Cyclic deformation of bidisperse two-dimensional foams

In-plane deformation of foams was studied experimentally by subjecting bidisperse foams to cycles of traction and compression at a prescribed rate. Each foam contained bubbles of two sizes with given area ratio and one of three initial arrangements: sorted perpendicular to the axis of deformation (iso-strain), sorted parallel to the axis of deformation (iso-stress), or randomly mixed. Image analysis was used to measure the characteristics of the foams, including the number of edges separating small from large bubbles N-sl, the perimeter (surface energy), the distribution of the number of sides of the bubbles, and the topological disorder mu(2)(N). Foams that were initially mixed were found to remain mixed after the deformation. The response of sorted foams, however, depended on the initial geometry, including the area fraction of small bubbles and the total number of bubbles. For a given experiment we found that (i) the perimeter of a sorted foam varied little; (ii) each foam tended towards a mixed state, measured through the saturation of N-sl; and (iii) the topological disorder mu(2)(N) increased up to an "equilibrium" value. The results of different experiments showed that (i) the change in disorder, Delta mu(2)(N), decreased with the area fraction of small bubbles under iso-strain, but was independent of it under iso-stress; and (ii) Delta mu(2)(N) increased with Delta N-sl under iso-strain, but was again independent of it under iso-stress. We offer explanations for these effects in terms of elementary topological processes induced by the deformations that occur at the bubble scale.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Bi-Dimensional Characterization of a Wimax Radio Channel at 3.5GHz

This paper presents the characterization of an indoor Wimax radio channel using the Finite-Difference Time-Domain (FDTD) [1] method complemented with the Convolutional Perfect Matched Layer (CPML) technique [2]. An indoor 2D scenario is simulated in the 3.5GHz band (IEEE 802.16d-2004 and IEEE 802.16e-2005 [3]). In this study, we used two complementary techniques in both analysis, technique A and B for fading based on delay spread and technique C and D for fading based on Doppler spread. Both techniques converge to the same result. Simulated results define the channel as flat, slow and without inter-symbolic interference (ISI), making the application of the spatial diversity the most appropriate scheme.

A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Growth of (Perylene)(2) [PD(MNT)(2)] crystals

The conditions for [pd(mnt)(2)]he growth of [pd(mnt)(2)]Perylene) [pd(mnt)(2)] [Pd(mnt) [pd(mnt)(2)]] crystals either by chemical oxidation and electrochemical routes are [pd(mnt)(2)]escribed. The electrocrystallisation is limited by close [pd(mnt)(2)]roximity of [pd(mnt)(2)]he oxidation [pd(mnt)(2)]otentials of [pd(mnt)(2)]he [pd(mnt)(2)]erylene [pd(mnt)(2)]onor and [Pd(mnt) [pd(mnt)(2)]] - anion, and [pd(mnt)(2)]epending on [pd(mnt)(2)]he experimental conditions [pd(mnt)(2)]ifferent [pd(mnt)(2)]orphologies can be obtained. [pd(mnt)(2)]Per) [pd(mnt)(2)] [Pd(mnt) [pd(mnt)(2)]] crystals obtained by elecrocrystallisation were found [pd(mnt)(2)]o be [pd(mnt)(2)]ainly of [pd(mnt)(2)]he β-polymorph with [pd(mnt)(2)]roperties comparable [pd(mnt)(2)]o [pd(mnt)(2)]he Cu, Ni and Pt analogues [pd(mnt)(2)]reviously [pd(mnt)(2)]escribed at variance with [pd(mnt)(2)]hose obtained by chemical oxidation which are [pd(mnt)(2)]ainly of [pd(mnt)(2)]he α-polymorph.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Constrains on the structure of Maio Island (Cape Verde) by a three-dimensional gravity model: Imaging partially exhumed magma chambers

We propose a 3-D gravity model for the volcanic structure of the island of Maio (Cape Verde archipelago) with the objective of solving some open questions concerning the geometry and depth of the intrusive Central Igneous Complex. A gravity survey was made covering almost the entire surface of the island. The gravity data was inverted through a non-linear 3-D approach which provided a model constructed in a random growth process. The residual Bouguer gravity field shows a single positive anomaly presenting an elliptic shape with a NWSE trending long axis. This Bouguer gravity anomaly is slightly off-centred with the island but its outline is concordant with the surface exposure of the Central Igneous Complex. The gravimetric modelling shows a high-density volume whose centre of mass is about 4500 m deep. With increasing depth, and despite the restricted gravimetric resolution, the horizontal sections of the model suggest the presence of two distinct bodies, whose relative position accounts for the elongated shape of the high positive Bouguer gravity anomaly. These bodies are interpreted as magma chambers whose coeval volcanic counterparts are no longer preserved. The orientation defined by the two bodies is similar to that of other structures known in the southern group of the Cape Verde islands, thus suggesting a possible structural control constraining the location of the plutonic intrusions.