Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Can dark matter decay in dark energy?

We analyze the interaction between dark energy and dark matter from a thermodynamical perspective. By assuming they have different temperatures, we study the possibility of occurring a decay from dark matter into dark energy, characterized by a negative parameter Q. We find that, if at least one of the fluids has nonvanishing chemical potential, for instance mu(x)< 0 and mu(dm)=0 or mu(x)=0 and mu(dm)> 0, the decay is possible, where mu(x) and mu(dm) are the chemical potentials of dark energy and dark matter, respectively. Using recent cosmological data, we find that, for a fairly simple interaction, the dark matter decay is favored with a probability of similar to 93% over the dark energy decay. This result comes from a likelihood analysis where only background evolution has been considered.

Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Uniform Decay of the Local Energy

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

Field theory model for dark matter and dark energy in interaction

We propose a field theory model for dark energy and dark matter in interaction. Comparing the classical solutions of the field equations with the observations of the CMB shift parameter, baryonic acoustic oscillations, lookback time, and the Gold supernovae sample, we observe a possible interaction between dark sectors with energy decay from dark energy into dark matter. The observed interaction provides an alleviation to the coincidence problem.

The roles of xylan and lignin in oxalic acid pretreated corncob during separate enzymatic hydrolysis and ethanol fermentation

High yields of hemicellulosic and cellulosic sugars are critical in obtaining economical conversion of agricultural residues to ethanol. To optimize pretreatment conditions, we evaluated oxalic acid loading rates, treatment temperatures and times in a 2(3) full factorial design. Response-surface analysis revealed an optimal oxalic acid pretreatment condition to release sugar from the cob of Zea mays L ssp. and for Pichia stipitis CBS 6054. To ferment the residual cellulosic sugars to ethanol following enzymatic hydrolysis, highest saccharification and fermentation yields were obtained following pretreatment at 180 degrees C for 50 min with 0.024 g oxalic acid/g substrate. Under these conditions, only 7.5% hemicellulose remained in the pretreated substrate. The rate of cellulose degradation was significantly less than that of hemicellulose and its hydrolysis was not as extensive. Subsequent enzymatic saccharification of the residual cellulose was strongly affected by the pretreatment condition with cellulose hydrolysis ranging between 26.0% and 76.2%. The residual xylan/lignin ratio ranged from 0.31 to 1.85 depending on the pretreatment condition. Fermentable sugar and ethanol were maximal at the lowest ratio of xylan/lignin and at high glucan contents. The model predicts optimal condition of oxalic acid pretreatment at 168 degrees C, 74 min and 0.027 g/g of oxalic acid. From these findings, we surmised that low residual xylan was critical in obtaining maximal glucose yields from saccharification. Published by Elsevier Ltd.

Perceptual compensation for effects of echo and of reverberation on speech identification

In an ideal "reverberant" room, the energy of the impulse responses decays smoothly, at a constant rate of dB/s, so that gradually-decaying tails are added at the ends of sounds. Conversely, a single echo gives a flat energy-decay up to the echo's arrival time, which then drops abruptly, so that sounds with only echoes lack the decaying-tail feature of reverberation. The perceptual effects of these types of reflection pattern were measured with test-words from a continuum of steps between "sir" and "stir", which were each embedded in a carrier phrase. When the proportion of reflected sound in test-words is increased, to a level above the amount in the carrier, the test words sound more like "sir". However, when the proportion of reflected sound in the carrier is also increased, to match the amount in the test word, there can be a perceptual compensation where test words sound more like "stir" again. A reference condition used real-room reverberation from recordings at different source to receiver distances. In a synthetic-reverberation condition, the reflection pattern was from a "colorless" impulse response, comprising exponentially-decaying reflections that were spaced at intervals. In a synthetic-echo condition, the reflection pattern was obtained from the synthetic reverberation by removing the intervals between reflections before delaying the resulting cluster relative to the direct sound. Compensation occurred in the reference condition and in different types of synthetic reverberation, but not in synthetic-echo conditions. This result indicates that the presence of tails from reverberation informs the compensation mechanism.

Controle na fronteira para um sistema de equações de ondas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

A new method for the estimation of the reverberation time from measured room impulse responses with application to Italian opera houses

The Schroeder's backward integration method is the most used method to extract the decay curve of an acoustic impulse response and to calculate the reverberation time from this curve. In the literature the limits and the possible improvements of this method are widely discussed. In this work a new method is proposed for the evaluation of the energy decay curve. The new method has been implemented in a Matlab toolbox. Its performance has been tested versus the most accredited literature method. The values of EDT and reverberation time extracted from the energy decay curves calculated with both methods have been compared in terms of the values themselves and in terms of their statistical representativeness. The main case study consists of nine Italian historical theatres in which acoustical measurements were performed. The comparison of the two extraction methods has also been applied to a critical case, i.e. the structural impulse responses of some building elements. The comparison underlines that both methods return a comparable value of the T30. Decreasing the range of evaluation, they reveal increasing differences; in particular, the main differences are in the first part of the decay, where the EDT is evaluated. This is a consequence of the fact that the new method returns a “locally" defined energy decay curve, whereas the Schroeder's method accumulates energy from the tail to the beginning of the impulse response. Another characteristic of the new method for the energy decay extraction curve is its independence on the background noise estimation. Finally, a statistical analysis is performed on the T30 and EDT values calculated from the impulse responses measurements in the Italian historical theatres. The aim of this evaluation is to know whether a subset of measurements could be considered representative for a complete characterization of these opera houses.

Metodología de análisis acústico de sitios arqueológicos de Mesoamérica

El presente trabajo busca llenar un vacío existente en cuanto a una metodología general en los estudios Arqueoacústicos para la zona Mesoamericana. El resultado mas importante de ésta tesis es la propuesta de un procedimiento y método para los cuales se detalla el conjunto de operaciones utilizadas en las mediciones particulares involucradas, parámetros y análisis relevantes (de los cuales destacan el decaimiento de energía, tiempos de reverberación, intensidades de sonido directo y total, claridad e inteligibilidad), tipos de simulaciones e incertidumbres y actividades técnicas propias de la Ingeniería Acústica que se proponen para la efectiva y útil integración de la dimensión sonora en el quehacer arqueológico. Una importante consideración de la propuesta metodológica aquí presentada, es la consideración, por un lado, de los resultados obtenidos experimentalmente del trabajo in situ en cada uno de los sitios arqueológicos de interés, y por otro los resultados obtenidos de las simulaciones y modelaciones por computadora de los mismos para su comparación y contraste. La propuesta de sistematización está dividida en tres momentos investigativos, como son la coordinación y trabajo logístico en sitios arqueológicos, su reconocimiento y prospección acústica; el trabajo de campo; y el análisis de los resultados obtenidos. Asimismo, dicha propuesta metodológica, se presenta dividida en tres objetos de estudio fundamentales en el quehacer arqueoacústico: los Fenómenos Sonoros encontrados en sitios arqueológicos; los objetos de generación de sonido, tengan éstos aplicaciones musicales o de otra índole; y finalmente los espacios y recintos arquitectónicos, ya sean cerrados o abiertos, y el estudio de su funcionalidad. El acercamiento a la descripción de cada una de dichas ramas, se realiza mediante la presentación de casos de estudio, para los que se contrastan dos áreas culturales representativas e interrelacionadas de Mesoamérica, la zona del Bajío y la zona Maya. Dicho contraste es llevado a cabo mediante el análisis acústico de 4 zonas arqueológicas que son Plazuelas, Peralta y Cañada de la Virgen, pertenecientes a la zona del Bajio, y Chichen Itzá perteneciente a la zona Maya. De particular importancia para el presente trabajo, es la funcionalidad de los espacios estudiados, específicamente de la de los patios hundidos, característicos de la arquitectura del Bajío, y las plazas públicas que constituyen una estructura integral en muchos sitios arqueológicos, centrales para la comprensión de las conexiones entre el fenómeno sonoro y el comportamiento de una cultura en particular. Asimismo, el análisis de los instrumentos de generación sonora ha permitido realizar inferencias sobre papel del sonido en el comportamiento humano de las culturas en cuestión, completando los modelos acústicos y posibilitando el situar las características de las fuentes sonoras en los espacios resonantes. Los resultados particulares de ésta tesis, han permitido establecer las características acústicas de dichos espacios e instrumentos, así como formular y validar las hipótesis sobre su usos y funciones como espacios para eventos públicos y sociales, así como para representaciones culturales multitudinarios. ABSTRACT The present work, aims to fill a void existing in terms of a general methodology in Archaeoacoustic studies for the Mesoamerican region. The most important result of this thesis is the proposal of a procedure and method for archaeoacoustical studies and its relevant analysis and parameters (of which stand out the energy decay, reverberation times, intensities, clarity and intelligibility), simulations and uncertainty considerations for the effective and useful integration of the sound dimension in the archaeological realm. An important methodological consideration in the present work is the comparison and contrast of the results obtained experimentally on site, and the results of simulations and computer modeling. The proposed systematization is divided into three distinct moments: logistics; fieldwork; and result analysis. Likewise, the presented methodological proposal is divided into three fundamental objects of study: Sound phenomena found in archaeological sites; sound generation objects and instruments; and architectural enclosures and the study of their functionality. Presenting case studies is the approach to the description of each of these branches. Two interrelated Mesoamerican cultural areas are considered, the Bajío and the Mayan. Their contrast is carried out by the acoustic analysis of four archaeological sites: Plazuelas, Peralta and Cañada de la Virgen, belonging to the area of the Bajío, and Chichen Itza belonging to the Maya area. Of particular relevance to this paper, is the acoustic functionality of the public spaces present in many archaeological sites, specifically that of the sunken patios, characteristic of the architecture of the Bajío. The analysis of the sound generation instruments has allowed certain inferences about the role of sound in human behavior of the cultures in question, thus completing the acoustic models. It has also enable the contrast of the characteristics of the sound sources and those of the resonant spaces. The results of this thesis have made it possible to develop and validate certain hypotheses about the uses and functions of certain spaces for public and social events as well as for mass cultural representations.

On the Stabilization of the Wave Equation by the Boundary

* Partially supported by CNPq (Brazil)

Modeling, simulation, and control of a formation of multirotor aircraft for cooperative transportation of suspended loads

The work presented in this thesis aims to contribute to innovation in the Urban Air Mobility and Delivery sector and represents a solid starting point for air logistics and its future scenarios. The dissertation focuses on modeling, simulation, and control of a formation of multirotor aircraft for cooperative load transportation, with particular attention to environmental sustainability. First, a simulation and test environment is developed to assess technologies for suspended load stabilization. Starting from the mathematical model of two identical multirotors, formation-flight-keeping and collision-avoidance algorithms are analyzed. This approach guarantees both the safety of the vehicles within the formation and that of the payload, which may be made of people in the very near future. Afterwards, a mathematical model for the suspended load is implemented, as well as an active controller for its stabilization. The key focus of this part is represented by both analysis and control of payload oscillatory motion, by thoroughly investigating load kinetic energy decay. At this point, several test cases were introduced, in order to understand which strategy is the most effective and safe in terms of future applications in the field of air logistics.

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) Lambda N -> nN of Lambda hypernuclei (4)(Lambda)He, (5)(Lambda)He, (12)(Lambda)C, (16)(Lambda)O, and (28)(Lambda)Si, as a function of the sum of kinetic energies E(nN)=E(n)+E(N) for N=n,p. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parametrization. Two versions of the independent-particle shell model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are as follows: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account and (b) IPSM-b, where the highly excited hole states are considered to be quasistationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All np and nn spectra exhibit a series of peaks in the energy interval 110 MeV < E(nN)< 170 MeV, one for each occupied shell-model state. Within the IPSM-a, and because of the recoil effect, each peak covers an energy interval proportional to A(-1) , going from congruent to 4 MeV for (28)(Lambda)Si to congruent to 40 MeV for (4)(Lambda)He. Such a description could be pretty fair for the light (4)(Lambda)He and (5)(Lambda)He hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to consider as well the spreading in strength of the deep-hole states and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final-state interactions and of the two-nucleon-induced decay mode.