mastercompliance curve over a total frequency range of about 12 decades.Measurements are based on the compressibility of a specimen confined to anoil-filled cavity resulting from pressurization by a piezoelectricdriver and response of a like receiver. Experimental problems addressinglimitations in resolution capability are discussed. The results arecompared with the classical measurements obtained by McKinney andBelcher over thirty years ago. Further comparison of the bulk with shearcompliance data shows that the extent of the transition ranges for thetwo material functions are comparable, but the two transitions belong todifferent time scales, that of the bulk response falling mostly into theglassy domain of the shear behavior. One concludes thus that forlinearly viscoelastic response the molecular mechanisms contributing toshear and bulk deformations have different conformational sources.

Physiologic motion phantom for MRI applications.

To address the need for a complex physiologic motion phantom for use in MR applications, such as the verification of techniques for measuring myocardial motion dynamics and motion insensitive pulse sequences, a computer-controlled motion phantom has been designed. The phantom, which consists of a deformable silicone gel annulus mounted on a translation stage, can undergo a range of bulk motions and deformations. Available motions include bulk rotation and translation, rotational shear, axial shear, and combinations of some or all of these motions. In this paper, the capability of the phantom to produce accurate constant and time-varying waveforms is demonstrated. In the current implementation, peak linear translation and rotation rates are 175 mm s-1 and 10 rad s-1, respectively. Cycle-to-cycle reproducibility is excellent, with variations of less than .003 radians over the period of hours while undergoing rotational shear. The phantom has been designed in a flexible fashion so that various test objects can be scanned while undergoing bulk translation and can be adapted to produce different deformations.

Hydrodynamic response of a water-rock system to chemical and thermal bulk deformations: L. Y. Yakovlev & L. V. Borevskiy, Geochemistry International, 32(2), 1995, pp 93–103; translated from: Geokhimiya, 7, 1994, pp 1002–1011

Hydrodynamic response of a water-rock system to chemical and thermal bulk deformations: L. Y. Yakovlev & L. V. Borevskiy, Geochemistry International, 32(2), 1995, pp 93–103; translated from: Geokhimiya, 7, 1994, pp 1002–1011

Anechoic and decoupling coating

An anechoic and decoupling coating for use on the surface of an underwatertructure for decoupling structural vibrations from the water and for absorbing waterborne acoustic waves directed toward the structure from an external source such as a sonar. The coating is an elastomeric matrix containing sealed air-filled cavities as well as random labyrinths of small water-filled passages running throughout and in open communication with a surface facing the water. Acoustic waves incident upon the water-facing surface cause time varying shear and bulk deformations within the matrix. As a result of these deformations, acoustic energy is dissipated by hysteretic damping of the elastomeric matrix as well as by viscosity due to water movement to and fro within the passages and into and out of the matrix. The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

A model of a drifting ice cover

Some theoretical ideas are developed concerning the dynamics of a drifting ice cover modelled by a four-phase two-dimensional continuous medium with elastic-plastic rheology under bulk and shearing deformations, including processes of hummocking and the formation of fractures [1]. Phase transition conditions are formulated in closed form, depending in general on eight functions that characterize the rheological properties of the sheet. New exact solutions are developed for the model equations, describing a diverging ice cover drifting in the field of an ocean eddy, the interaction of a diverging ice cover with surface waves, the plastic flow of a close pack ice cover under the influence of a localized sea current, and the collision of a close pack ice massif with a rigid, wedge-shaped wall.

Estimation of paleostress orientation within deformation zones between two mobile plates

The orientation of the principal stress axes within deformation zones between two mobile plates is modeled here analytically, using a thin-plate theory. The simple analytical approach helps to explain why plates cease to move after collision. Orogenic periods last only several tens of million years because the stress associated with a particular constant driving force (causing a constant strain rate) is no longer able to maintain a significant horizontal displacement. In contrast, the uplift rate increases rapidly as the horizontal velocity decreases, and this may explain why the termination of orogenic epochs are usually heralded by the rapid deposition of thick sequences of immature sedimentary rocks or flysch. The analytical model also elaborates the relationship between homogeneous bulk deformations driven by a constant stress orientation and those due to a fixed displacement direction of physical boundaries of the deformation zone. Two major kinematic possibilities are considered: (1) plates converging either orthogonally or obliquely, making the deformation zone an analogue for orogenic collision; and (2) plates diverging either orthogonally or obliquely, so that the deformation zone is dynamically similar to initiating rift basins. The theoretical investigation led to the formulation of the following rules. Deformation zones between converging plates have the major axis of bulk deviatoric stress coinciding with the bisector of the acute angle between the relative plate velocity vector and the normal to the deformation- zone boundary. In case of extension within a deformation or rift zone separating diverging plates, the bisector will outline the minor axis of the bulk deviatoric stress. The deformation tensor of the analytical model yields a new method for estimating the orientation of paleostress in natural examples, here applied to the deformed wall rock of the Moroccan Border fault. The marker used is a competent sequence of Devonian sandstone and limestone asymmetrically folded adjacent to the dextral Border fault. The steeply plunging Z-folds of the marker beds suggest that the principal deviatoric paleostress, τ 1 , was oriented 37°-44° to the fault trace. The age of the Moroccan Border fault is poorly constrained and may be Variscan or younger. The τ 1 orientation implies a major component of simple shear parallel to the strike-slip fault and a minor component of extension perpendicular to the fault trace. The implied crustal movement is compatible with the modern tectonics of the Eurasian-African collision zone where part of the differential motion between the Eurasian and African plates is accommodated by strike-slip faults.

Mathematical modeling of the transformation processes of supercooled austenite in eutectoid steels

A dilatometric investigation of the kinetics of the structural transformations for steel 75Kh2GNMF on a LINSEIS-built dilatometer, which was equipped with an electronic unit for recording displacements and temperature, was conducted to substantiate the algorithm for computing the phase composition and bulk deformations.

A New Generation Process and Matrix Representation of Disclinations in Nematic and Cholesteric Liquid Crystals

Abstract Disclinations in nematic liquid crystals are described as transitions between two different states of quantized bulk deformations in a layer. The quantized states of deformation are due to well defined uniform boundary conditions, which allow only discrete solutions of the partial Euler differential equations governing the deformation. A new continuous generation process for the non-singular disclinations of integer strength is discussed. The local turns of the director field, involved in this process, can be used for an algebraic description of the topological properties of the disclinations. This formalism can also be applied to disclinations of half integer strength and to disclinations in cholesteric liquid crystals. From this theory, the existence of stable disclinations of the strength s = 0 can be predicted. Disclinations of integer strength are created by an experimental process analogous to the new theoretical generation process. Experimental evidence for the existence of disclinations o...

Characteristic features of the deformation process on creep and secondary creep of polymers under conditions of monaxial tensioning. Part I

Experiments carried out in the field of linear and nonlinear creep of a filled polyethylene and Teflon resin, including two complete cycles of creep and deformation recovery at monaxial tensioning, show that the bulk deformations ϑ(t) change nonmonotonically, and relationships computed by summation of terms containing a function of time cannot be used to approximate the deformation.

Creep and the time dependence of the strength in rocks

1. Experiments reveal not only a quantitative difference but also a qualitative discrepancy between the model of a continuous medium on which the mechanics of deformed bodies is based and the properties of a real solid. Thus for salt rocks it is found that the volume increases owing to gradual opening-up and development of defects and microcracks. The effect of compaction, found in Cambrian clay, is influenced by drying-out of the material during an experiment, by closing of pores and gaps, and by recrystallization processes which occur during longterm tests. The time factor involves serious changes in our ideas on the behavior of a solid under load. Bulk deformations may exert a serious influence on the formation of the state of stress in the solid rock; in particular, in the abutment pressure zone, the expansion effect may create an additional force which tends to eject the rock into the worked-out area this is especially important in the problem of shock bumps and rock bursts. A decrease of volume reduces the repulsive force directed towards the worked-out area. 2. As a result of laboratory tests on creep and long-term strength in specimens of potash salt and Cambrian clay, it is found that the creep rate\(\dot \varepsilon _1\) is related, within the investigated range of conditions, to the stress as follows: $$\dot \varepsilon _1 = \dot \varepsilon _0 e^{\alpha \sigma }$$ (1) . The relation between the endurance t and the stress is $$t = t_0 e^{ - \alpha \sigma }$$ (2) . 3. Experiments reveal that the coefficient \ga in Eq. (1) is nearly equal to that in Eq. (2). 4. Since the absolute values of \ga in Eqs. (1) and (2) are nearly equal, it is suggested that the acting stresses and times to fracture of salt pillars should be determined from the known creep rates.