A review of load models for the prediction of footfall-induced vibration in structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadium, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lag among individuals inside the crowd. This paper presents the testing done on a structure designed to be a gymnasium. Two series of dynamic test were performed on the gym slab. For the first test an electrodynamic shaker was placed at several locations and during the second one people located inside a marked area bounced and jumped guided by different metronome rates. A finite element model (FEM) is presented and a comparison of numerically predicted and experimentally observed vibration modes and frequencies has been used to assess its validity. The second group of measurements will be compared with predictions made using the FEM model and three alternatives for crowd induced load modelling.

Implications of agricultural production, policy and land use changes on water resource assessment

Una gestión más eficiente y equitativa del agua a escala de cuenca no se puede centrar exclusivamente en el recurso hídrico en sí, sino también en otras políticas y disciplinas científicas. Existe un consenso creciente de que, además de la consideración de las cambiantes condiciones climáticas, es necesaria una integración de ámbitos de investigación tales como la agronomía, planificación del territorio y ciencias políticas y económicas a fin de satisfacer de manera sostenible las demandas de agua por parte de la sociedad y del medio natural. La Política Agrícola Común (PAC) es el principal motor de cambio en las tendencias de paisajes rurales y sistemas agrícolas, pero el deterioro del medio ambiente es ahora una de las principales preocupaciones. Uno de los cambios más relevantes se ha producido con la expansión e intensificación del olivar en España, principalmente con nuevas zonas de regadío o la conversión de olivares de secano a sistemas en regadío. Por otra parte, el cambio de las condiciones climáticas podría ejercer un papel importante en las tendencias negativas de las aportaciones a los ríos, pero no queda claro el papel que podrían estar jugando los cambios de uso de suelo y cobertura vegetal sobre las tendencias negativas de caudal observadas. Esta tesis tiene como objetivo mejorar el conocimiento de los efectos de la producción agrícola, política agraria y cambios de uso de suelo y cobertura vegetal sobre las condiciones de calidad del agua, respuesta hidrológica y apropiación del agua por parte de la sociedad. En primer lugar, el estudio determina las tendencias existentes de nitratos y sólidos en suspensión en las aguas superficiales de la cuenca del río Guadalquivir durante el periodo de 1998 a 2009. Desde una perspectiva de política agraria, la investigación trata de evaluar mediante un análisis de datos de panel las principales variables, incluyendo la reforma de la PAC de 2003, que están teniendo una influencia en ambos indicadores de calidad. En segundo lugar, la apropiación del agua y el nivel de contaminación por nitratos debido a la producción del aceite de oliva en España se determinan con una evaluación de la huella hídrica (HH), teniendo en cuenta una variabilidad espacial y temporal a largo de las provincias españolas y entre 1997 y 2008. Por último, la tesis analiza los efectos de los cambios de uso de suelo y cobertura vegetal sobre las tendencias negativas observadas en la zona alta del Turia, cabecera de la cuenca del río Júcar, durante el periodo 1973-2008 mediante una modelización ecohidrológica. En la cuenca del Guadalquivir cerca del 20% de las estaciones de monitoreo muestran tendencias significativas, lineales o cuadráticas, para cada indicador de calidad de agua. La mayoría de las tendencias significativas en nitratos están aumentando, y la mayoría de tendencias cuadráticas muestran un patrón en forma de U. Los modelos de regresión de datos de panel muestran que las variables más importantes que empeoran ambos indicadores de calidad del agua son la intensificación de biomasa y las exportaciones de ambos indicadores de calidad procedentes de aguas arriba. En regiones en las que el abandono agrícola y/o desintensificación han tenido lugar han mejorado las condiciones de calidad del agua. Para los nitratos, el desacoplamiento de las subvenciones a la agricultura y la reducción de la cuantía de las subvenciones a tierras de regadío subyacen en la reducción observada de la concentración de nitratos. Las medidas de modernización de regadíos y el establecimiento de zonas vulnerables a nitratos reducen la concentración en subcuencas que muestran una tendencia creciente de nitratos. Sin embargo, el efecto de las exportaciones de nitratos procedente de aguas arriba, la intensificación de la biomasa y los precios de los cultivos presentan un mayor peso, explicando la tendencia creciente observada de nitratos. Para los sólidos en suspensión, no queda de forma evidente si el proceso de desacoplamiento ha influido negativa o positivamente. Sin embargo, los mayores valores de las ayudas agrarias aún ligadas a la producción, en particular en zonas de regadío, conllevan un aumento de las tasas de erosión. Aunque la cuenca del Guadalquivir ha aumentado la producción agrícola y la eficiencia del uso del agua, el problema de las altas tasas de erosión aún no ha sido mitigado adecuadamente. El estudio de la huella hídrica (HH) revela que en 1 L de aceite de oliva español más del 99,5% de la HH está relacionado con la producción de la aceituna, mientras que menos del 0,5% se debe a otros componentes, es decir, a la botella, tapón y etiqueta. Durante el período estudiado, la HH verde en secano y en regadío representa alrededor del 72% y 12%, respectivamente, del total de la HH. Las HHs azul y gris representan 6% y 10%, respectivamente. La producción de aceitunas se concentra en regiones con una HH menor por unidad de producto. La producción de aceite de oliva ha aumentado su productividad del agua durante 1997-2008, incentivado por los crecientes precios del aceite, como también lo ha hecho la cantidad de exportaciones de agua virtual. De hecho, las mayores zonas productoras presentan una eficiencia alta del uso y de productividad del agua, así como un menor potencial de contaminación por nitratos. Pero en estas zonas se ve a la vez reflejado un aumento de presión sobre los recursos hídricos locales. El aumento de extracciones de agua subterránea relacionadas con las exportaciones de aceite de oliva podría añadir una mayor presión a la ya estresada cuenca del Guadalquivir, mostrando la necesidad de equilibrar las fuerzas del mercado con los recursos locales disponibles. Los cambios de uso de suelo y cobertura vegetal juegan un papel importante en el balance del agua de la cuenca alta del Turia, pero no son el principal motor que sustenta la reducción observada de caudal. El aumento de la temperatura es el principal factor que explica las mayores tasas de evapotranspiración y la reducción de caudales. Sin embargo, los cambios de uso de suelo y el cambio climático han tenido un efecto compensatorio en la respuesta hidrológica. Por un lado, el caudal se ha visto afectado negativamente por el aumento de la temperatura, mientras que los cambios de uso de suelo y cobertura vegetal han compensado positivamente con una reducción de las tasas de evapotranspiración, gracias a los procesos de disminución de la densidad de matorral y de degradación forestal. El estudio proporciona una visión que fortalece la interdisciplinariedad entre la planificación hidrológica y territorial, destacando la necesidad de incluir las implicaciones de los cambios de uso de suelo y cobertura vegetal en futuros planes hidrológicos. Estos hallazgos son valiosos para la gestión de la cuenca del río Turia, y el enfoque empleado es útil para la determinación del peso de los cambios de uso de suelo y cobertura vegetal en la respuesta hidrológica en otras regiones. ABSTRACT Achieving a more efficient and equitable water management at catchment scale does not only rely on the water resource itself, but also on other policies and scientific knowledge. There is a growing consensus that, in addition to consideration of changing climate conditions, integration with research areas such as agronomy, land use planning and economics and political science is required to meet sustainably the societal and environmental water demands. The Common Agricultural Policy (CAP) is a main driver for trends in rural landscapes and agricultural systems, but environmental deterioration is now a principal concern. One of the most relevant changes has occurred with the expansion and intensification of olive orchards in Spain, taking place mainly with new irrigated areas or with the conversion from rainfed to irrigated systems. Moreover, changing climate conditions might exert a major role on water yield trends, but it remains unclear the role that ongoing land use and land cover changes (LULCC) might have on observed river flow trends. This thesis aims to improve the understanding of the effects of agricultural production, policies and LULCC on water quality conditions, hydrological response and human water appropriation. Firstly, the study determines the existing trends for nitrates and suspended solids in the Guadalquivir river basin’s surface waters (south Spain) during the period from 1998 to 2009. From a policy perspective, the research tries to assess with panel data analysis the main drivers, including the 2003 CAP reform, which are having an influence on both water quality indicators. Secondly, water appropriation and nitrate pollution level originating from the production of olive oil in Spain is determined with a water footprint (WF) assessment, considering a spatial temporal variability across the Spanish provinces and from 1997 to 2008 years. Finally, the thesis analyzes the effects of the LULCC on the observed negative trends over the period 1973-2008 in the Upper Turia basin, headwaters of the Júcar river demarcation (east Spain), with ecohydrological modeling. In the Guadalquivir river basin about 20% of monitoring stations show significant trends, linear or quadratic, for each water quality indicator. Most significant trends of nitrates are augmenting than decreasing, and most significant quadratic terms of both indicators exhibit U-shaped patterns. The panel data models show that the most important drivers that are worsening nitrates and suspended solids in the basin are biomass intensification and exports of both water quality indicators from upland regions. In regions that agricultural abandonment and/or de-intensification have taken place the water quality conditions have improved. For nitrates, the decoupling of agricultural subsidies and the reduction of the amount of subsidies to irrigated land underlie the observed reduction of nitrates concentration. Measures of irrigation modernization and establishment of vulnerable zones to nitrates ameliorate the concentration of nitrates in subbasins showing an increasing trend. However, the effect of nitrates load from upland areas, intensification of biomass and crop prices present a greater weight leading to the final increasing trend in this subbasins group, where annual crops dominate. For suspended solids, there is no clear evidence that decoupling process have influenced negatively or positively. Nevertheless, greater values of subsidies still linked to production, particularly in irrigated regions, lead to increasing erosion rates. Although agricultural production has augmented in the basin and water efficiency in the agricultural sector has improved, the issue of high erosion rates has not yet been properly faced. The water footprint (WF) assessment reveals that for 1 L Spanish olive oil more than 99.5% of the WF is related to the olive fruit production, whereas less than 0.5% is due to other components i.e. bottle, cap and label. Over the studied period, the green WF in rainfed and irrigated systems represents about 72% and 12%, respectively, of the total WF. Blue and grey WFs represent 6% and 10%, respectively. The olive production is concentrated in regions with the smallest WF per unit of product. The olive oil production has increased its apparent water productivity from 1997 to 2008 incentivized by growing trade prices, but also did the amount of virtual water exports. In fact, the largest producing areas present high water use efficiency per product and apparent water productivity as well as less nitrates pollution potential, but this enhances the pressure on the available water resources. Increasing groundwater abstractions related to olive oil exports may add further pressure to the already stressed Guadalquivir basin. This shows the need to balance the market forces with the available local resources. Concerning the effects of LULCC on the Upper Turia basin’s streamflow, LULCC play a significant role on the water balance, but it is not the main driver underpinning the observed reduction on Turia's streamflow. Increasing mean temperature is the main factor supporting larger evapotranspiration rates and streamflow reduction. In fact, LULCC and climate change have had an offsetting effect on the streamflow generation during the study period. While streamflow has been negatively affected by increasing temperature, ongoing LULCC have positively compensated with reduced evapotranspiration rates, thanks to mainly shrubland clearing and forest degradation processes. The research provides insight for strengthening the interdisciplinarity between hydrological and spatial planning, highlighting the need to include the implications of LULCC in future hydrological plans. These findings are valuable for the management of the Turia river basin, as well as a useful approach for the determination of the weight of LULCC on the hydrological response in other regions.

On the layout of a least weight single span structure with uniform load. Some comments and improvements

Beghini et al (Struct Multidisc Optim doi:10.1007/s00158-013-1030-6, 2013) have published a very interesting paper arriving to practically the same nearly optimal solutions for the so named “bridge prob- lem” that the Writers published a year before, but using an alternative and remarkable approach to the problem. In spite of this general agreement, the Writers think that some details of the paper can be improved and there are results that can be given a clear and mean- ingful interpretation thanks to an old and practically unknown theorem on optimal slenderness.

Discrete element analysis for the assessment of the accuracy of load cell-based dynamic weighing systems in grape harvesters under different ground conditions

Dynamic weighing systems based on load cells are commonly used to estimate crop yields in the field. There is lack of data, however, regarding the accuracy of such weighing systems mounted on harvesting machinery, especially on that used to collect high value crops such as fruits and vegetables. Certainly, dynamic weighing systems mounted on the bins of grape harvesters are affected by the displacement of the load inside the bin when moving over terrain of changing topography. In this work, the load that would be registered in a grape harvester bin by a dynamic weighing system based on the use of a load cell was inferred by using the discrete element method (DEM). DEM is a numerical technique capable of accurately describing the behaviour of granular materials under dynamic situations and it has been proven to provide successful predictions in many different scenarios. In this work, different DEM models of a grape harvester bin were developed contemplating different influencing factors. Results obtained from these models were used to infer the output given by the load cell of a real bin. The mass detected by the load cell when the bin was inclined depended strongly on the distribution of the load within the bin, but was underestimated in all scenarios. The distribution of the load was found to be dependent on the inclination of the bin caused by the topography of the terrain, but also by the history of inclination (inclination rate, presence of static periods, etc.) since the effect of the inertia of the particles (i.e., representing the grapes) was not negligible. Some recommendations are given to try to improve the accuracy of crop load measurement in the field.

Limit load instabilities in structural elements

Este trabajo analiza distintas inestabilidades en estructuras formadas por distintos materiales. En particular, se capturan y se modelan las inestabilidades usando el método de Riks. Inicialmente, se analiza la bifurcación en depósitos cilíndricos formados por material anisótropo sometidos a carga axial y presión interna. El análisis de bifurcación y post-bifurcación asociados con cilindros de pared gruesa se formula para un material incompresible reforzado con dos fibras que son mecánicamente equivalentes y están dispuestas simétricamente. Consideramos dos casos en la naturaleza de la anisotropía: (i) Fibras refuerzo que tienen una influencia particular sobre la respuesta a cortante del material y (ii) Fibras refuerzo que influyen sólo si la fibra cambia de longitud con la deformación. Se analiza la propagación de las inestabilidades. En concreto, se diferencia en el abultamiento (bulging) entre la propagación axial y la propagación radial de la inestabilidad. Distintos modelos sufren una u otra propagación. Por último, distintas inestabilidades asociadas al mecanismo de ablandamiento del material (material softening) en contraposición al de endurecimiento (hardening) en una estructura (viga) de a: hormigón y b: hormigón reforzado son modeladas utilizando una metodología paralela a la desarrollada en el análisis de inestabilidades en tubos sometidos a presión interna. This present work deals with the instability of structures made of various materials. It captures and models different types of instabilities using numerical analysis. Firstly, we consider bifurcation for anisotropic cylindrical shells subject to axial loading and internal pressure. Analysis of bifurcation and post bifurcation of inflated hyperelastic thick-walled cylinder is formulated using a numerical procedure based on the modified Riks method for an incompressible material with two preferred directions which are mechanically equivalent and are symmetrically disposed. Secondly, bulging/necking motion in doubly fiber-reinforced incompressible nonlinearly elastic cylindrical shells is captured and we consider two cases for the nature of the anisotropy: (i) reinforcing models that have a particular influence on the shear response of the material and (ii) reinforcing models that depend only on the stretch in the fiber direction. The different instability motions are considered. Axial propagation of the bulging instability mode in thin-walled cylinders under inflation is analyzed. We present the analytical solution for this particular motion as well as for radial expansion during bulging evolution. For illustration, cylinders that are made of either isotropic incompressible non-linearly elastic materials or doubly fiber reinforced incompressible non-linearly elastic materials are considered. Finally, strain-softening constitutive models are considered to analyze two concrete structures: a reinforced concrete beam and an unreinforced notch beam. The bifurcation point is captured using the Riks method used previously to analyze bifurcation of a pressurized cylinder.

Contribution to Load-Frequency Regulation of a Hydropower Plant with Long Tail-Race Tunnel

In this paper, a hydroelectric power plant with long tail-race tunnel has been modelled for assessing its contribution to secondary regulation reserve. Cavitation problems, caused by the discharge conduit length, are expected downstream the turbine where low pressure appears during regulation manoeuvres. Therefore, governor's gains should be selected taking into account these phenomena. On the other hand, regulation services bidden by the plant operator should fulfil TSO (Transmission System Operator) quality requirements. A methodology for tuning governor PI gains is proposed and applied to a Hydro power plant in pre-design phase in northwest area of Spain. The PI gains adjustment proposed provides a proper plant response, according to some established indexes, while avoiding cavitation phenomena.

Transversal load distribution on bridge decks

An orthotropic rectangular plate is analysed. The plate has been considered simply supported in two opposite edges and general boundary conditions along the remainder edges. Matrix formulation, very convenient for programming on a digital computer, is used through the text. This technique is applied to an actual bridge deck and the results are compared with those obtained by means of the Guyon-Massonet-Rowe method

Bridge damage identification from moving load induced deflection based on wavelet transform and Lipschitz exponent

The wavelet transform and Lipschitz exponent perform well in detecting signal singularity.With the bridge crack damage modeled as rotational springs based on fracture mechanics, the deflection time history of the beam under the moving load is determined with a numerical method. The continuous wavelet transformation (CWT) is applied to the deflection of the beam to identify the location of the damage, and the Lipschitz exponent is used to evaluate the damage degree. The influence of different damage degrees,multiple damage, different sensor locations, load velocity and load magnitude are studied.Besides, the feasibility of this method is verified by a model experiment.

Optical sensing of the fatigue damage state of CFRP under realistic aeronautical load sequences

We present an optical sensing methodology to estimate the fatigue damage state of structures made of carbon fiber reinforced polymer (CFRP), by measuring variations on the surface roughness. Variable amplitude loads (VAL), which represent realistic loads during aeronautical missions of fighter aircraft (FALSTAFF) have been applied to coupons until failure. Stiffness degradation and surface roughness variations have been measured during the life of the coupons obtaining a Pearson correlation of 0.75 between both variables. The data were compared with a previous study for Constant Amplitude Load (CAL) obtaining similar results. Conclusions suggest that the surface roughness measured in strategic zones is a useful technique for structural health monitoring of CFRP structures, and that it is independent of the type of load applied. Surface roughness can be measured in the field by optical techniques such as speckle, confocal perfilometers and interferometry, among others.

The major allergens of birch pollen and cow milk, Bet v 1 and Bos d 5, are structurally related to human licocalin 2, enabling them to manipulate T-helper cells depending on their load with siderophore-bound iron

We conclude that Bet v 1 and Bos d 5 not only structurally mimic human LCN2, but also functionally by their ability to bind iron via siderophores. The apo-forms promote Th2 cells, whereas the holo-forms appear to be immunosuppressive. These results provide for the first time a functional understanding on the principle of allergenicity of major allergens from entirely independent sources, like birch and milk.

HLA alleles determine human T-lymphotropic virus-I (HTLV-I) proviral load and the risk of HTLV-I-associated myelopathy

The risk of disease associated with persistent virus infections such as HIV-I, hepatitis B and C, and human T-lymphotropic virus-I (HTLV-I) is strongly determined by the virus load. However, it is not known whether a persistent class I HLA-restricted antiviral cytotoxic T lymphocyte (CTL) response reduces viral load and is therefore beneficial or causes tissue damage and contributes to disease pathogenesis. HTLV-I-associated myelopathy (HAM/TSP) patients have a high virus load compared with asymptomatic HTLV-I carriers. We hypothesized that HLA alleles control HTLV-I provirus load and thus influence susceptibility to HAM/TSP. Here we show that, after infection with HTLV-I, the class I allele HLA-A*02 halves the odds of HAM/TSP (P < 0.0001), preventing 28% of potential cases of HAM/TSP. Furthermore, HLA-A*02+ healthy HTLV-I carriers have a proviral load one-third that (P = 0.014) of HLA-A*02− HTLV-I carriers. An association of HLA-DRB1*0101 with disease susceptibility also was identified, which doubled the odds of HAM/TSP in the absence of the protective effect of HLA-A*02. These data have implications for other persistent virus infections in which virus load is associated with prognosis and imply that an efficient antiviral CTL response can reduce virus load and so prevent disease in persistent virus infections.

The load dependence of kinesin’s mechanical cycle

Kinesin is a dimeric motor protein that transports organelles in a stepwise manner toward the plus-end of microtubules by converting the energy of ATP hydrolysis into mechanical work. External forces can influence the behavior of kinesin, and force-velocity curves have shown that the motor will slow down and eventually stall under opposing loads of ≈5 pN. Using an in vitro motility assay in conjunction with a high-resolution optical trapping microscope, we have examined the behavior of individual kinesin molecules under two previously unexplored loading regimes: super-stall loads (>5 pN) and forward (plus-end directed) loads. Whereas some theories of kinesin function predict a reversal of directionality under high loads, we found that kinesin does not walk backwards under loads of up to 13 pN, probably because of an irreversible transition in the mechanical cycle. We also found that this cycle can be significantly accelerated by forward loads under a wide range of ATP concentrations. Finally, we noted an increase in kinesin’s rate of dissociation from the microtubule with increasing load, which is consistent with a load dependent partitioning between two recently described kinetic pathways: a coordinated-head pathway (which leads to stepping) and an independent-head pathway (which is static).

Fluctuating silicate:nitrate ratios and coastal plankton food webs

Marine diatoms require dissolved silicate to form an external shell, and their growth becomes Si-limited when the atomic ratio of silicate to dissolved inorganic nitrogen (Si:DIN) approaches 1:1, also known as the “Redfield ratio.” Fundamental changes in the diatom-to-zooplankton-to-higher trophic level food web should occur when this ratio falls below 1:1 and the proportion of diatoms in the phytoplankton community is reduced. We quantitatively substantiate these predictions by using a variety of data from the Mississippi River continental shelf, a system in which the Si:DIN loading ratio has declined from around 3:1 to 1:1 during this century because of land-use practices in the watershed. We suggest that, on this shelf, when the Si:DIN ratio in the river decreases to less than 1:1, then (i) copepod abundance changes from >75% to <30% of the total mesozooplankton, (ii) zooplankton fecal pellets become a minor component of the in situ primary production consumed, and (iii) bottom-water oxygen consumption rates become less dependent on relatively fast-sinking (diatom-rich) organic matter packaged mostly as zooplankton fecal pellets. This coastal ecosystem appears to be a pelagic food web dynamically poised to be either a food web composed of diatoms and copepods or one with potentially disruptive harmful algal blooms. The system is directed between these two ecosystem states by Mississippi River water quality, which is determined by land-use practices far inland.

The Arabidopsis CHL1 protein plays a major role in high-affinity nitrate uptake

The CHL1 (NRT1) gene of Arabidopsis encodes a nitrate-inducible nitrate transporter that is thought to be a component of the low-affinity (mechanism II) nitrate-uptake system in plants. A search was performed to find high-affinity (mechanism I) uptake mutants by using chlorate selections on plants containing Tag1 transposable elements. Chlorate-resistant mutants defective in high-affinity nitrate uptake were identified, and one had a Tag1 insertion in chl1, which was responsible for the phenotype. Further analysis showed that chl1 mutants have reduced high-affinity uptake in induced plants and are missing a saturable component of the constitutive, high-affinity uptake system in addition to reduced low-affinity uptake. The contribution of CHL1 to constitutive high-affinity uptake is higher when plants are grown at more acidic pH, conditions that increase the level of CHL1 mRNA. chl1 mutants show reduced membrane depolarization in root epidermal cells in response to low (250 μM) and high (10 mM) concentrations of nitrate. Low levels of nitrate (100 μM) induce a rapid increase in CHL1 mRNA. These results show that CHL1 is an important component of both the high-affinity and the low-affinity nitrate-uptake systems and indicate that CHL1 may be a dual-affinity nitrate transporter.

Dual pathways for regulation of root branching by nitrate

Root development is extremely sensitive to variations in nutrient supply, but the mechanisms are poorly understood. We have investigated the processes by which nitrate (NO3−), depending on its availability and distribution, can have both positive and negative effects on the development and growth of lateral roots. When Arabidopsis roots were exposed to a locally concentrated supply of NO3− there was no increase in lateral root numbers within the NO3−-rich zone, but there was a localized 2-fold increase in the mean rate of lateral root elongation, which was attributable to a corresponding increase in the rate of cell production in the lateral root meristem. Localized applications of other N sources did not stimulate lateral root elongation, consistent with previous evidence that the NO3− ion is acting as a signal rather than a nutrient. The axr4 auxin-resistant mutant was insensitive to the stimulatory effect of NO3−, suggesting an overlap between the NO3− and auxin response pathways. High rates of NO3− supply to the roots had a systemic inhibitory effect on lateral root development that acted specifically at the stage when the laterals had just emerged from the primary root, apparently delaying final activation of the lateral root meristem. A nitrate reductase-deficient mutant showed increased sensitivity to this systemic inhibitory effect, suggesting that tissue NO3− levels may play a role in generating the inhibitory signal. We present a model in which root branching is modulated by opposing signals from the plant’s internal N status and the external supply of NO3−.