Asociación Argentina de Limnología (AAL)

Este año se cumplieron veinticinco años de la creación de la Asociación Argentina de Limnología. En 1984, en la vieja aula magna de la Facultad de Ciencias Naturales y Museo (en esa época esta unidad académica funcionaba en las instalaciones del Museo de La Plata) un conjunto de mujeres y hombres relacionados con esta disciplina concretaban ese ansiado anhelo aprobando los fundamentos de su formación y eligiendo su primer comisión directiva. Los años siguientes fueron de gran impulso concretando la realización de talleres reuniones, ediciones de boletines y una gran comunicación entre sus asociados. En 1991 se realiza la primer reunión internacional en la ciudad de La Plata con gran repercusión y convocatoria, posteriormente se hacen los congresos de 1994 y 1998 en la ciudades de Tucumán y Buenos Aires respectivamente. A partir de esta fecha comienza a diluirse la actividad de la asociación para desaparecer en los primeros años del presente siglo. No obstante, ya sin el marco de la asociación, se realizan congresos en 2004 y 2008, en las ciudades de Chascomús y San Carlos de Bariloche respectivamente, con singular éxito. Este archivo es una pequeña muestra de algo que unió a un grupo de profesionales con un objetivo común: el desarrollo y proyección regional de esta disciplina. A simple vista lo podríamos calificar de un nuevo fracaso, ya que tuvo el mismo fin de la ALOA (Asociación Limnológica y Oceanográfica Argentina), pero no sería totalmente cierto, ya que la magnitud de las últimas reuniones nos indica que el crecimiento de esta ciencia es importante. Por ello, me parece adecuado que dejemos a un sociólogo y un historiador de la ciencia la interpretación de este fragmento de la rica historia del “limnobios” en nuestro país.

Optimally robust shortcuts to population inversion in two-level quantum systems

19 p.

Geometric multiplicity margin for a submatrix

AMS Classification: 15A18, 15A21, 15A60.

粘弹性材料界面裂纹的瞬态响应和散射研究

本文研究粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的稳态散射。相对于已有广泛研究的弹性材料裂纹瞬态响应和稳态散射问题，本文的研究有三个突出特点：1）粘弹性材料；2）界面裂纹；3）广义平面波入射。粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的散射尚无开展研究，本文在弹性材料相应问题的研究基础上，首先开展了这一问题的研究。对于冲击载荷下粘弹性界面裂纹的瞬态响应问题，利用Laplace积分变换方法，将粘弹性材料卷积型本构方程转化为Laplace变换域内的代数型本构方程，从而可以在Laplace变换域内象处理弹性材料的冲击响应一样，将相应的混合边值问题归结为关于裂纹张开位移COD的对偶积分方程，并进一步引入裂纹位错密度函数CDD （Crack Dislocation Density），将对偶积分方程化成关于CDD的奇异积分方程（SIE）。用数值方法求解奇异积分方程得到变换域内的动应力强度因子数值解，最后利用Laplace积分逆变换数值方法得到时间域内的动应力强度因子的时间响应。理论分析考虑了两种裂纹模型，即Griffith界面裂纹和柱面圆弧型界面裂纹。考虑的载荷包括反平面冲击载荷和平面冲击载荷。对于平面冲击载荷，通过对裂尖应力场的奇性分析，首次发现粘弹性界面裂纹裂尖动应力场奇性指数不是常数0.5，而是与震荡指数一样依赖材料参数。针对反平面冲击载荷给出了一个算例，计算了裂尖动应力强度因子的时间响应，并与弹性材料的结果作了比较，发现粘弹性效应的影响不仅使过冲击峰值降低，而且使峰值点后移。粘性效应较大时，过冲击现象甚至不出现。关于粘弹性界面裂纹对广东省义平面波的散射问题，首先研究广义平面波在无裂纹存在的理想界面的反射和透射，再研究由于界面裂纹的存在而产生的附加散射场。利用粘弹性材料的复模量理论，可将粘弹性材料的卷积型相构方程化成频率域内的代数型本构方程。类似弹性平面波的处理，在频率域内将问题最终归结为关于裂纹位错密度CDD的奇异积分方程。数值方法求解奇异积分方程即可得到频率域内的散射场，并进而得到裂尖动应力强度因子和远场位移型函数和散射截面。理论分析考虑了两种裂纹模型：Griffith界面裂纹和柱面圆弧型界面裂纹。研究的入射波有广义的SH波和P波。对于广义平面P波入射的情况，通过对裂尖应力场的奇性分析，同样发现粘弹性界面裂纹裂尖动应力场奇性指数不地常数0.5，而是与震荡指数一样依赖于材料参数。对柱面裂纹散射远场的渐近分析，发现远场位移和应力除含有几何衰减因子外，都含有一个材料衰减速因子。散射截面由于材料衰减因子的存在也成为依赖散射半径的量。为了使散射截面仍有意义，文中提出一种修正办法。对Griffith界面裂纹，给出了一个广义平面SH波入射的算例；对柱面界面裂纹，给出了一个广义平面P波入射的算例。计算了不同入射角和入射频率下裂纹的张开位移和动就应力强度因子，并分析了其依赖关系。求解奇异积分方程的数值方法和Laplace积分逆变换数值方法是本文的基本数值方法。本文对这两种方法作了大量的调研和系统的研究。在对比分析的基础上，对现有的各种方法从原理，适用范围，计数效率，优势及特点进行了归纳总结。并尝试了奇异积分方程的最新数值方法--分片连续函数法，证实了其适用性和方便性．

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899(2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 0° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves VLFWs� are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [ Li et al., AIAA J. 46, 2899 (2008) ], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

Adaptive Scalable SVD Unit for Fast Processing of Large LSE Problems

Singular Value Decomposition (SVD) is a key linear algebraic operation in many scientific and engineering applications. In particular, many computational intelligence systems rely on machine learning methods involving high dimensionality datasets that have to be fast processed for real-time adaptability. In this paper we describe a practical FPGA (Field Programmable Gate Array) implementation of a SVD processor for accelerating the solution of large LSE problems. The design approach has been comprehensive, from the algorithmic refinement to the numerical analysis to the customization for an efficient hardware realization. The processing scheme rests on an adaptive vector rotation evaluator for error regularization that enhances convergence speed with no penalty on the solution accuracy. The proposed architecture, which follows a data transfer scheme, is scalable and based on the interconnection of simple rotations units, which allows for a trade-off between occupied area and processing acceleration in the final implementation. This permits the SVD processor to be implemented both on low-cost and highend FPGAs, according to the final application requirements.

Studies of the equation of state and elasticity of mantle minerals

Because the Earth’s upper mantle is inaccessible to us, in order to understand the chemical and physical processes that occur in the Earth’s interior we must rely on both experimental work and computational modeling. This thesis addresses both of these geochemical methods. In the first chapter, I develop an internally consistent comprehensive molar volume model for spinels in the oxide system FeO-MgO-Fe₂O₃-Cr₂O₃-Al₂O₃-TiO₂. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure. In the second chapter, I calibrate a molar volume model for cubic garnets in the system SiO₂-Al₂O₃-TiO₂-Fe₂O₃-Cr₂O₃-FeO-MnO-MgO-CaO-Na₂O. I use the method of singular value analysis to calibrate excess volume of mixing parameters for the garnet model. The implications the model has for the density of the lithospheric mantle are explored. In the third chapter, I discuss the nuclear inelastic X-ray scattering (NRIXS) method, and present analysis of three orthopyroxene samples with different Fe contents. Longitudinal and shear wave velocities, elastic parameters, and other thermodynamic information are extracted from the raw NRIXS data.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

The flow between rotating coaxial disks

Numerical approximations of nonunique solutions of the Navier-Stokes equations are obtained for steady viscous incompressible axisymmetric flow between two infinite rotating coaxial disks. For example, nineteen solutions have been found for the case when the disks are rotating with the same speed but in opposite direction. Bifurcation and perturbed bifurcation phenomena are observed. An efficient method is used to compute solution branches. The stability of solutions is analyzed. The rate of convergence of Newton's method at singular points is discussed. In particular, recovery of quadratic convergence at "normal limit points" and bifurcation points is indicated. Analytical construction of some of the computed solutions using singular perturbation techniques is discussed.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.

Topics in linear and nonlinear dispersive waves

The various singularities and instabilities which arise in the modulation theory of dispersive wavetrains are studied. Primary interest is in the theory of nonlinear waves, but a study of associated questions in linear theory provides background information and is of independent interest.

The full modulation theory is developed in general terms. In the first approximation for slow modulations, the modulation equations are solved. In both the linear and nonlinear theories, singularities and regions of multivalued modulations are predicted. Higher order effects are considered to evaluate this first order theory. An improved approximation is presented which gives the true behavior in the singular regions. For the linear case, the end result can be interpreted as the overlap of elementary wavetrains. In the nonlinear case, it is found that a sufficiently strong nonlinearity prevents this overlap. Transition zones with a predictable structure replace the singular regions.

For linear problems, exact solutions are found by Fourier integrals and other superposition techniques. These show the true behavior when breaking modulations are predicted.

A numerical study is made for the anharmonic lattice to assess the nonlinear theory. This confirms the theoretical predictions of nonlinear group velocities, group splitting, and wavetrain instability, as well as higher order effects in the singular regions.

Determinantal hypersurface from a geometric perspective

In this paper, we give a geometric interpretation of determinantal forms, both in the case of general matrices and symmetric matrices. We will prove irreducibility of the determinantal singular loci and state its dimension. We also provide detailed description of the singular locus for small dimensions.

A dynamical systems analysis of vortex pinch-off

Vortex rings constitute the main structure in the wakes of a wide class of swimming and flying animals, as well as in cardiac flows and in the jets generated by some moss and fungi. However, there is a physical limit, determined by an energy maximization principle called the Kelvin-Benjamin principle, to the size that axisymmetric vortex rings can achieve. The existence of this limit is known to lead to the separation of a growing vortex ring from the shear layer feeding it, a process known as `vortex pinch-off', and characterized by the dimensionless vortex formation number. The goal of this thesis is to improve our understanding of vortex pinch-off as it relates to biological propulsion, and to provide future researchers with tools to assist in identifying and predicting pinch-off in biological flows.

To this end, we introduce a method for identifying pinch-off in starting jets using the Lagrangian coherent structures in the flow, and apply this criterion to an experimentally generated starting jet. Since most naturally occurring vortex rings are not circular, we extend the definition of the vortex formation number to include non-axisymmetric vortex rings, and find that the formation number for moderately non-axisymmetric vortices is similar to that of circular vortex rings. This suggests that naturally occurring vortex rings may be modeled as axisymmetric vortex rings. Therefore, we consider the perturbation response of the Norbury family of axisymmetric vortex rings. This family is chosen to model vortex rings of increasing thickness and circulation, and their response to prolate shape perturbations is simulated using contour dynamics. Finally, the response of more realistic models for vortex rings, constructed from experimental data using nested contours, to perturbations which resemble those encountered by forming vortices more closely, is simulated using contour dynamics. In both families of models, a change in response analogous to pinch-off is found as members of the family with progressively thicker cores are considered. We posit that this analogy may be exploited to understand and predict pinch-off in complex biological flows, where current methods are not applicable in practice, and criteria based on the properties of vortex rings alone are necessary.