Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.

Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.

In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.

Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Formulação supersimétrica de processos estocásticos com ruído multiplicativo

Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi.

Collective dynamics of glass-forming polymers at intermediate length scales: a synergetic combination of neutron scattering, atomistic simulations and theoretical modelling

Qens/wins 2014 - 11th International Conference on Quasielastic Neutron Scattering and 6th International Workshop on Inelastic Neutron Spectrometers / editado por:Frick, B; Koza, MM; Boehm, M; Mutka, H

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Uma selva entre o céu e o inferno: representações iconográficas e literárias dos índios do Brasil pelos portugueses nos séculos XVI e XVII

A partir de abril de 1500 a armada de Pedro Álvares Cabral dá início ao contato e ao registro através das páginas da carta de seu escrivão, Pero Vaz de Caminha de um novo mundo e uma nova humanidade: os índios que habitavam o território que atualmente conhecemos por Brasil. No desenrolar dos quinhentos, estes diferentes povos e culturas foram decodificados e reinterpretados de diversas maneiras em cartas, livros e demais documentos manuscritos. No campo das artes visuais portuguesas, não foi diferente. Esse outro assume um papel coadjuvante quase sempre inserido em duas temáticas principais, a arte religiosa e as grandes navegações mas nem por isso menos interessante: o gosto pelo exótico, característica marcante durante o período das expansões ultramarinas, não só em Portugal, mas em outras regiões europeias, aliado ao etnocentrismo e a influência do Cristianismo, acabou por caracterizar os índios do Brasil, mutatis mutandis, como novos homens selvagens. Para uns, são como bestas, mais perto do inferno; para outros, são cristãos em potencial, mais próximos do céu

Croissance et détermination de l'âge par lecture d'écailles d'un poisson plat de Côte d'Ivoire, Cynoglossus canariensis (Steind. 1882)

Cynoglossus canariensis has a very rapid growth. The rate of the males is 0,36 and the female one is 0,32. The asymptotic size is 55,0cm for the females and 50,5cm for the males. Females and males younger than three years (40cm), which represent 90 per cent of the Côte d'Ivoire stock have a similar growth, so the average equation: Lt=53,5 (1-e -0,34(t+1)) will be used.

Mutações no gene JARID1C e rearranjos subteloméricos como causas de deficiência intelectual familiar de etiologia idiopática

A Deficiência Intelectual (DI) é uma condição complexa, que acomete 2-3% da população mundial, constituindo um importante problema de saúde pública. No entanto, uma parcela significativa dos casos de DI permanece sem um diagnóstico definitivo, o que demonstra que muitos fatores etiológicos associados a esta condição ainda precisam ser elucidados. Há um consenso de que o número de homens com DI supera em 30% o número de mulheres, um achado atribuído à presença de mutações em genes localizados no cromossomo X. Dentre os genes presentes neste cromossomo que são expressos no cérebro, o Jumonji AT-rich interactive domain 1C (JARID1C) foi identificado como um potencial candidato a estar relacionado à DI ligada ao X (DILX). O gene JARID1C codifica uma desmetilase da lisina 4 da histona H3 (H3K4), imprescindível para a regulação epigenética. Tão importante quanto o estudo do gene JARID1C em pacientes com DI é a busca por variações no número de cópias gênicas (VNCs) em regiões cromossômicas subteloméricas. Genes relacionados ao desenvolvimento cerebral são enriquecidos em VNCs e as regiões subteloméricas são mais susceptíveis à formação destes rearranjos. Diante do exposto, neste estudo, investigamos mutações no gene JARID1C (exons 3, 4, 5, 8, 10, 14 e 23) em 148 homens portadores de DI pertencentes a famílias com padrão de segregação sugestivo de DILX. Paralelamente, analisamos VNCs subteloméricas em 174 homens com DI familiar de etiologia idiopática, independente do padrão de segregação. Para todos os indivíduos selecionados, amostras de DNA genômico foram extraídas a partir de sangue periférico e alterações genéticas frequentemente relacionadas à DI foram previamente excluídas (expansões trinucleotídicas nos loci FRAXA e FRAXE e mutações nos genes MECP2 e ARX). A análise do gene JARID1C foi realizada pela técnica de PCR, seguida da análise dos produtos amplificados por sequenciamento. Foram identificadas quatro variantes silenciosas (c.564G>A, c.633G>C, c.1884G>A, c.1902C>A). Através da análise in silico de sequências exônicas acentuadoras de splicing (ESEs) localizadas nas posições das variantes encontradas, foi possível classificar a variante c.1884G>A como neutra e as três variantes restantes como possíveis criadoras de ESEs. Já para a investigação das VNCs subteloméricas, foi utilizada a metodologia de Multiplex Ligation-dependent Probe Amplification (MLPA), capaz de identificar microdeleções e microduplicações nas 46 regiões subteloméricas. Para este fim, inicialmente, os indivíduos foram investigados pelo kit de MLPA P036, enquanto que para aqueles que exibiram alterações também foi utilizado o kit P070. A validação das VNCs encontradas foi realizada por PCR quantitativo em Tempo Real. A análise por MLPA revelou um indivíduo apresentando duas deleções (9p e 13q), um indivíduo apresentando duas amplificações (1p e 2p), dois indivíduos apresentando uma deleção e uma amplificação (18p e 18q; 4p e 8p), quatro indivíduos portadores de uma deleção cada (10p, 20p, 3q e 22q) e dois indivíduos com uma amplificação cada (7q e 20p). Algumas das alterações subteloméricas encontradas (2,87%) representam VNCs de relevância clínica para o estudo da DI, reforçando a importância do rastreamento de rotina de VNCs subteloméricas na DI familiar. Consideramos que a elucidação de novos genes ou mecanismos moleculares diretamente relacionados à DI é um caminho promissor e urgente para o estabelecimento de novas estratégias terapêuticas possíveis.

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

A meta-analytic approach to quantifying scientific uncertainty in stock assessments

Quantifying scientific uncertainty when setting total allowable catch limits for fish stocks is a major challenge, but it is a requirement in the United States since changes to national fisheries legislation. Multiple sources of error are readily identifiable, including estimation error, model specification error, forecast error, and errors associated with the definition and estimation of reference points. Our focus here, however, is to quantify the influence of estimation error and model specification error on assessment outcomes. These are fundamental sources of uncertainty in developing scientific advice concerning appropriate catch levels and although a study of these two factors may not be inclusive, it is feasible with available information. For data-rich stock assessments conducted on the U.S. west coast we report approximate coefficients of variation in terminal biomass estimates from assessments based on inversion of the assessment of the model’s Hessian matrix (i.e., the asymptotic standard error). To summarize variation “among” stock assessments, as a proxy for model specification error, we characterize variation among multiple historical assessments of the same stock. Results indicate that for 17 groundfish and coastal pelagic species, the mean coefficient of variation of terminal biomass is 18%. In contrast, the coefficient of variation ascribable to model specification error (i.e., pooled among-assessment variation) is 37%. We show that if a precautionary probability of overfishing equal to 0.40 is adopted by managers, and only model specification error is considered, a 9% reduction in the overfishing catch level is indicated.

Demographic characteristics of exploited tropical lutjanids: a comparative analysis

Demographic parameters from seven exploited coral reef lutjanid species were compared as a case study of the implications of intrafamily variation in life histories for multispecies harvest management. Modal lengths varied by 4 cm among four species (Lutjanus fulviflamma, L. vitta, L. carponotatus, L. adetii), which were at least 6 cm smaller than the modal lengths of the largest species (L. gibbus, Symphorus nematophorus, Aprion virescens). Modal ages, indicating ages of full selection to fishing gear, were 10 years or less for all species, but maximum ages ranged from 12 (L. gibbus) to 36 years (S. nematophorus). Each species had a unique growth pattern, with differences in length-at-age and mean asymptotic fork length (L∞), but smaller species generally grew fast during the first 1–2 years of life and larger species grew more slowly over a longer period. Total mortality rates varied among species; L. gibbus had the highest mortality and L. fulviflamma, the lowest mortality. The variability in life history strategies of these tropical lutjanids makes generalizations about lutjanid life histories difficult, but the fact that all seven had characteristics that would make them particularly vulnerable to fishing indicates that harvest of tropical lutjanids should be managed with caution.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Age, growth, and reproduction of dolphinfish (Coryphaena hippurus) caught off the coast of North Carolina

Age, growth, and reproductive data were obtained from dolphinfish (Coryphaena hippurus, size range: 89 to 1451 mm fork length [FL]) collected between May 2002 and May 2004 off North Carolina. Annual increments from scales (n=541) and daily increments from sagittal otoliths (n=107) were examined; estimated von Bertalanffy parameters were L∞ (asymptotic length)=1299 mm FL and k (growth coefficient)=1.08/yr. Daily growth increments reduced much of the residual error in length-at-age estimates for age-0 dolphinfish; the estimated average growth rate was 3.78 mm/day during the first six months. Size at 50% maturity was slightly smaller for female (460 mm FL) than male (475 mm FL) dolphinfish. Based on monthly length-adjusted gonad weights, peak spawning occurs from April through July off North Carolina; back-calculated hatching dates from age-0 dolphinfish and prior reproductive studies on the east coast of Florida indicate that dolphinfish spawning occurs year round off the U.S. east coast and highest levels range from January through June. No major changes in length-at-age or size-at-maturity have occurred since the early 1960s, even after substantial increases in fishery landings.