Self-bound droplet of Bose and Fermi atoms in one dimension: Collective properties in mean-field and Tonks-Girardeau regimes

We investigate a dilute mixture of bosons and spin-polarized fermions in one dimension. With an attractive Bose-Fermi scattering length the ground state is a self-bound droplet, i.e., a Bose-Fermi bright soliton where the Bose and Fermi clouds are superimposed. We find that the quantum fluctuations stabilize the Bose-Fermi soliton such that the one-dimensional bright soliton exists for any finite attractive Bose-Fermi scattering length. We study density profile and collective excitations of the atomic bright soliton showing that they depend on the bosonic regime involved: mean-field or Tonks-Girardeau.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An improved three-dimensional model for growth of oxide films induced by laser heating

In this paper we consider a three-dimensional heat diffusion model to explain the growth of oxide films which takes place when a laser beam is shined on and heats a metallic layer deposited on a glass substrate in a normal atmospheric environment. In particular, we apply this model to the experimental results obtained for the dependence of the oxide layer thickness on the laser density power for growth of TiO2 films grown on Ti-covered glass slides. We show that there is a very good agreement between the experimental results and the theoretical predictions from our proposed three-dimensional model, improving the results obtained with the one-dimensional heat diffusion model previously reported. Our theoretical results also show the occurrence of surface cooling between consecutive laser pulses, and that the oxide track surface profile closely follows the spatial laser profile indicating that heat diffusive effects can be neglected in the growth of oxide films by laser heating. © 2001 Elsevier Science B.V.

Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Detecção de danos em estruturas guiadas usando ondas de alta frequência

Pós-graduação em Engenharia Mecânica - FEIS

A new approach to the electronic structure of two dimensional disordered alloys

We propose a novel method to calculate the electronic Density of States (DOS) of a two dimensional disordered binary alloy. The method is highly reliable and numerically efficient, and Short Range Order (SRO) correlations can be included with no extra computational cost. The approach devised rests on one dimensional calculations and is applied to very long stripes of finite width, the bulk regime being achieved with a relatively small number of chains in the disordered case. Our approach is exact for the pure case and predicts the correct DOS structure in important limits, such as the segregated, random, and ordered alloy regimes. We also suggest important extensions of the present work. © 1995.

Planar magneto-photonic and gradient-photonic structures : crystals and metamaterials.

In the field of photonics, two new types of material structures, photonic crystals and metamaterials, are presently of great interest. Both are studied in the present work, which focus on planar magnetic materials in the former and planar gradient metamaterials in the latter. These planar periodic structures are easy to handle and integrate into optical systems. The applications are promising field for future optical telecommunication systems and give rise to new optical, microwave and radio technologies. The photonic crystal part emphasizes the utilization of magnetic material based photonic crystals due to its remarkable magneto-optical characteristics. Bandgaps tuning by magnetic field in bismuth-gadolinium-substituted lutetium iron garnet (Bi0.8 Gd0.2 Lu2.0 Fe5 O12) based one- dimensional photonic crystals are investigated and demonstrated in this work. Magnetic optical switches are fabricated and tested. Waveguide formulation for band structure in magneto photonic crystals is developed. We also for the first time demonstrate and test two- dimensional magneto photonic crystals optical. We observe multi-stopbands in two- dimensional photonic waveguide system and study the origin of multi-stopbands. The second part focus on studying photonic metamaterials and planar gradient photonic metamaterial design. We systematically study the effects of varying the geometry of the fishnet unit cell on the refractive index in optical frequency. It is the first time to design and demonstrate the planar gradient structure in the high optical frequency. Optical beam bending using planar gradient photonic metamaterials is observed. The technologies needed for the fabrication of the planar gradient photonic metamaterials are investigated. Beam steering devices, shifter, gradient optical lenses and etc. can be derived from this design.

Numerical study of Anderson localization of terahertz waves in disordered waveguides

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO3 waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Two-Dimensional Failure Modeling with Minimal Repair

In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a rnanufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. (C) 2003 Wiley Periodicals, Inc.

Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

Random distributed feedback fibre laser

The concept of random lasers making use of multiple scattering in amplifying disordered media to generate coherent light has attracted a great deal of attention in recent years. Here, we demonstrate a fibre laser with a mirrorless open cavity that operates via Rayleigh scattering, amplified through the Raman effect. The fibre waveguide geometry provides transverse confinement and effectively one-dimensional random distributed feedback, leading to the generation of a stationary near-Gaussian beam with a narrow spectrum, and with efficiency and performance comparable to regular lasers. Rayleigh scattering due to inhomogeneities within the glass structure of the fibre is extremely weak, making the operation and properties of the proposed random distributed feedback lasers profoundly different from those of both traditional random lasers and conventional fibre lasers.

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.