Evidence for Fisher renormalization in the compressible phi4 model

We present novel Fourier Monte Carlo simulations of a compressible phi4-model on a simple-cubic lattice with linear-quadratic coupling of order parameter and strain, focusing on the detection of fluctuation-induced first-order transitions and deviations from standard critical behavior. The former is indeed observed in the constant stress ensemble and for auxetic systems at constant strain, while for regular isotropic systems at constant strain, we find strong evidence for Fisher-renormalized critical behavior and are led to predict the existence of a tricritical point.     

Interfaces of correlated electron systems: proposed mechanism for colossal electroresistance

Mott's metal-insulator transition at an interface due to band bending is studied by the density matrix renormalization group approach. We show that the result can be recovered by a simple modification of the conventional Poisson's equation approach used in semiconductor heterojunctions. A novel mechanism of colossal electroresistance is proposed, which incorporates the hysteretic behavior of the transition in higher dimensions.     

Giant Auxetic Behaviour in Engineered Graphene

Graphene monolayers engineered to adopt a corrugated conformation are found to exhibit very pronounced lateral expansion characteristics upon uniaxial stretching in specific directions, i.e. giant negative Poisson's ratio (auxeticity). Such anomalous properties are manifested in‐plane and may be controlled through the shape and amplitude of the wave‐like pattern of the corrugation, which in the case of graphene may be controlled through the introduction of patterned ‘defects’. This confirms that auxeticity via corrugation can be achieved even at the nanoscale, as demonstrated here for graphene with patterned ‘defects’, suggesting that this mechanism should be operational at different scales of structures, thus providing a new blueprint for the design or manufacture of auxetic materials and metamaterials which can have tailor‐made giant negative Poisson's ratio properties.     

Pressure-driven "molecular metal" to "atomic metal" transition in crystalline Ga

We present the ultrasonic study of gallium (Ga I) under high pressure up to 1.7 GPa, including the measurements of the density and elastic properties during phase transitions to Ga II and to a liquid state. The observed large drop of both bulk and shear moduli (by 30% and 55%, correspondingly) during the phase transition to Ga II, as well as the increase of the Poisson's ratio from typically "covalent" ( approximately 0.22) to "metallic" ( approximately 0.32) values, experimentally testifies to the coexistence of a molecular and metallic behavior in Ga I and to the disappearance of the "covalency" during the transition to Ga II. A high value of the pressure derivative of the bulk modulus for Ga I and the increase in the Poisson's ratio can be associated with the weakening of the covalency in compressed Ga I and considered as a precursor of the transition to normal metal.     

Universal negative poisson ratio of self-avoiding fixed-connectivity membranes

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be sigma = -0.37(6), in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes sigma = -0.32(4). Together with the equality of critical exponents, this result implies a unique universality class for fixed-connectivity membranes. Our findings thus establish that physical fixed-connectivity membranes provide a wide class of auxetic (negative Poisson ratio) materials with significant potential applications in materials science.     

On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

晶体非线弹性变形的原子级模拟研究

采用分子静力学结合量子修正Sutten-Chen型多体势研究了Ni单晶体在受单向拉伸和压缩载荷作用下的弹性响应.考虑了三种加载方式,即［001］,［011］和［111］单向加载.模拟的结果表明：晶体在［011］单向加载下的弹性变形表现出强烈的非线性效应,然而沿［001］和［111］单向加载时,它的横向变形表现为各向同性.进一步讨论了杨氏模量和泊松比与应变的关系,并和第一性原理计算的结果做了比较. 关键词： 晶体 弹性变形 分子静力学     

Effects of the orientational distribution of cracks in solids

We derive a theory for the elastic characterization of multicracked solids based on a homogenization technique. We consider a material containing a two-dimensional arbitrary distribution of parallel slit cracks which is elastically equivalent to a crystal with orthorhombic symmetry. We obtain explicit expressions for the macroscopic elastic stiffness tensor which is found to depend upon both the density of cracks and their angular distribution, here described by a suitable order parameter. For the isotropic case, we find that the degradation depends exponentially on the crack density. In addition, we show an unusual elastic behavior of a multicracked medium in the plane strain condition: for a negative Poisson ratio, we obtain an effective Young modulus greater than the actual value of the host matrix.     

基于等效参数反演的敷设声学覆盖层的水下圆柱壳体声散射研究

应用了一种等效方法计算敷设声学覆盖层无限长圆柱壳体水下声散射特性.等效方法的核心是忽略复杂声学覆盖层内部的声学结构,将其作为具有等效材料参数的均匀阻尼层进行建模,该均匀阻尼层具有和原覆盖层相同的复反射系数.进而,应用COMSOL Multiphysics软件建立敷设均匀阻尼层圆柱壳体的有限元模型并求解其声散射特性.等效方法的关键是等效材料参数的获取.采用充水阻抗管实验和有限元数值实验两种方法获取声学覆盖层贴敷在与壳体具有相同厚度、相同材料背衬条件下的复反射系数,在此基础上,基于遗传算法反演材料的等效参数.研究表明,等效参数具有频变特性,且尽管等效杨氏模量和等效泊松比在频率范围内存在较大波动,但是等效前后复反射系数仍保持一致.为了验证等效方法求解壳体声散射特性的准确性,同时建立了敷设声学覆盖层壳体的完整有限元模型,将覆盖层内部声学结构进行精细建模,并求其声散射特性.结果表明,两种方法求得的形态函数符合得较好,在整个频率范围内平均误差大约为1 d B.     

Jump relations for shocks in an anisotropic magnetized plasma

The jump relations for shocks moving into a collision-free anisotropic magnetized plasma are investigated under the assumption of isotropy of the plasma behind the shock front. The plasma ahead of the shock is assumed to be stable against the fire-hose instability and the mirror instability. In order to facilitate comparison with the work of Bazer and Ericson on isotropic shocks our nomenclature has been adapted to theirs. It turns out that as in the case of isotropic shocks the density ratio can be at most four corresponding to γ=5/3, that the change in magnetic field is bounded and that except for the case of Alfvén shocks the transverse parts of the magnetic field are collinear. It is further shown that the influence of the anisotropy is greatest for nearly equal thermal and magnetic energy densities. In the case of negative anisotropy no compressive shocks are possible with a major decrease in magnetic field if the thermal energy density much exceeds the magnetic energy density. A new kind of shock is shown to result from the analysis, the major effect of which is to destroy the anisotropy with only small changes in density, magnetic field and velocity vector. Its propagation speed is unbounded. Furthermore it has turned out that compressive, magnetic field increasing shocks have lower bounds in the density jump and magnetic field change for negative and positive anisotropy, respectively. In the collision-free case no unique entropy condition depending only on the total pressure components and densities can be given before the solution of the problem of shock structure. Therefore even expansive shocks may be admissible. The applicability of the isotropy assumption and ad-hoc-assumptions of other authors are briefly discussed.     

Non-equilibrium critical behavior of O(n)-symmetric systems

Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures and in - and -dimensional subspaces, respectively. In the case of the Sasvári-Schwabl-Szépfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the -dimensional sector in wavevector space with lower noise temperature . The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for .We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and , i.e., about the equilibrium theory.     

Estimation of dynamic elastic constants from the amplitude and velocity of Rayleigh waves

In this paper a method is proposed to characterize the elasticity of isotropic linear materials from the generation and detection of an acoustic surface wave. For the calculation of the elastic constants, it is sufficient that only one of the faces of the sample be accessible. The methodology is based on both the measurement of the Rayleigh wave velocity and on the determination of the normal to longitudinal amplitude ratio calculated from the normal and longitudinal components of the displacement of a point. The detection of two consecutive surface wave pulses using a single experimental setup permits the determination of the elastic constants. The method is applied to calculate Young's modulus and Poisson's ratio of an aluminum sample as well as their systematic uncertainties. The results obtained give a relative uncertainty for Young's modulus on the order of the sixth part of that calculated for Poisson's ratio.     

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson's ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.     

Representation surfaces of Young''s modulus and Poisson''s ratio for BCC transition metals

 The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l) along an arbitrary direction [h k l] are given for cubic crystals. The representation surfaces, for which the length of the radius vector in the [h k l] direction equals to E(h k l) or υ(h k l), are constructed for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic, both representation surfaces of Young's modulus and Poisson's ratio are spherical surfaces. The remaining BCC transition metals may be grouped into two classes. In the first group (Cr, Mo, Nb and V) with negative values of s_A, Young's modulus surface has eight depressed corners and six rounded protuberances at the centers of the faces. In the second group (Fe and Ta) with positive values of s_A, on the contrary, Young's modulus surface has eight rounded protuberance corners and six depressions at the centers of the faces. The contrary conclusions are obtained for Poisson's ratio.     

Auxetic metamaterials exhibiting giant negative Poisson's ratios

Auxetic metamaterials have generated a great deal of interest in recent years. In this letter, a novel approach which can be used to produce such auxetic metamaterials is presented. This method involves the introduction of patterned slit perforations within a sheet/block of material in order to create systems which resemble a large variety of auxetic systems ranging from rotating units to chiral honeycombs. These perforated systems have also been shown to have the potential to exhibit giant negative Poisson's ratios. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

A universe embedded in a five-dimensional flat space

Since a homogeneous isotropic universe can be embedded in a flat space of five dimensions, the question is considered under what conditions a more general universe can be embedded in a five-dimensional flat space. On the assumption that the deviation from homogeneity is small, it is found that real inhomogeneities can occur only in the case of a universe filled with radiation, or a universe containing at least two different substances with different equations of state, as for example radiation and matter. In the case of a radiation-filled universe, the inhomogeneities can be of arbitrary size and can conceivably be the precursors of galaxies.     

结构和变形对单壁碳纳米管力学性能的影响

使用分子动力学方法模拟了单壁碳纳米管的拉伸变形行为和泊松比,并从单壁碳纳米管晶胞单元的结构特征角度,系统分析了管径、螺旋性和应变对力学性能的影响．模拟结果显示,单臂性碳纳米管(8,8)-(22,22)和锯齿性碳纳米管(9,0)-(29,0)的拉伸弹性变形可以分别达到35％-38％和20％-27％,拉伸条件下这些碳纳米管的弹性模量随管径的增大从960 GPa下降到750 GPa,并且锯齿性碳纳米管的弹性模量比单臂性碳纳米管的弹性模量要高．通过对三根具有相同直径和不同螺旋性的碳纳米管(9,9),(12,6)和(16,0)分别在拉伸和压缩条件下的模拟发现,随着变形的增大,碳纳米管的泊松比将减小;在相同的拉伸应变下,碳纳米管的泊松比随其螺旋角的减小而减小,而在相同的压缩应变下,碳纳米管的泊松比随其螺旋角的减小而增大．     

Elastic characterization of closed cell foams from impedance tube absorption tests

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.     

A study of the secular equation for rayleigh waves using the root locus method

In a recent note Rahman and Barber [Trans. ASME 62 (1995) 250] proposed an exact expression for the roots of the secular equation for the Rayleigh waves in an isotropic half-space. Using the root locus method, we describe in a very simpler manner the evolution of the roots versus the Poisson's ratio and we derive easily the critical value for which the nature of the roots changes.     

Spin-controlled negative magnetoresistance resulting from exchange interactions

We studied conductivity of AlGaAs–GaAs quantum well structures (where centers of the wells were doped by Be) at temperatures higher than 4 K in magnetic fields up 10 T. Throughout all the temperature region considered the conductivity demonstrated activated behavior. At moderate magnetic fields 0.1 T < H < 1 T, we observed negative isotropic magnetoresistance, which was linear in magnetic field while for magnetic field normal with respect to the plane of the wells the magnetoresistance was positive at H > 2T. To the best of our knowledge, it was the first observation of linear negative magnetoresistance, which would be isotropic with respect to the direction of magnetic field. While the isotropic character of magnetoresistance apparently evidences role of spins, the existing theoretical considerations concerning spin effects in conductance fail to explain our experimental results. We believe that such a behavior can be attributed to spin effects supported by exchange interactions between localized states.