961 resultados para Frequency response dynamics


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In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

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In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

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Background: Differently from HIV-1, HIV-2 disease progression usually takes decades without antiretroviral therapy and the majority of HIV-2 infected individuals survive as elite controllers with normal CD4+ T cell counts and low or undetectable plasma viral load. Neutralizing antibodies (Nabs) are thought to play a central role in HIV-2 evolution and pathogenesis. However, the dynamic of the Nab response and resulting HIV-2 escape during acute infection and their impact in HIV-2 evolution and disease progression remain largely unknown. Our objective was to characterize the Nab response and the molecular and phenotypic evolution of HIV-2 in association with Nab escape in the first years of infection in two children infected at birth. Results: CD4+ T cells decreased from about 50% to below 30% in both children in the first five years of infection and the infecting R5 viruses were replaced by X4 viruses within the same period. With antiretroviral therapy, viral load in child 1 decreased to undetectable levels and CD4+ T cells recovered to normal levels, which have been sustained at least until the age of 12. In contrast, viral load increased in child 2 and she progressed to AIDS and death at age 9. Beginning in the first year of life, child 1 raised high titers of antibodies that neutralized primary R5 isolates more effectively than X4 isolates, both autologous and heterologous. Child 2 raised a weak X4-specific Nab response that decreased sharply as disease progressed. Rate of evolution, nucleotide and amino acid diversity, and positive selection, were significantly higher in the envelope of child 1 compared to child 2. Rates of R5-to-X4 tropism switch, of V1 and V3 sequence diversification, and of convergence of V3 to a β-hairpin structure were related with rate of escape from the neutralizing antibodies. Conclusion: Our data suggests that the molecular and phenotypic evolution of the human immunodeficiency virus type 2 envelope are related with the dynamics of the neutralizing antibody response providing further support for a model in which Nabs play an important role in HIV-2 pathogenesis.

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Polyimide co-polymers have been prepared based on different diamines as co-monomers: a diamine without CN groups and a novel synthesized diamine with two CN groups prepared by polycondensation reaction followed by thermal cyclodehydration. Dielectric spectroscopy measurements were performed and the dielectric complex function, ac conductivity and electric modulus of the co-polymers were investigated as a function of CN group content in the frequency range from 0.1 Hz to 107 Hz at temperatures from 25 to 260 °C. For all samples and temperatures above 150ºC, the dielectric constant increases with increasing temperature due to increaseing conductivity. The α-relaxation is just detected for the sample without CN groups, being this relaxation overlapped by the electrical conductivity contributions in the remaining samples. For the copolymer samples and the polymer with CN groups an important Maxwell-Wagner-Sillars contribution is detected. The mechanisms responsible for the dielectric relaxation, conduction process and electric modulus response have been discussed as a function of the CN groups content present in the samples.

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Sensory cortex, neuroprosthetics, brain-machine-interfaces, neurodynamics, learning, perception, embodied cognition

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Genetic polymorphism can be maintained over time by negative frequency-dependent (FD) selection induced by Rock-paper-scissors (RPS) social systems. RPS games produce cyclic dynamics, and have been suggested to exist in lizards, insects, isopods, plants, and bacteria. Sexual selection is predicted to accentuate the survival of the future progeny during negative FD survival selection. More specifically, females are predicted to select mates that produce progeny genotypes that exhibit highest survival during survival selection imposed by adult males. However, no empirical evidence demonstrates the existence of FD sexual selection with respect to fitness payoffs of genetic polymorphisms. Here we tested this prediction using the common lizard Zootoca vivipara, a species with three male color morphs (orange, white, yellow) that exhibit morph frequency cycles. In a first step we tested the congruence of the morph frequency change with the predicted change in three independent populations, differing in male color morph frequency and state of the FD morph cycle. Thereafter we ran standardized sexual selection assays in which we excluded alternative mechanisms that potentially induce negative FD selection, and we quantified inter-sexual behavior. The patterns of sexual selection and the observed behavior were in line with context-dependent female mate choice and male behavior played a minor role. Moreover, the strength of the sexual selection was within the magnitude of selection required to produce the observed 3-4-year and 6-8 year morph frequency cycles at low and high altitudes, respectively. In summary, the study provides the first experimental evidence that underpins the crucial assumption of the RPS games suggested to exist in lizards, insects, isopods, and plants; namely, that sexual selection produces negative-FD selection. This indicates that sexual selection, in our study exert by females, might be a crucial driver of the maintenance of genetic polymorphisms.

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A new metabolite profiling approach combined with an ultrarapid sample preparation procedure was used to study the temporal and spatial dynamics of the wound-induced accumulation of jasmonic acid (JA) and its oxygenated derivatives in Arabidopsis thaliana. In addition to well known jasmonates, including hydroxyjasmonates (HOJAs), jasmonoyl-isoleucine (JA-Ile), and its 12-hydroxy derivative (12-HOJA-Ile), a new wound-induced dicarboxyjasmonate, 12-carboxyjasmonoyl-l-isoleucine (12-HOOCJA-Ile) was discovered. HOJAs and 12-HOOCJA-Ile were enriched in the midveins of wounded leaves, strongly differentiating them from the other jasmonate metabolites studied. The polarity of these oxylipins at physiological pH correlated with their appearance in midveins. When the time points of accumulation of different jasmonates were determined, JA levels were found to increase within 2-5 min of wounding. Remarkably, these changes occurred throughout the plant and were not restricted to wounded leaves. The speed of the stimulus leading to JA accumulation in leaves distal to a wound is at least 3 cm/min. The data give new insights into the spatial and temporal accumulation of jasmonates and have implications in the understanding of long-distance wound signaling in plants.

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Résumé grand public :Le cerveau se compose de cellules nerveuses appelées neurones et de cellules gliales dont font partie les astrocytes. Les neurones communiquent entre eux par signaux électriques et en libérant des molécules de signalisation comme le glutamate. Les astrocytes ont eux pour charge de capter le glucose depuis le sang circulant dans les vaisseaux sanguins, de le transformer et de le transmettre aux neurones pour qu'ils puissent l'utiliser comme source d'énergie. L'astrocyte peut ensuite utiliser ce glucose de deux façons différentes pour produire de l'énergie : la première s'opère dans des structures appelées mitochondries qui sont capables de produire plus de trente molécules riches en énergie (ATP) à partir d'une seule molécule de glucose ; la seconde possibilité appelée glycolyse peut produire deux molécules d'ATP et un dérivé du glucose appelé lactate. Une théorie couramment débattue propose que lorsque les astrocytes capturent le glutamate libéré par les neurones, ils libèrent en réponse du lactate qui servirait de base énergétique aux neurones. Cependant, ce mécanisme n'envisage pas une augmentation de l'activité des mitochondries des astrocytes, ce qui serait pourtant bien plus efficace pour produire de l'énergie.En utilisant la microscopie par fluorescence, nous avons pu mesurer les changements de concentrations ioniques dans les mitochondries d'astrocytes soumis à une stimulation glutamatergique. Nous avons démontré que les mitochondries des astrocytes manifestent des augmentations spontanées et transitoires de leur concentrations ioniques, dont la fréquence était diminuée au cours d'une stimulation avec du glutamate. Nous avons ensuite montré que la capture de glutamate augmentait la concentration en sodium et acidifiait les mitochondries des astrocytes. En approfondissant ces mécanismes, plusieurs éléments ont suggéré que l'acidification induite diminuerait le potentiel de synthèse d'énergie d'origine mitochondriale et la consommation d'oxygène dans les astrocytes. En résumé, l'ensemble de ces travaux suggère que la signalisation neuronale impliquant le glutamate dicte aux astrocytes de sacrifier temporairement l'efficacité de leur métabolisme énergétique, en diminuant l'activité de leurs mitochondries, afin d'augmenter la disponibilité des ressources énergétiques utiles aux neurones.Résumé :La remarquable efficacité du cerveau à compiler et propager des informations coûte au corps humain 20% de son budget énergétique total. Par conséquent, les mécanismes cellulaires responsables du métabolisme énergétique cérébral se sont adéquatement développés pour répondre aux besoins énergétiques du cerveau. Les dernières découvertes en neuroénergétique tendent à démontrer que le site principal de consommation d'énergie dans le cerveau est situé dans les processus astrocytaires qui entourent les synapses excitatrices. Un nombre croissant de preuves scientifiques a maintenant montré que le transport astrocytaire de glutamate est responsable d'un coût métabolique important qui est majoritairement pris en charge par une augmentation de l'activité glycolytique. Cependant, les astrocytes possèdent également un important métabolisme énergétique de type mitochondrial. Par conséquent, la localisation spatiale des mitochondries à proximité des transporteurs de glutamate suggère l'existence d'un mécanisme régulant le métabolisme énergétique astrocytaire, en particulier le métabolisme mitochondrial.Afin de fournir une explication à ce paradoxe énergétique, nous avons utilisé des techniques d'imagerie par fluorescence pour mesurer les modifications de concentrations ioniques spontanées et évoquées par une stimulation glutamatergique dans des astrocytes corticaux de souris. Nous avons montré que les mitochondries d'astrocytes au repos manifestaient des changements individuels, spontanés et sélectifs de leur potentiel électrique, de leur pH et de leur concentration en sodium. Nous avons trouvé que le glutamate diminuait la fréquence des augmentations spontanées de sodium en diminuant le niveau cellulaire d'ATP. Nous avons ensuite étudié la possibilité d'une régulation du métabolisme mitochondrial astrocytaire par le glutamate. Nous avons montré que le glutamate initie dans la population mitochondriale une augmentation rapide de la concentration en sodium due à l'augmentation cytosolique de sodium. Nous avons également montré que le relâchement neuronal de glutamate induit une acidification mitochondriale dans les astrocytes. Nos résultats ont indiqué que l'acidification induite par le glutamate induit une diminution de la production de radicaux libres et de la consommation d'oxygène par les astrocytes. Ces études ont montré que les mitochondries des astrocytes sont régulées individuellement et adaptent leur activité selon l'environnement intracellulaire. L'adaptation dynamique du métabolisme énergétique mitochondrial opéré par le glutamate permet d'augmenter la quantité d'oxygène disponible et amène au relâchement de lactate, tous deux bénéfiques pour les neurones.Abstract :The remarkable efficiency of the brain to compute and communicate information costs the body 20% of its total energy budget. Therefore, the cellular mechanisms responsible for brain energy metabolism developed adequately to face the energy needs. Recent advances in neuroenergetics tend to indicate that the main site of energy consumption in the brain is the astroglial process ensheating activated excitatory synapses. A large body of evidence has now shown that glutamate uptake by astrocytes surrounding synapses is responsible for a significant metabolic cost, whose metabolic response is apparently mainly glycolytic. However, astrocytes have also a significant mitochondrial oxidative metabolism. Therefore, the location of mitochondria close to glutamate transporters raises the question of the existence of mechanisms for tuning their energy metabolism, in particular their mitochondrial metabolism.To tackle these issues, we used real time imaging techniques to study mitochondrial ionic alterations occurring at resting state and during glutamatergic stimulation of mouse cortical astrocytes. We showed that mitochondria of intact resting astrocytes exhibited individual spontaneous and selective alterations of their electrical potential, pH and Na+ concentration. We found that glutamate decreased the frequency of mitochondrial Na+ transient activity by decreasing the cellular level of ATP. We then investigated a possible link between glutamatergic transmission and mitochondrial metabolism in astrocytes. We showed that glutamate triggered a rapid Na+ concentration increase in the mitochondrial population as a result of plasma-membrane Na+-dependent uptake. We then demonstrated that neuronally released glutamate also induced a mitochondrial acidification in astrocytes. Glutamate induced a pH-mediated and cytoprotective decrease of mitochondrial metabolism that diminished oxygen consumption. Taken together, these studies showed that astrocytes contain mitochondria that are individually regulated and sense the intracellular environment to modulate their own activity. The dynamic regulation of astrocyte mitochondrial energy output operated by glutamate allows increasing oxygen availability and lactate production both being beneficial for neurons.

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Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

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Rock-paper-scissors (RPS) dynamics, which maintain genetic polymorphisms over time through negative frequency-dependent (FD) selection, can evolve in short-lived species with no generational overlap, where they produce rapid morph frequency cycles. However, most species have overlapping generations and thus, rapid RPS dynamics are thought to require stronger FD selection, the existence of which yet needs to be proved. Here, we experimentally demonstrate that two cumulative selective episodes, FD sexual selection reinforced by FD selection on offspring survival, generate sufficiently strong selection to generate rapid morph frequency cycles in the European common lizard Zootoca vivipara, a multi-annual species with major generational overlap. These findings show that the conditions required for the evolution of RPS games are fulfilled by almost all species exhibiting genetic polymorphisms and suggest that RPS games may be responsible for the maintenance of genetic diversity in a wide range of species.

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We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

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The frequency dynamics of gain-switched singlemode semiconductor lasers subject to optical injection is investigated. The requirements for low time jitter and reduced frequency chirp operation are studied as a function of the frequency mismatch between the master and slave lasers. Suppression of the power overshoot, typical during gain-switched operation, can be achieved for selected frequency detunings.

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Summary Ecotones are sensitive to change because they contain high numbers of species living at the margin of their environmental tolerance. This is equally true of tree-lines, which are determined by attitudinal or latitudinal temperature gradients. In the current context of climate change, they are expected to undergo modifications in position, tree biomass and possibly species composition. Attitudinal and latitudinal tree-lines differ mainly in the steepness of the underlying temperature gradient: distances are larger at latitudinal tree-lines, which could have an impact on the ability of tree species to migrate in response to climate change. Aside from temperature, tree-lines are also affected on a more local level by pressure from human activities. These are also changing as a consequence of modifications in our societies and may interact with the effects of climate change. Forest dynamics models are often used for climate change simulations because of their mechanistic processes. The spatially-explicit model TreeMig was used as a base to develop a model specifically tuned for the northern European and Alpine tree-line ecotones. For the latter, a module for land-use change processes was also added. The temperature response parameters for the species in the model were first calibrated by means of tree-ring data from various species and sites at both tree-lines. This improved the growth response function in the model, but also lead to the conclusion that regeneration is probably more important than growth for controlling tree-line position and species' distributions. The second step was to implement the module for abandonment of agricultural land in the Alps, based on an existing spatial statistical model. The sensitivity of its most important variables was tested and the model's performance compared to other modelling approaches. The probability that agricultural land would be abandoned was strongly influenced by the distance from the nearest forest and the slope, bath of which are proxies for cultivation costs. When applied to a case study area, the resulting model, named TreeMig-LAb, gave the most realistic results. These were consistent with observed consequences of land-abandonment such as the expansion of the existing forest and closing up of gaps. This new model was then applied in two case study areas, one in the Swiss Alps and one in Finnish Lapland, under a variety of climate change scenarios. These were based on forecasts of temperature change over the next century by the IPCC and the HadCM3 climate model (ΔT: +1.3, +3.5 and +5.6 °C) and included a post-change stabilisation period of 300 years. The results showed radical disruptions at both tree-lines. With the most conservative climate change scenario, species' distributions simply shifted, but it took several centuries reach a new equilibrium. With the more extreme scenarios, some species disappeared from our study areas (e.g. Pinus cembra in the Alps) or dwindled to very low numbers, as they ran out of land into which they could migrate. The most striking result was the lag in the response of most species, independently from the climate change scenario or tree-line type considered. Finally, a statistical model of the effect of reindeer (Rangifer tarandus) browsing on the growth of Pinus sylvestris was developed, as a first step towards implementing human impacts at the boreal tree-line. The expected effect was an indirect one, as reindeer deplete the ground lichen cover, thought to protect the trees against adverse climate conditions. The model showed a small but significant effect of browsing, but as the link with the underlying climate variables was unclear and the model was not spatial, it was not usable as such. Developing the TreeMig-LAb model allowed to: a) establish a method for deriving species' parameters for the growth equation from tree-rings, b) highlight the importance of regeneration in determining tree-line position and species' distributions and c) improve the integration of social sciences into landscape modelling. Applying the model at the Alpine and northern European tree-lines under different climate change scenarios showed that with most forecasted levels of temperature increase, tree-lines would suffer major disruptions, with shifts in distributions and potential extinction of some tree-line species. However, these responses showed strong lags, so these effects would not become apparent before decades and could take centuries to stabilise. Résumé Les écotones son sensibles au changement en raison du nombre élevé d'espèces qui y vivent à la limite de leur tolérance environnementale. Ceci s'applique également aux limites des arbres définies par les gradients de température altitudinaux et latitudinaux. Dans le contexte actuel de changement climatique, on s'attend à ce qu'elles subissent des modifications de leur position, de la biomasse des arbres et éventuellement des essences qui les composent. Les limites altitudinales et latitudinales diffèrent essentiellement au niveau de la pente des gradients de température qui les sous-tendent les distance sont plus grandes pour les limites latitudinales, ce qui pourrait avoir un impact sur la capacité des espèces à migrer en réponse au changement climatique. En sus de la température, la limite des arbres est aussi influencée à un niveau plus local par les pressions dues aux activités humaines. Celles-ci sont aussi en mutation suite aux changements dans nos sociétés et peuvent interagir avec les effets du changement climatique. Les modèles de dynamique forestière sont souvent utilisés pour simuler les effets du changement climatique, car ils sont basés sur la modélisation de processus. Le modèle spatialement explicite TreeMig a été utilisé comme base pour développer un modèle spécialement adapté pour la limite des arbres en Europe du Nord et dans les Alpes. Pour cette dernière, un module servant à simuler des changements d'utilisation du sol a également été ajouté. Tout d'abord, les paramètres de la courbe de réponse à la température pour les espèces inclues dans le modèle ont été calibrées au moyen de données dendrochronologiques pour diverses espèces et divers sites des deux écotones. Ceci a permis d'améliorer la courbe de croissance du modèle, mais a également permis de conclure que la régénération est probablement plus déterminante que la croissance en ce qui concerne la position de la limite des arbres et la distribution des espèces. La seconde étape consistait à implémenter le module d'abandon du terrain agricole dans les Alpes, basé sur un modèle statistique spatial existant. La sensibilité des variables les plus importantes du modèle a été testée et la performance de ce dernier comparée à d'autres approches de modélisation. La probabilité qu'un terrain soit abandonné était fortement influencée par la distance à la forêt la plus proche et par la pente, qui sont tous deux des substituts pour les coûts liés à la mise en culture. Lors de l'application en situation réelle, le nouveau modèle, baptisé TreeMig-LAb, a donné les résultats les plus réalistes. Ceux-ci étaient comparables aux conséquences déjà observées de l'abandon de terrains agricoles, telles que l'expansion des forêts existantes et la fermeture des clairières. Ce nouveau modèle a ensuite été mis en application dans deux zones d'étude, l'une dans les Alpes suisses et l'autre en Laponie finlandaise, avec divers scénarios de changement climatique. Ces derniers étaient basés sur les prévisions de changement de température pour le siècle prochain établies par l'IPCC et le modèle climatique HadCM3 (ΔT: +1.3, +3.5 et +5.6 °C) et comprenaient une période de stabilisation post-changement climatique de 300 ans. Les résultats ont montré des perturbations majeures dans les deux types de limites de arbres. Avec le scénario de changement climatique le moins extrême, les distributions respectives des espèces ont subi un simple glissement, mais il a fallu plusieurs siècles pour qu'elles atteignent un nouvel équilibre. Avec les autres scénarios, certaines espèces ont disparu de la zone d'étude (p. ex. Pinus cembra dans les Alpes) ou ont vu leur population diminuer parce qu'il n'y avait plus assez de terrains disponibles dans lesquels elles puissent migrer. Le résultat le plus frappant a été le temps de latence dans la réponse de la plupart des espèces, indépendamment du scénario de changement climatique utilisé ou du type de limite des arbres. Finalement, un modèle statistique de l'effet de l'abroutissement par les rennes (Rangifer tarandus) sur la croissance de Pinus sylvestris a été développé, comme première étape en vue de l'implémentation des impacts humains sur la limite boréale des arbres. L'effet attendu était indirect, puisque les rennes réduisent la couverture de lichen sur le sol, dont on attend un effet protecteur contre les rigueurs climatiques. Le modèle a mis en évidence un effet modeste mais significatif, mais étant donné que le lien avec les variables climatiques sous jacentes était peu clair et que le modèle n'était pas appliqué dans l'espace, il n'était pas utilisable tel quel. Le développement du modèle TreeMig-LAb a permis : a) d'établir une méthode pour déduire les paramètres spécifiques de l'équation de croissance ä partir de données dendrochronologiques, b) de mettre en évidence l'importance de la régénération dans la position de la limite des arbres et la distribution des espèces et c) d'améliorer l'intégration des sciences sociales dans les modèles de paysage. L'application du modèle aux limites alpines et nord-européennes des arbres sous différents scénarios de changement climatique a montré qu'avec la plupart des niveaux d'augmentation de température prévus, la limite des arbres subirait des perturbations majeures, avec des glissements d'aires de répartition et l'extinction potentielle de certaines espèces. Cependant, ces réponses ont montré des temps de latence importants, si bien que ces effets ne seraient pas visibles avant des décennies et pourraient mettre plusieurs siècles à se stabiliser.

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The AASHO specifications for highway bridges require that in designing a bridge, the live load must be multiplied by an impact factor for which a formula is given, dependent only upon the length of the bridge. This formula is a result of August Wohler's tests on fatigue in metals, in which he determined that metals which are subjected to large alternating loads will ultimately fail at lower stresses than those which are subjected only to continuous static loads. It is felt by some investigators that this present impact factor is not realistic, and it is suggested that a consideration of the increased stress due to vibrations caused by vehicles traversing the span would result in a more realistic impact factor than now exists. Since the current highway program requires a large number of bridges to be built, the need for data on dynamic behavior of bridges is apparent. Much excellent material has already been gathered on the subject, but many questions remain unanswered. This work is designed to investigate further a specific corner of that subject, and it is hoped that some useful light may be shed on the subject. Specifically this study hopes to correlate, by experiment on a small scale test bridge, the upper limits of impact utilizing a stationary, oscillating load to represent axle loads moving past a given point. The experiments were performed on a small scale bridge which is located in the basement of the Iowa Engineering Experiment Station. The bridge is a 25 foot simply supported span, 10 feet wide, supported by four beams with a composite concrete slab. It is assumed that the magnitude of the predominant forcing function is the same as the magnitude of the dynamic force produced by a smoothly rolling load, which has a frequency determined by the passage of axles. The frequency of passage of axles is defined as the speed of the vehicle divided by the axle spacing. Factors affecting the response of the bridge to this forcing function are the bridge stiffness and mass, which determine the natural frequency, and the effects of solid damping due to internal structural energy dissipation.