Local Bifurcations in a Nonlinear Model of a Bioreactor

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.

On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

A Perturbed Iterative Method for a General Class of Variational Inequalities

The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

Rétractes Absolus de Voisinage Algébriques

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.

Dropout dynamics in pulsed quantum dot lasers due to mode jumping

We examine the response of a pulse pumped quantum dot laser both experimentally and numerically. As the maximum of the pump pulse comes closer to the excited-state threshold, the output pulse shape becomes unstable and leads to dropouts. We conjecture that these instabilities result from an increase of the linewidth enhancement factor α as the pump parameter comes close to the excitated state threshold. In order to analyze the dynamical mechanism of the dropout, we consider two cases for which the laser exhibits either a jump to a different single mode or a jump to fast intensity oscillations. The origin of these two instabilities is clarified by a combined analytical and numerical bifurcation diagram of the steady state intensity modes.

Generation of decelerating Airy pulses

The explicit expression for spatial-temporal Airy pulse is derived from the Maxwell's equations in paraxial approximation. The trajectory of the pulse in the time-space coordinates is analysed. The existence of a bifurcation point that separates regions with qualitatively different features of the pulse propagation is demonstrated. At this point the velocity of the pulse becomes infinite and the orientation of it changes to the opposite. © 2011 IEEE.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Improving civil jury decision-making: Evidentiary and procedural issues

The civil jury has been under attack in recent years for being unreliable and incompetent. Considering the myriad causes for poor civil juror decision-making, the current investigation explores both procedural and evidentiary issues that impact juror's decisions. Specifically, the first phase of this dissertation examines how jurors (mis)use evidence pertaining to the litigants when determining liability and awarding damages. After investigating how jurors utilize evidence, the focus shifts to exploring the utility of procedural reforms designed to improve decision-making (specifically revising the instructions on the laws in the case and bifurcating the damage phases of the trial). Using the results from the first two phases of the research, the final study involves manipulating pieces of evidence related to the litigants while exploring the effects that revising the judicial instructions have on the utilization of evidence in particular and on decision-making in general. ^ This dissertation was run on-line, allowing participants to access the study materials at their convenience. After giving consent, participants read the scenario of a fictitious product liability case with the litigant manipulations incorporated into the summary. Participants answered several attitudinal, case-specific, and comprehension questions, and were instructed to find in favor of one side and award any damages they felt warranted. Exploratory factor analyses, Probit and linear regressions, and path analyses were used to analyze the data (M-plus and SPSS were the software packages used to conduct the analyses). Results indicated that misuse of evidence was fairly frequent, though the mock jurors also utilized evidence appropriately. Although the results did not support bifurcation as a viable procedural reform, revising the judicial instructions did significantly increase comprehension rates. Trends in the data suggested that better decision-making occurred when the revised instructions were used, thus providing empirical support for this procedural reform as a means of improving civil jury decision-making. Implications for actual trials and attorneys are discussed. ^

A middleware to support services delivery in a domain-specific virtual machine

The increasing use of model-driven software development has renewed emphasis on using domain-specific models during application development. More specifically, there has been emphasis on using domain-specific modeling languages (DSMLs) to capture user-specified requirements when creating applications. The current approach to realizing these applications is to translate DSML models into source code using several model-to-model and model-to-code transformations. This approach is still dependent on the underlying source code representation and only raises the level of abstraction during development. Experience has shown that developers will many times be required to manually modify the generated source code, which can be error-prone and time consuming. ^ An alternative to the aforementioned approach involves using an interpreted domain-specific modeling language (i-DSML) whose models can be directly executed using a Domain Specific Virtual Machine (DSVM). Direct execution of i-DSML models require a semantically rich platform that reduces the gap between the application models and the underlying services required to realize the application. One layer in this platform is the domain-specific middleware that is responsible for the management and delivery of services in the specific domain. ^ In this dissertation, we investigated the problem of designing the domain-specific middleware of the DSVM to facilitate the bifurcation of the semantics of the domain and the model of execution (MoE) while supporting runtime adaptation and validation. We approached our investigation by seeking solutions to the following sub-problems: (1) How can the domain-specific knowledge (DSK) semantics be separated from the MoE for a given domain? (2) How do we define a generic model of execution (GMoE) of the middleware so that it is adaptable and realizes DSK operations to support delivery of services? (3) How do we validate the realization of DSK operations at runtime? ^ Our research into the domain-specific middleware was done using an i-DSML for the user-centric communication domain, Communication Modeling Language (CML), and for microgrid energy management domain, Microgrid Modeling Language (MGridML). We have successfully developed a methodology to separate the DSK and GMoE of the middleware of a DSVM that supports specialization for a given domain, and is able to perform adaptation and validation at runtime. ^

Ecologia e história natural de população Hemidactylus agrius (Squamata: Gekkonidae) em área de Caatinga, com avaliação da distribuição das espécies nativas do gênero no nordeste do Brasil

The genus Hemidactylus Oken, 1817 has cosmopolite distribution, with three species occurring in Brazil, two of them native, H. brasilianus and H. agrius, and one exotic, H. mabouia. Considering the studies about ecology of lizards conducted in the Ecological Station of the Seridó, from 2001 to 2011, this study aimed (1) to re-evaluate the occurrence of the species of Hemidactylus in this ESEC; (2) to analyze ecological and biological aspects of the H. agrius population; and (3) to investigate the current and potential distribution of the native species of the genus in northeastern Brazil, analyzing the suitability of ESEC to this taxon. For the first two objectives, a sampling area consisting of five transects of 200 x 20 m, was inspected in alternating daily shifts for three consecutive days, from August 2012 to August 2013. For the latter objective, occurrence points of H. agrius and H. brasilianus from literature and from the database of Herpetological Collections of the UFRN and the UNICAMP were consulted to build predictive maps via the Maximum Entropy algorithm (MaxEnt). In ESEC Seridó, 62 H. agrius individuals were collected (25 females, 18 males and 19 juveniles), and two neonates were obtained from a communal nest incubated in the laboratory. No record was made for the other two species of the genus. Hemidactylus agrius demonstrated to be a nocturnal species specialized in habitats with rocky outcrops; but this species is generalist regarding microhabitat use. In the population studied, females had an average body length greater than males, and showed higher frequencies of caudal autotomy. Regarding diet, H. agrius is a moderately generalist species that consumes arthropods, especially insect larvae, Isoptera and Araneae; and vertebrates, with a case of cannibalism registered in the population. With respect to seasonal differences, only the number of food items ingested differed between seasons. The diet was similar between sexes, but ontogenetic differences were recorded for the total volume and maximum length of the food items. Significant relationships were found between lizard body/head size measurements and the maximum length of prey consumed. Cases of polydactyly and tail bifurcation were recorded in the population, with frequencies of 1.6% and 3.1%, respectively. In relation xv to the occurrence points of the native species, 27 were identified, 14 for H. agrius and 13 for H. brasilianus. The first species presented restricted distribution, while the second showed a wide distribution. In both models generated, the ESEC Seridó area showed medium to high suitability. The results of this study confirm the absence of H. brasilianus and H. mabouia this ESEC, and reveal H. agrius as a dietary opportunist and cannibal species. Further, the results confirm the distribution patterns shown by native species of Hemidactylus, and point ESEC Seridó as an area of probable occurrence for the species of the genus, the establishing of H. brasilianus and H. mabouia are probably limited by biotic factors, a fact yet little understood

Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Multistabilities and symmetry-broken one-color and two-color states in closely coupled single-mode lasers

We theoretically investigate the dynamics of two mutually coupled, identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-color states are shown to be stable. In this case the light outputs of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-color states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. Using a five-dimensional model, we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-color and two-color states. Several of these states give rise to multistabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.

Evaporation maps for ternary non-ideal liquid mixtures

This thesis deals with the evaporation of non-ideal liquid mixtures using a multicomponent mass transfer approach. It develops the concept of evaporation maps as a convenient way of representing the dynamic composition changes of ternary mixtures during an evaporation process. Evaporation maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly-used residue curve maps of simple distillation processes. The evaporation process initially considered in this work involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one of the ternary components. To explore multicomponent masstransfer effects, a model is developed that uses an exact solution to the Maxwell-Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperaturecomposition space, which are then projected onto a ternary diagram to form the map. Novel algorithms are developed for computation of pseudo-azeotropes in the evaporating mixture, and for calculation of the multicomponent wet-bulb temperature at a given liquid composition. A numerical continuation method is used to track the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal composition in the liquid. A simple homotopy method is developed to track the locations of the various possible pseudo-azeotropes in the mixture. The stability of pseudo-azeotropes in the gas-phase limited case is examined using a linearized analysis of the governing equations. Algorithms for the calculation of separation boundaries in the evaporation maps are developed using an optimization-based method, as well as a method employing eigenvectors derived from the linearized analysis. The flexure of the wet-bulb temperature surface is explored, and it is shown how evaporation trajectories cross ridges and valleys, so that ridges and valleys of the surface do not coincide with separation boundaries. Finally, the assumption of gas-phase limited mass transfer is relaxed, by employing a model that includes diffusion in the liquid phase. A finite-volume method is used to solve the system of partial differential equations that results. The evaporation trajectories for the distributed model reduce to those of the lumped (gas-phase limited) model as the diffusivity in the liquid increases; under the same gas-phase conditions the permissible terminal compositions of the distributed and lumped models are the same.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.