Effective stiffness properties (D) of nanosized structural elements such as plates and beams differ from those predicted by standard continuum mechanics (D c ). These differences (D − D c )/D c depend on the size of the structural element. A simple model is constructed to predict this size dependence of the effective properties. The important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk. In general, the non-dimensional difference in the elastic properties from continuum predictions (D − D c )/D c is found to scale as αS/Eh, where α is a constant which depends on the geometry of the structural element considered, S is a surface elastic constant, E is a bulk elastic modulus and h a length defining the size of the structural element. Thus, the quantity S/E is identified as a material length scale for elasticity of nanosized structures. The model is compared with direct atomistic simulations of nanoscale structures using the embedded atom method for FCC Al and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.
Elastic properties of crystal surfaces are useful in understanding mechanical properties of nanostructures. This paper presents a fully nonlinear treatment of surface stress and surface elastic constants. A method for the determination of surface elastic properties from atomistic simulations is developed. This method is illustrated with examples of several crystal faces of some fcc metals modeled with embedded atom potentials. The key finding in this study is the importance of accounting for the additional relaxations of atoms at the crystal surface due to strain. Although these relaxations do not affect the values of surface stress ͑as had been determined in previous works͒, they have a profound effect on the surface elastic constants. Failure to account for these relaxations can lead to values of elastic constants that are incorrect not only in magnitude but also in sign. A possible method for the experimental determination of the surface elastic constants is outlined.
We investigate a new type of surface instability of a thin elastic film subjected to surface interactions such as van der Waals and electrostatic forces from another solid surface in its vicinity. It is found that a sufficiently soft (shear modulus <10 MPa) and nearly incompressible film deforms to form an undulating pattern without any mass transport. A novel feature is that the characteristic length scale of the pattern is nearly independent of the nature and magnitude of the external force, but varies linearly with the film thickness. These results explain some recent experiments and are applicable to problems such as adhesion and friction at soft solid interfaces, peeling of adhesives, patterning of solid surfaces, etc.
5We investigate the ground state of interacting spin-1 2 fermions in 3D at a finite density (ρ ∼ k 3 F ) 6 in the presence of a uniform non-Abelian gauge field. The gauge field configuration (GFC) described 7 by a vector λ ≡ (λx, λy, λz), whose magnitude λ determines the gauge coupling strength, generates 8 a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel 9 described by a small negative scattering length (kF |as| 1), the ground state in the absence of the 10 gauge field (λ = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs.
11With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS 12 ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction
A new kind of meniscus instability leading to the formation of stationary fingers with a well-defined spacing has been observed in experiments with elastomeric films confined between a plane rigid glass and a thin curved glass plate. The wavelength of the instability increases linearly with the thickness of the confined film, but it is remarkably insensitive to the compliance and the energetics of the system. However, lateral amplitude (length) of the fingers depends on the compliance of the system and on the radius of curvature of the glass plate. A simple linear stability analysis is used to explain the underlying physics and the key observed features of the instability.
Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films.
We study the bound states of two spin-1 2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in 3D space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba type spin-orbit interaction is described by three coupling parameters (λx, λy, λz). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the "BCS side" of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., λx = λy = λz) for which there is a two body bound state for any scattering length however small and negative. Remarkably, the bound state wave functions obtained for high-symmetry configurations have nematic spin structure similar to those found in liquid 3 He. Our results show that the BCS-BEC crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.
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