The dynamics of cracks in torn thin sheets

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.Comment: 7 pages, 11 figure

Flexoelectric effect in finite samples

Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where there is the polarization is nonzero at the surface, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It was argued that this conflict may be resolved when using modified mechanical boundary conditions. It was also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including the material with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect

Frictional sliding without geometrical reflection symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.Comment: 14 pages, 5 figures + Supplementary Material. Minor change in the title, extended analysis in the second par

Conformational transitions of heteropolymers in dilute solutions

In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are transformed to a form containing only the mean squared distances between pairs of monomers. These equations are further expressed in terms of instantaneous gradients of the variational free energy. The method allowed us to study exhaustively the stability and conformational structure of some periodic and random aperiodic sequences. A typical phase diagram of a fairly long amphiphilic heteropolymer chain is found to contain phases of the extended coil, the homogeneous globule, the micro-phase separated globule, and a large number of frustrated states, which result in conformational phases of the random coil and the frozen globule. We have also found that for a certain class of sequences the frustrated phases are suppressed. The kinetics of folding from the extended coil to the globule proceeds through non-equilibrium states possessing locally compacted, but partially misfolded and frustrated, structure. This results in a rather complicated multistep kinetic process typical of glassy systems.Comment: 15 pages, RevTeX, 20 ps figures, accepted for publication in Phys. Rev.

Pinning of a two-dimensional membrane on top of a patterned substrate: the case of graphene

We study the pinning of a two-dimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the strain dominated regimes. We find that both the in-plane strains and the bending rigidity can lead to depinning. We show from energetic arguments that the system experiences a first order phase transition between the attached configuration to a partially detached one when the relevant parameters of the substrate are varied, and we construct a qualitative phase diagram. Our results are confirmed through analytical solutions for some simple geometries of the substrate's profile.Comment: Minor changes. Final version, as publishe

Is it possible to assign physical meaning to field theory with higher derivatives?

To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in mechanical engineering. It enables one to introduce the notion of a "mechanical" energy in such field models that is wittingly positive definite. This approach can be applied at least to the higher derivative models which effectively describe the extended localized solutions in usual first order field theories (vortex solutions in Higgs models and so on). Any problems with a negative norm ghost states and unitarity violation do not arise here.Comment: 16 pp, LaTeX, JINR E2-93-19

Hydration of a B-DNA Fragment in the Method of Atom-atom Correlation Functions with the Reference Interaction Site Model Approximation

We propose an efficient numerical algorithm for solving integral equations of the theory of liquids in the Reference Interaction Site Model (RISM) approximation for infinitely dilute solution of macromolecules with a large number of atoms. The algorithm is based on applying the nonstationary iterative methods for solving systems of linear algebraic equations. We calculate the solvent-solute atom-atom correlation functions for a fragment of the B-DNA duplex d(GGGGG).d(CCCCC) in infinitely dilute aqueous solution. The obtained results are compared with available experimental data and results from computer simulations.Comment: 9 pages, RevTeX, 9 pages of ps figures, accepted for publications in JC

Relationship between cyclooxygenase-2 and human epidermal growth factor receptor 2 in vascular endothelial growth factor C up-regulation and lymphangiogenesis in human breast cancer

Both cyclooxygenase (COX)-2 and human epidermal growth factor receptor (HER)-2 promote breast cancer progression; however, the relationship between the two molecules remains unclear. We utilized human breast cancer tissues and cell lines to examine whether COX-2 and HER-2 played independent or interdependent roles in vascular endothelial growth factor (VEGF)-C up-regulation and lymphangiogenesis. A paired correlation of immunodetectable levels of COX-2, VEGF-C, and HER-2 proteins and lymphovascular density (LVD; D2-40-immunolabeled) in 55 breast cancer specimens revealed a positive correlation between COX-2 and HER-2 irrespective of clinicopathological status. However COX-2 alone positively correlated with LVD. In 10 independent specimens, mRNA levels showed a positive correlation between HER-2 and COX-2 or VEGF-C but not LYVE-1 (lymphovascular endothelial marker). These findings implicate COX-2, but not HER-2, in breast cancer-associated lymphangiogenesis. Manipulation of the COX-2 or HER-2 genes in breast cancer cell lines varying widely in COX-2 and HER-2 expression revealed a direct role of COX-2 and an indirect COX-2 dependent role of HER-2 in VEGF-C up-regulation: (i) high VEGF-C expression in high COX-2/low HER-2 expressing MDA-MB-231 cells was reduced by siRNA-mediated down-regulation of COX-2, but not HER-2; (ii) integration of HER-2 in these cells simultaneously up-regulated COX-2 protein as well as VEGF-C secretion; and (iii) low VEGF-C secretion by high HER-2/low COX-2 expressing SK-BR-3 cells was stimulated by COX-2 overexpression. These findings of the primary role of COX-2 and the COX-2-dependent role of HER-2, if any, in VEGF-C up-regulation and lymphangiogenesis suggest that COX-2 inhibitors may abrogate lymphatic metastasis in breast cancer irrespective of HER-2 status. © 2010 Japanese Cancer Association

Mechanical Instabilities of Biological Tubes

We study theoretically the shapes of biological tubes affected by various pathologies. When epithelial cells grow at an uncontrolled rate, the negative tension produced by their division provokes a buckling instability. Several shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all of which are found in pathologies of tracheal, renal tubes or arteries. The final shape depends crucially on the mechanical parameters of the tissues : Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey information as to what causes the pathology. We calculate a phase diagram of tubular instabilities which could be a helpful guide for investigating the underlying genetic regulation