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.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Modeling for control design of a multi-reach water canal

This article addresses the problem of obtaining reduced complexity models of multi-reach water delivery canals that are suitable for robust and linear parameter varying (LPV) control design. In the first stage, by applying a method known from the literature, a finite dimensional rational transfer function of a priori defined order is obtained for each canal reach by linearizing the Saint-Venant equations. Then, by using block diagrams algebra, these different models are combined with linearized gate models in order to obtain the overall canal model. In what concerns the control design objectives, this approach has the advantages of providing a model with prescribed order and to quantify the high frequency uncertainty due to model approximation. A case study with a 3-reach canal is presented, and the resulting model is compared with experimental data. © 2014 IEEE.

Modeling for control design of a multi-reach water canal

This article addresses the problem of obtaining reduced complexity models of multi-reach water delivery canals that are suitable for robust and linear parameter varying (LPV) control design. In the first stage, by applying a method known from the literature, a finite dimensional rational transfer function of a priori defined order is obtained for each canal reach by linearizing the Saint-Venant equations. Then, by using block diagrams algebra, these different models are combined with linearized gate models in order to obtain the overall canal model. In what concerns the control design objectives, this approach has the advantages of providing a model with prescribed order and to quantify the high frequency uncertainty due to model approximation. A case study with a 3-reach canal is presented, and the resulting model is compared with experimental data. © 2014 IEEE.

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nernatic is investigated i) analytically using the tenser order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nernatic director changes from oblique to perpendicular.

The nature of the ordered phase of the confined self-assembled rigid Rod model

We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite temperatures becomes uniaxial in the thermodynamic limit, by contrast to the ground state (partial) order where the orientation of the uncorrelated layers is perpendicular to one of the three lattice directions. The increase of the orientational correlation between layers as the number of layers increases suggests that the unconfined model may also exhibit uniaxial ordering at finite temperatures.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Transport properties in microcrystalline silicon solar cells under AM1.5 illumination analysed by two-dimensional numerical simulation

Microcrystalline silicon is a two-phase material. Its composition can be interpreted as a series of grains of crystalline silicon imbedded in an amorphous silicon tissue, with a high concentration of dangling bonds in the transition regions. In this paper, results for the transport properties of a mu c-Si:H p-i-n junction obtained by means of two-dimensional numerical simulation are reported. The role played by the boundary regions between the crystalline grains and the amorphous matrix is taken into account and these regions are treated similar to a heterojunction interface. The device is analysed under AM1.5 illumination and the paper outlines the influence of the local electric field at the grain boundary transition regions on the internal electric configuration of the device and on the transport mechanism within the mu c-Si:H intrinsic layer.

Magnetized strangelets at finite temperature

The main properties of strangelets, namely their energy per baryon, radius and electric charge, are studied in the unpaired magnetized strange quark matter (MSQM) and paired magnetized colour flavour locked (MCFL) phases. Temperature effects are taken into account in order to study their stability compared to the Fe-56 isotope and nonmagnetized strangelets within the framework of the MIT bag model. We conclude that the presence of a magnetic field tends to stabilize the strangelets more, even when temperature is considered. It is also shown that MCFL strangelets are more stable than ordinary MSQM strangelets for typical gap values of the order of O(100) MeV. A distinctive feature in the detection of strangelets either in cosmic rays or in heavy-ion collider experiments could be their electric charge. We find that the electric charge is modified in the presence of the magnetic field, leading to higher (lower) charge values for MSQM (MCFL) strangelets, when compared to the nonmagnetized case.

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4771591]

Five models for lepton mixing

We produce five flavour models for the lepton sector. All five models fit perfectly well - at the 1 sigma level - the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type I seesaw mechanism, on a Z(2) symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange - or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for the phase delta in lepton mixing; the fifth model also predicts a correlation between the lepton mixing angles theta(12) and theta(23).

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

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.

How foam-like is the shear-induced lamellar phase of an ionic liquid crystal?

Philosophical Magazine Letters Volume 88, Issue 9-10, 2008 Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes