On the third- and fourth-order constants of incompressible isotropic elasticity

Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity μ, ā, and D are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.     

Acoustic radiation force optical coherence elastography for elasticity assessment of soft tissues

Biomechanical properties of soft tissues are important indicators of tissue functions which can be used for clinical diagnosis and disease monitoring. Elastography, incorporating the principles of elasticity measurements into imaging modalities, provides quantitative assessment of elastic properties of biological tissues. Benefiting from high-resolution, noninvasive, and three-dimensional optical coherence tomography, optical coherence elastography (OCE) is an emerging optical imaging modality to characterize and map biomechanical properties of soft tissues. Recently, acoustic radiation force (ARF)–OCE has been developed for elasticity measurements of ocular tissues, detection of vascular lesions, and monitoring of blood coagulation based on remote and noninvasive ARF excitation to both internal and superficial tissues. Here, we describe the advantages of the ARF–OCE technique, the measurement methods in ARF–OCE, the applications in biomedical detection, current challenges, and advances. ARF–OCE technology has the potential to become a powerful tool for in vivo elasticity assessment of biological samples in a noncontact, noninvasive, and high-resolution nature.     

On soft gluon emission and the transverse momentum properties of final state particles

We discuss the infrared problem in a theory with confined quarks and gluons. In QED, the infrared cutoff depends on the adjustable experimental energy resolution. For QCD, the physical observables of the asymptotic final state are the hadron momenta whereas the gluon momenta do not correspond to observable quantities. Thus the energy resolution of a “gluon detector” is determined by the hadronic mass scale. In particular, we study the effect of soft gluon emission on the transverse momentum of the hadrons.     

Decomposition of (Co)isotropic Relations

We identify 13 isomorphism classes of indecomposable coisotropic relations between Poisson vector spaces and show that every coisotropic relation between finite-dimensional Poisson vector spaces may be decomposed as a direct sum of multiples of these indecomposables. We also find a list of 13 invariants, each of which is the dimension of a space constructed from the relation, such that the 13-vector of multiplicities and the 13-vector of invariants are related by an invertible matrix over \({\mathbb{Z}}\). It turns out to be simpler to do the analysis above for isotropic relations between presymplectic vector spaces. The coisotropic/Poisson case then follows by a simple duality argument.     

Phase transitions and soft elasticity of smectic elastomers

Smectic-C elastomers can be prepared by cross-linking, e.g., liquid crystal polymers, in the smectic-A phase followed by a cooling through the smectic-A to smectic-C phase transition. This transition from D(infinityh) to C(2h) symmetry spontaneously breaks rotational symmetry in the smectic plane as does the transition from a smectic-A to a biaxial smectic phase with D(2h) symmetry. We study these transitions and the emergent elasticity of the smectic-C and biaxial phases in three related models and show that these phases exhibit soft elasticity analogous to that of nematic elastomers.     

Biomechanical properties of soft tissues

Viscoelasticity is the primary mechanical property of bio-soft tissues. It has been widely applied in basic research of biological tissues including cornea, lung, heart and blood vessels. Along with the development of tissue engineering research, the evaluation of soft tissue viscoelasticity is becoming more and more important. In this paper, using the Whittaker function, we give an approximate power series of the exponential integralE ₁(X) and the parametersC, ?₁ and ?₂ of the generalized relaxation functionG(t) and generalized creep functionJ(t). With expanded skin as an example, the relationship between stress relaxation, creep and stress-strain finite deformation are studied.     

Morphogenesis of growing soft tissues

Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behavior in biology, chemistry, and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the F?ppl-von Kármán type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.     

On the microscopic foundations of elasticity

The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first step, microscopically exact expressions for the displacement, strain and stress fields are derived. Conditions under which linear elastic constitutive relations hold are studied theoretically and numerically. It turns out that standard continuum elasticity is not self-evident, and applies only above certain spatial scales, which depend on details of the considered system and boundary conditions. Possible relevance to granular materials is briefly discussed. Received 18 March 2002 and Received in final form 29 May 2002     

Diffraction enhanced imaging of soft tissues

The APS hosted a two-day workshop on Catalysis Research at the APS on September 12-13, 2005. The goal of the workshop was to evaluate current catalysis-related research at the APS and to plan future directions. The outcome of the meeting will be a report with recommendations to promote new, and support current, catalysis research at the APS. The workshop was attended by 82 participants representing industry, national laboratories, and universities.     

On the nonergodicity of the transverse magnetization in the transverse Ising model

The nonergodic behavior exhibited by the transverse spin correlation function _q=0 ^xx (t) the transverse Ising model obtained as the solution of approximate kinetic equations (derived on the basis of Résibois and De Leener's method), is shown to be an intrinsic property of the model and not the result of the approximations made in the derivation of the kinetic equations.Chargé de Recherches au Fonds National Belge de la Recherche Scientifique.     

Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–54, December, 1985.     

水平层状横向同性地层中频率测深资料全参数快速迭代反演

提出水平层状横向同性地层中频率测深资料的全参数快速迭代反演算法,以便从测量资料中同时确定各个地层的横向、 纵向电导率及层界面深度.首先,利用水平层状介质中电磁场并矢Green函数在频率波数域中的解析解和Sommerfeld积分的 快速计算技术确定正演响应.然后,利用摄动理论和Fourier逆变换公式,研究建立一套快速求解全参数Fréchet导数的 有效算法,并利用规范化处理和奇异值分解技术给出迭代反演过程.最后,给出数值试验证明反演理论的有效性以及反演算法 的抗噪声能力.     

Anisotropic elasticity of DyScO(3) substrates

The full elastic tensor of orthorhombic dysprosium scandate (DyScO(3)) at room temperature was determined by resonant ultrasound spectroscopy (RUS). Measurements were performed on three 500?μm thick substrates with orientations (110), (100) and (001) in the Pbnm (a?相似文献   

On the coherent self-oscillation mechanism under transverse breakdown in n-InSb (T = 77 K)

A nonlinear theory of self-oscillation in crossed electric and magnetic fields is worked out. Effects of the magnetic field intensity, sample dimensions, and surface recombination rate on the generation conditions of coherent (monochromatic) self-oscillations are studied. A domain model of coherent self-oscillations excited under transvere breakdown and strong magnetoconcentration effect is proposed. Numerical calculations for n-InSb (T = 77 K) are carried out. Coherent self-oscillations are shown to be induced for frequencies ～ 10¹⁰ Hz.     

The role of the 14N(n,p)14C reaction in neutron irradiation of soft tissues

The cell-killing potential of the ¹⁴N(n,p)¹⁴C reaction was considered with regard to neutron absorption in human nuclear DNA and respiratory phosphates for: (A) 10¹² thermal neutrons in 1 kg of soft tissue, (B) a mono-energetic beam of 2 MeV neutrons incident in 1 kg of soft tissue such that the total collision kerma was 10 J/kg, and (C) an evenly distributed 0–66 MeV neutron beam, also incident in 1 kg such that the total collision kerma was 20 J/kg. For case (A) 0.0017 ¹⁴N(n,p)¹⁴C reactions could be expected per DNA double strand, case (B) 0.053, and case (C) 0.0039. The probabilities that a proton emitted outside the nucleus would cross nuclear DNA were estimated from ¹⁴N tissue content for adult skeletal muscle, liver, and kidney tissues, for (1) nuclear DNA being concentrated in a sphere of 1.8 μm diameter, and (2) nuclear DNA being evenly distributed in a spherical nucleus 5 μm in diameter. It was concluded that even in a nitrogen-rich tissue exposed to a collision kerma of 20 J/kg by a 0–66 MeV fast neutron beam, the ¹⁴N(n,p)¹⁴C reaction directly kills at most 10 cells in every 1000, 4 of these by DNA nitrogen absorption and 6 by the ¹⁴N(n,p)¹⁴C protons emitted elsewhere in the cell. However, the dose due to the ¹⁴N(n,p)¹⁴C reaction should be measured where exposure to thermal neutron fluxes is significant. For therapeutic neutron doses the number of respiratory phosphate molecules in which the ¹⁴N(n,p)¹⁴C reaction occurs is insignificant, and doses from ¹⁴C-decay after neutron therapy are also negligible.     

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke’s law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.