Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection

A reaction-diffusion-convection equation with a nonlocal term is studied; the nonlocal operator acts to conserve the spatial integral of the unknown function as time evolves. The equations are parameterised by µ, and for µ = 1 the equation arises as a similarity solution of the Navier-Stokes equations and the nonlocal term plays the role of pressure. For µ = 0, the equation is a nonlocal reaction-diffusion problem. The aim of the paper is to determine for which values of the parameter µ blow-up occurs and to study its form. In particular, interest is focused on the three cases µ 1/2, and µ → 1. It is observed that, for any 0 ≤ µ ≤ 1/2, nonuniform global blow-up occurs; if 1/2 < µ < 1, then the blow-up is global and uniform, while for µ = 1 (the Navier-Stokes equations) there are exact solutions with initial data of arbitrarily large L_∞, L_2, and H^1 norms that decay to zero. Furthermore, one of these exact solutions is proved to be nonlinearly stable in L_2 for arbitrarily large supremum norm. An understanding of this transition from blow-up behaviour to decay behaviour is achieved by a combination of analysis, asymptotics, and numerical techniques

miR-9 Acts as an OncomiR in Prostate Cancer through Multiple Pathways That Drive Tumour Progression and Metastasis

Identification of dysregulated microRNAs (miRNAs) in prostate cancer is critical not only for diagnosis, but also differentiation between the aggressive and indolent forms of the disease. miR-9 was identified as an oncomiR through both miRNA panel RT-qPCR as well as high-throughput sequencing analysis of the human P69 prostate cell line as compared to its highly tumorigenic and metastatic subline M12, and found to be consistently upregulated in other prostate cell lines including DU-145 and PC3. While miR-9 has been characterized as dysregulated either as an oncomiR or tumour suppressor in a variety of other cancers including breast, ovarian, and nasopharyngeal carcinomas, it has not been previously evaluated and proven as an oncomiR in prostate cancer. miR-9 was confirmed an oncomiR when found to be overexpressed in tumour tissue as compared to adjacent benign glandular epithelium through laser-capture microdissection of radical prostatectomy biopsies. Inhibition of miR-9 resulted in reduced migratory and invasive potential of the M12 cell line, and reduced tumour growth and metastases in male athymic nude mice. Analysis showed that miR-9 targets e-cadherin and suppressor of cytokine signalling 5 (SOCS5), but not NF-ĸB mRNA. Expression of these proteins was shown to be affected by modulation in expression of miR-9

A heat transfer with a source: the complete set of invariant difference schemes

In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where a few invariant models for heat transfer equations were presented.Comment: arxiv version is already officia

On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids

The effect of using grid adaptation on the numerical solution of model convection-diffusion equations with a conservation form is studied. The grid adaptation technique studied is based on moving a fixed number of mesh points to equidistribute a generalization of the arc-length of the solution. In particular, a parameter-dependent monitor function is introduced which incorporates fixed meshes, approximate arc-length equidistribution, and equidistribution of the absolute value of the solution, in a single framework. Thus the resulting numerical method is a coupled nonlinear system of equations for the mesh spacings and the nodal values. A class of singularly perturbed problems, including Burgers's equation in the limit of small viscosity, is studied. Singular perturbation and bifurcation techniques are used to analyze the solution of the discretized equations, and numerical results are compared with the results from the analysis. Computation of the bifurcation diagram of the system is performed numerically using a continuation method and the results are used to illustrate the theory. It is shown that equidistribution does not remove spurious solutions present on a fixed mesh and that, furthermore, the spurious solutions can be stable for an appropriate moving mesh method

Singular and regular solutions of a non-linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.Comment: 16 page

Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure

The CSIRO Mk3L climate system model version 1.0 – Part 1: Description and evaluation

The CSIRO Mk3L climate system model is a coupled general circulation model, designed primarily for millennial-scale climate simulations and palaeoclimate research. Mk3L includes components which describe the atmosphere, ocean, sea ice and land surface, and combines computational efficiency with a stable and realistic control climatology. This paper describes the model physics and software, analyses the control climatology, and evaluates the ability of the model to simulate the modern climate. &lt;br&gt;&lt;br&gt; Mk3L incorporates a spectral atmospheric general circulation model, a &lt;i&gt;z&lt;/i&gt;-coordinate ocean general circulation model, a dynamic-thermodynamic sea ice model and a land surface scheme with static vegetation. The source code is highly portable, and has no dependence upon proprietary software. The model distribution is freely available to the research community. A 1000-yr climate simulation can be completed in around one-and-a-half months on a typical desktop computer, with greater throughput being possible on high-performance computing facilities. &lt;br&gt;&lt;br&gt; Mk3L produces realistic simulations of the larger-scale features of the modern climate, although with some biases on the regional scale. The model also produces reasonable representations of the leading modes of internal climate variability in both the tropics and extratropics. The control state of the model exhibits a high degree of stability, with only a weak cooling trend on millennial timescales. Ongoing development work aims to improve the model climatology and transform Mk3L into a comprehensive earth system model