Sensitivity analysis of an optimized bar-spring model with hill-top branching

Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point.     

Writhing instabilities of twisted rods: from infinite to finite length

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.     

Hard collisions of spinning protons: Past,present and future

There will be a review of the history of polarized proton beams, and a discussion of the unexpected and still unexplained large transverse spin effects found in several high-energy proton-proton spin experiments at the ZGS, AGS and Fermilab. Next, there will be a discussion of present and possible future experiments on the violent elastic collisions of polarized protons at IHEP-Protvino's 70GeV U-70 accelerator in Russia and the new high-intensity 50GeV J-PARC facility being built at Tokai in Japan.     

Point load determination of static elastic moduli using laser speckle interferometry

Electronic speckle interferometry (ESPI) is used to determine the Young's modulus E and Poisson ratio ν of an isotropic material. Micron scale deformations of the surface of the block of polymethyl-methacrylate (PMMA) are induced by normal application of a known near-point force. These deformations are recorded in speckle interferometric fringe patterns. An iterative minimum error inversion technique is developed to obtain the elastic properties from the positions of fringe peaks and troughs observed in the fringe patterns. Sensitivity tests of the method on calculated fringe patterns using measured experimental uncertainties suggest the technique will provide measures of the elastic moduli to better than 5%. In an experimental test on a bloc of PMMA (acrylic) the technique gave values of E and ν that differed from corresponding measures obtained using more conventional strain-gauge methods by less than 4%.     

Dynamic supercoiling bifurcations of growing elastic filaments

Certain bacteria form filamentous colonies when the cells fail to separate after dividing. In Bacillus subtilis, Bacillus thermus, and Cyanobacteria, the filaments can wrap into complex supercoiled structures as the cells grow. The structures may be solenoids or plectonemes, with or without branches in the latter case. Any microscopic theory of these morphological instabilities must address the nature of pattern selection in the presence of growth, for growth renders the problem nonautonomous and the bifurcations dynamic. To gain insight into these phenomena, we formulate a general theory for growing elastic filaments with bending and twisting resistance in a viscous medium, and study an illustrative model problem: a growing filament with preferred twist, closed into a loop. Growth depletes the twist, inducing a twist strain. The closure of the loop prevents the filament from unwinding back to the preferred twist; instead, twist relaxation is accomplished by the formation of supercoils. Growth also produces viscous stresses on the filament which even in the absence of twist produce buckling instabilities. Our linear stability analysis and numerical studies reveal two dynamic regimes. For small intrinsic twist the instability is akin to Euler buckling, leading to solenoidal structures, while for large twist it is like the classic writhing of a twisted filament, producing plectonemic windings. This model may apply to situations in which supercoils form only, or more readily, when axial rotation of filaments is blocked. Applications to specific biological systems are proposed.     

Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust

This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.     

基于变截面梁的光纤光栅线性无啁啾调谐

从理论上分析了利用变截面（等强度）弹性梁实现光纤光栅波长线性、无啁啾调谐的基本原理，给出了实现无啁啾波长调谐的弹性梁截面满足条件及其设计方案，并讨论了矩形等截面和变截面悬臂梁调谐方案的特点.理论分析与实验结果均表明，通过对变截面梁侧向施加载荷，可以实现光纤光栅中心波长的线性无啁啾调谐，且系统结构简单、易于设计.     

Elastic incoherent neutron scattering studies on glass forming hydrogen-bonded systems

Neutron incoherent elastic scattering data have been collected on homologues disaccharides (trehalose, maltose, sucrose)/H₂O mixtures as a function of temperature. The results show a dynamical transition at T238 K, T235 K and T233 K for trehalose, maltose and sucrose/H₂O mixtures, respectively, marking a cross-over in molecular fluctuations between harmonic and non-harmonic dynamical regimes, proving a higher ‘rigidity’ of trehalose mixture with respect to maltose and sucrose mixtures. This finding accounts for the higher cryptobiotic effectiveness of trehalose, namely a capability to encapsulate biostructures in a more rigid environment.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

Elliptic cross section without warping under torsion

The object of this paper is the pure torsion of the nonhomogeneous anisotropic elastic beam. The results of Saint-Venant’s theory of uniform torsion are used to prove a nonwarping property of elliptic cylinders.