Interplay of internal stresses, electric stresses and surface diffusion in polymer films

We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and second due to an externally applied electric field normal to the film's free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes as e.g. spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films: when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and the free surface.Comment: 14 pages, 7 figures, 1 tabl

Finite-time Singularities in Surface-Diffusion Instabilities are Cured by Plasticity

A free material surface which supports surface diffusion becomes unstable when put under external non-hydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.Comment: 4 pages, 3 figure

Structural instability in an autophosphorylating kinase switch

We analyse a simple kinase model that exhibits bistability when there is no protein turnover, and show analytically that the property of being bistable is not necessarily conserved when degradation and synthesis of the kinase are taken into account

Anisotropy and Morphology of Strained III-V Heteroepitaxial Films

Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V 3D heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and the diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed In$_x$Ga$_{1-x}$As/GaAs films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface diffusion anisotropy if not more so, in contrast to previous suppositions.Comment: 2 figures version includes one corrected inline equatio

Conformal Dynamics of Precursors to Fracture

An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure

Causal Responsibility and Robust Causation

How do people judge the degree of causal responsibility that an agent has for the outcomes of her actions? We show that a relatively unexplored factor – the robustness (or stability) of the causal chain linking the agent’s action and the outcome – influences judgments of causal responsibility of the agent. In three experiments, we vary robustness by manipulating the number of background circumstances under which the action causes the effect, and find that causal responsibility judgments increase with robustness. In the first experiment, the robustness manipulation also raises the probability of the effect given the action. Experiments 2 and 3 control for probability-raising, and show that robustness still affects judgments of causal responsibility. In particular, Experiment 3 introduces an Ellsberg type of scenario to manipulate robustness, while keeping the conditional probability and the skill deployed in the action fixed. Experiment 4, replicates the results of Experiment 3, while contrasting between judgments of causal strength and of causal responsibility. The results show that in all cases, the perceived degree of responsibility (but not of causal strength) increases with the robustness of the action-outcome causal chain

A hierarchical cluster system based on Horton-Strahler rules for river networks

We consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river number

Phase-field-crystal model for liquid crystals

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various nonequilibrium situations in liquid crystals

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure

Model of surface instabilities induced by stress

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is studied numerically in two and three dimensions. Inherent in the description is the proper treatment of nonlinearities. We find these nonlinearities can lead to competitive coarsening of interfacial structures, corresponding to different wavenumbers, as strain is relieved. We suggest ways to experimentally measure this coarsening.Comment: 4 pages (3 figures included