946 resultados para Systems of nonlinear equations


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The aim of this work is to investigate, using extensive Monte Carlo computer simulations, composite materials consisting of liquid crystals doped with nanoparticles. These systems are currently of great interest as they offer the possibility of tuning the properties of liquid crystals used in displays and other devices as well as providing a way of obtaining regularly organized systems of nanoparticles exploiting the molecular organization of the liquid crystal medium. Surprisingly enough, there is however a lack of fundamental knowledge on the properties and phase behavior of these hybrid materials, making the route to their application an essentially empirical one. Here we wish to contribute to the much needed rationalization of these systems studying some basic effects induced by different nanoparticles on a liquid crystal host. We investigate in particular the effects of nanoparticle shape, size and polarity as well as of their affinity to the liquid crystal solvent on the stability of the system, monitoring phase transitions, order and molecular organizations. To do this we have proposed a coarse grained approach where nanoparticles are modelled as a suitably shaped (spherical, rod and disk like) collection of spherical Lennard-Jones beads, while the mesogens are represented with Gay-Berne particles. We find that the addition of apolar nanoparticles of different shape typically lowers the nematic–isotropic transition of a non-polar nematic, with the destabilization being greater for spherical nanoparticles. For polar mesogens we have studied the effect of solvent affinity of the nanoparticles showing that aggregation takes places for low solvation values. Interestingly, if the nanoparticles are polar the aggregates contribute to stabilizing the system, compensating the shape effect. We thus find the overall effects on stability to be a delicate balance of often contrasting contributions pointing to the relevance of simulations studies for understanding these complex systems.

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A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

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Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

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The main objective of this project is to experimentally demonstrate geometrical nonlinear phenomena due to large displacements during resonant vibration of composite materials and to explain the problem associated with fatigue prediction at resonant conditions. Three different composite blades to be tested were designed and manufactured, being their difference in the composite layup (i.e. unidirectional, cross-ply, and angle-ply layups). Manual envelope bagging technique is explained as applied to the actual manufacturing of the components; problems encountered and their solutions are detailed. Forced response tests of the first flexural, first torsional, and second flexural modes were performed by means of a uniquely contactless excitation system which induced vibration by using a pulsed airflow. Vibration intensity was acquired by means of Polytec LDV system. The first flexural mode is found to be completely linear irrespective of the vibration amplitude. The first torsional mode exhibits a general nonlinear softening behaviour which is interestingly coupled with a hardening behaviour for the unidirectional layup. The second flexural mode has a hardening nonlinear behaviour for either the unidirectional and angle-ply blade, whereas it is slightly softening for the cross-ply layup. By using the same equipment as that used for forced response analyses, free decay tests were performed at different airflow intensities. Discrete Fourier Trasform over the entire decay and Sliding DFT were computed so as to visualise the presence of nonlinear superharmonics in the decay signal and when they were damped out from the vibration over the decay time. Linear modes exhibit an exponential decay, while nonlinearities are associated with a dry-friction damping phenomenon which tends to increase with increasing amplitude. Damping ratio is derived from logarithmic decrement for the exponential branch of the decay.

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In consequence of rapidly changing market demands companies are permanently encouraged to review their own processes and structures and to modify them. Being one of these developments, order-picking is involved as part of an intra-logistics system. But to take appropriate actions, system performance and system costs have to be measured permanently. Concerning this the use of performance measurement-systems as further development of traditional systems of key figures is suitable. In this paper various performance measurement-systems are compared and their suitability for an implementation in order-picking systems is estimated. On the basis of the result of the evaluation a first concept of a performance measurement-system for order-picking will be developed by using typical key figures that are mentioned in academic literature. Finally, hints for a necessary detailed implementation and evaluation in practice will be given.

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To determine the potential inhalatory risk posed by carbon nanotubes (CNTs), a tier-based approach beginning with an in vitro assessment must be adopted. The purpose of this study therefore was to compare 4 commonly used in vitro systems of the human lung (human blood monocyte-derived macrophages [MDM] and monocyte-derived dendritic cells [MDDC], 16HBE14o- epithelial cells, and a sophisticated triple cell co-culture model [TCC-C]) via assessment of the biological impact of different CNTs (single-walled CNTs [SWCNTs] and multiwalled CNTs [MWCNTs]) over 24h. No significant cytotoxicity was observed with any of the cell types tested, although a significant (p < .05), dose-dependent increase in tumor necrosis factor (TNF)-α following SWCNT and MWCNT exposure at concentrations up to 0.02mg/ml to MDM, MDDC, and the TCC-C was found. The concentration of TNF-α released by the MDM and MDDC was significantly higher (p < .05) than the TCC-C. Significant increases (p < .05) in interleukin (IL)-8 were also found for both 16HBE14o- epithelial cells and the TCC-C after SWCNTs and MWCNTs exposure up to 0.02mg/ml. The TCC-C, however, elicited a significantly (p < .05) higher IL-8 release than the epithelial cells. The oxidative potential of both SWCNTs and MWCNTs (0.005-0.02mg/ml) measured by reduced glutathione (GSH) content showed a significant difference (p < .05) between each monoculture and the TCC-C. It was concluded that because only the co-culture system could assess each endpoint adequately, that, in comparison with monoculture systems, multicellular systems that take into consideration important cell type-to-cell type interactions could be used as predictive in vitro screening tools for determining the potential deleterious effects associated with CNTs.

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Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

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Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

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There have been multiple reports which indicate that variations in $\beta$AR expression affect the V$\sb{\rm max}$ observed for the agonist-dependent activation of adenylylcyclase. This observation has been ignored by most researchers when V$\sb{\rm max}$ values obtained for wild type and mutant receptors are compared. Such an imprecise analysis may lead to erroneous conclusions concerning the ability of a receptor to activate adenylylcyclase. Equations were derived from the Cassel-Selinger model of GTPase activity and Tolkovsky and Levitzki's Collision Coupling model which predict that the EC$\sb{50}$ and V$\sb{\rm max}$ for the activation of adenylylcyclase are a function of receptor number. Experimental results for L cell clones in which either hamster or human $\beta$AR were transfected at varying levels showed that EC$\sb{50}$ decreases and V$\sb{\rm max}$ increases as receptor number increases. Comparison of these results with simulations obtained from the equations describing EC$\sb{50}$ and V$\sb{\rm max}$ showed a close correlation. This documents that the kinetic parameters of adenylylcyclase activation change with the level of receptor expression and relates this phenomenon to a theoretical framework concerning the mechanisms involved in $\beta$AR signal transduction.^ One of the terms used in the equations which expressed the EC$\sb{50}$ and V$\sb{\rm max}$ as a function of receptor number is coupling efficiency, defined as $\rm k\sb1/k\sb{-1}$. Calculation of $\rm k\sb1/k\sb{-1}$ can be accomplished for wild type receptors with the easily measured experimental values of agonist K$\sb{\rm d}$, EC$\sb{50}$ and receptor number. This was demonstrated for hamster $\beta$AR which yielded a coupling efficiency of 0.15 $\pm$ 0.003 and human $\beta$AR which yielded a coupling efficiency of 0.90 $\pm$ 0.031. $\rm k\sb1/k\sb{-1}$ replaces the traditional qualitative evaluation of the ability to activate adenylylcyclase, which utilizes V$\sb{\rm max}$ without correction for variation in receptor number, with a quantitative definition that more accurately describes the ability of $\beta$AR to couple to G$\sb{\rm s}$.^ The equations which express the EC$\sb{50}$ and V$\sb{\rm max}$ for adenylylcyclase activation as a function of receptor number and coupling efficiency were tested to determine whether they could accurately simulate the changes seen in these parameters during desensitization. Data from original desensitization experiments and data from the literature (24,25,52,54,83) were compared to simulated changes in EC$\sb{50}$ and V$\sb{\rm max}$. In a variety of systems the predictions of the equations were consistent with the changes observed in EC$\sb{50}$ and V$\sb{\rm max}$. In addition reductions in the calculated value of $\rm k\sb1/k\sb{-1}$ was shown to correlate well with $\beta$AR phosphorylation and to be minimally affected by sequestration and down-regulation. ^

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Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

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A feasibility study by Pail et al. (Can GOCE help to improve temporal gravity field estimates? In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, 2011b) shows that GOCE (‘Gravity field and steady-state Ocean Circulation Explorer’) satellite gravity gradiometer (SGG) data in combination with GPS derived orbit data (satellite-to-satellite tracking: SST-hl) can be used to stabilize and reduce the striping pattern of a bi-monthly GRACE (‘Gravity Recovery and Climate Experiment’) gravity field estimate. In this study several monthly (and bi-monthly) combinations of GRACE with GOCE SGG and GOCE SST-hl data on the basis of normal equations are investigated. Our aim is to assess the role of the gradients (solely) in the combination and whether already one month of GOCE observations provides sufficient data for having an impact in the combination. The estimation of clean and stable monthly GOCE SGG normal equations at high resolution ( >  d/o 150) is found to be difficult, and the SGG component, solely, does not show significant added value to monthly and bi-monthly GRACE gravity fields. Comparisons of GRACE-only and combined monthly and bi-monthly solutions show that the striping pattern can only be reduced when using both GOCE observation types (SGG, SST-hl), and mainly between d/o 45 and 60.

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The notion that changes in synaptic efficacy underlie learning and memory processes is now widely accepted even if definitive proof of the synaptic plasticity and memory hypothesis is still lacking. When learning occurs, patterns of neural activity representing the occurrence of events cause changes in the strength of synaptic connections within the brain. Reactivation of these altered connections constitutes the experience of memory for these events and for other events with which they may be associated. These statements summarize a long-standing theory of memory formation that we refer to as the synaptic plasticity and memory hypothesis. Since activity-dependent synaptic plasticity is induced at appropriate synapses during memory formation, and is both necessary and sufficient for the information storage, we can speculate that a methodological study of the synapse will help us understand the mechanism of learning. Random events underlie a wide range of biological processes as diverse as genetic drift and molecular diffusion, regulation of gene expression and neural network function. Additionally spatial variability may be important especially in systems with nonlinear behavior. Since synapse is a complex biological system we expect that stochasticity as well as spatial gradients of different enzymes may be significant for induction of plasticity. ^ In that study we address the question "how important spatial and temporal aspects of synaptic plasticity may be". We developed methods to justify our basic assumptions and examined the main sources of variability of calcium dynamics. Among them, a physiological method to estimate the number of postsynaptic receptors as well as a hybrid algorithm for simulating postsynaptic calcium dynamics. Additionally we studied how synaptic geometry may enhance any possible spatial gradient of calcium dynamics and how that spatial variability affect plasticity curves. Finally, we explored the potential of structural synaptic plasticity to provide a metaplasticity mechanism specific for the synapse. ^

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Crops growing in the Iberian Peninsula may be subjected to damagingly high temperatures during the sensitive development periods of flowering and grain filling. Such episodes are considered important hazards and farmers may take insurance to offset their impact. Increases in value and frequency of maximum temperature have been observed in the Iberian Peninsula during the 20th century, and studies on climate change indicate the possibility of further increase by the end of the 21st century. Here, impacts of current and future high temperatures on cereal cropping systems of the Iberian Peninsula are evaluated, focusing on vulnerable development periods of winter and summer crops. Climate change scenarios obtained from an ensemble of ten Regional Climate Models (multimodel ensemble) combined with crop simulation models were used for this purpose and related uncertainty was estimated. Results reveal that higher extremes of maximum temperature represent a threat to summer-grown but not to winter-grown crops in the Iberian Peninsula. The study highlights the different vulnerability of crops in the two growing seasons and the need to account for changes in extreme temperatures in developing adaptations in cereal cropping systems. Finally, this work contributes to clarifying the causes of high-uncertainty impact projections from previous studies.

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The purpose of this work is to propose a structure for simulating power systems using behavioral models of nonlinear DC to DC converters implemented through a look-up table of gains. This structure is specially designed for converters whose output impedance depends on the load current level, e.g. quasi-resonant converters. The proposed model is a generic one whose parameters can be obtained by direct measuring the transient response at different operating points. It also includes optional functionalities for modeling converters with current limitation and current sharing in paralleling characteristics. The pusposed structured also allows including aditional characteristics of the DC to DC converter as the efficency as a function of the input voltage and the output current or overvoltage and undervoltage protections. In addition, this proposed model is valid for overdamped and underdamped situations.