Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Approaches to Provisioning Network Topology of Virtual Machines in Cloud Systems

The current infrastructure as a service (IaaS) cloud systems, allow users to load their own virtual machines. However, most of these systems do not provide users with an automatic mechanism to load a network topology of virtual machines. In order to specify and implement the network topology, we use software switches and routers as network elements. Before running a group of virtual machines, the user needs to set up the system once to specify a network topology of virtual machines. Then, given the user’s request for running a specific topology, our system loads the appropriate virtual machines (VMs) and also runs separated VMs as software switches and routers. Furthermore, we have developed a manager that handles physical hardware failure situations. This system has been designed in order to allow users to use the system without knowing all the internal technical details.

Immobilized Microalgae for Nutrient Recovery from Source Separated Urine

Shortages in supply of nutrients and freshwater for a growing human population are critical global issues. Traditional centralized sewage treatment can prevent eutrophication and provide sanitation, but is neither efficient nor sustainable in terms of water and resources. Source separation of household wastes, combined with decentralized resource recovery, presents a novel approach to solve these issues. Urine contains within 1 % of household waste water up to 80 % of the nitrogen (N) and 50 % of the phosphorus (P). Since microalgae are efficient at nutrient uptake, growing these organisms in urine might be a promising technology to concomitantly clean urine and produce valuable biomass containing the major plant nutrients. While state-of-the-art suspension systems for algal cultivation have mayor shortcomings in their application, immobilized cultivation on Porous Substrate Photobioreactors (PSBRs) might be a feasible alternative. The aim of this study was to develop a robust process for nutrient recovery from minimally diluted human urine using microalgae on PSBRs. The green alga Desmodesmus abundans strain CCAC 3496 was chosen for its good growth, after screening 96 algal strains derived from urine-specific isolations and culture collections. Treatment of urine, 1:1 diluted with tap water and without addition of nutrients, was performed at a light intensity of 600 μmol photons m-2 s-1 with 2.5 % CO2 and at pH 6.5. A growth rate of 7.2 g dry weight m-² day-1 and removal efficiencies for N and P of 13.1 % and 94.1 %, respectively, were determined. Pre-treatment of urine with activated carbon was found to eliminate possible detrimental effects of pharmaceuticals. These results provide a basis for further development of the technology at pilot-scale. If found to be safe in terms human and environmental health, the biomass produced from three persons could provide the P for annual production of 31 kg wheat grain and 16 kg soybean, covering the caloric demand in food for almost one month of the year for such a household. In combination with other technologies, PSBRs could thus be applied in a decentralized resource recovery system, contributing to locally close the link between sanitation and food production.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.