Differential Equations for Definition and Evaluation of Feynman Integrals

It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that presented formalism is convenient for practical calculations of Feynman integrals.Comment: pages, LaTEX, MSU-PHYS-HEP-Lu2/9

Scaling ozone responses of forest trees to the ecosystem level in a changing climate

Many uncertainties remain regarding how climate change will alter the structure and function of forest ecosystems. At the Aspen FACE experiment in northern Wisconsin, we are attempting to understand how an aspen/birch/maple forest ecosystem responds to long-term exposure to elevated carbon dioxide (CO 2 ) and ozone (O 3 ), alone and in combination, from establishment onward. We examine how O 3 affects the flow of carbon through the ecosystem from the leaf level through to the roots and into the soil micro-organisms in present and future atmospheric CO 2 conditions. We provide evidence of adverse effects of O 3 , with or without co-occurring elevated CO 2 , that cascade through the entire ecosystem impacting complex trophic interactions and food webs on all three species in the study: trembling aspen ( Populus tremuloides Michx . ), paper birch ( Betula papyrifera Marsh), and sugar maple ( Acer saccharum Marsh). Interestingly, the negative effect of O 3 on the growth of sugar maple did not become evident until 3 years into the study. The negative effect of O 3 effect was most noticeable on paper birch trees growing under elevated CO 2 . Our results demonstrate the importance of long-term studies to detect subtle effects of atmospheric change and of the need for studies of interacting stresses whose responses could not be predicted by studies of single factors. In biologically complex forest ecosystems, effects at one scale can be very different from those at another scale. For scaling purposes, then, linking process with canopy level models is essential if O 3 impacts are to be accurately predicted. Finally, we describe how outputs from our long-term multispecies Aspen FACE experiment are being used to develop simple, coupled models to estimate productivity gain/loss from changing O 3 .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72464/1/j.1365-3040.2005.01362.x.pd

Zeitliche und räumliche Skalen der Fluss-Grundwasser-Interaktion : ein multidimensionaler hydrogeologischer Untersuchungsansatz

Die Prozesse der Fluss-Grundwasser-Interaktionen sind stark skalenabhängig und im Allgemeinen stark instationär. Einen für das Prozessverständnis wichtigen Aspekt betreffen die kleinräumigen Strömungsverhältnisse an der Grenzschicht zwischen Oberflächengewässer und Grundwasser im hyporheischen Interstitial. Dies betrifft insbesondere auch Fragestellungen zu Strömungsverhältnissen in Forellenlaichgruben kiesführender Flüsse. Exemplarisch für kleinere mit Sohlschwellen verbaute und kanalisierte Fließgewässer wurden am voralpinen Schweizer Fluss Enziwigger verschiedene Methoden entwickelt, getestet und kombiniert, die es erlauben die vier Dimensionen (drei räumliche und eine zeitliche) der Interaktion Oberflächengewässer-Interstitialraum-Grundwasser für einzelne Flussabschnitte zu erfassen. Der Aufbau eines Messnetzes sowie die Durchführung von Feldmessungen lieferten Grundlagen für eine Grundwasserströmungsmodellierung. Kontinuierliche Zeitreihen der Hydraulik, Temperatur und elektrischen Leitfähigkeit im Fließgewässer, an der Gewässersohle sowie im flussnahen Grundwasser dienten zudem der Identifizierung von Zonen mit signifikantem Fluss-Grundwasser-Austausch und von zeitlich instationären bevorzugten Fließpfaden im Grundwasser bei unterschiedlichen hydrologischen Randbedingungen. Die Resultate der Feldmessungen in Kombination mit der instationären Modellierung und Szenarienentwicklung illustrieren die Bedeutung von sich dynamisch verändernden Infiltrations- und Exfiltrationsmustern im Flussbett. Abstract River-groundwater interactions show strong scale-dependencies and are often strongly transient. In this regard, small-scale flow conditions in the hyporheic zone at the interface between surface- and groundwater can be important for process-understanding. This especially includes questions concerning flow conditions in salmonid redds of gravel-bed rivers. The Swiss subalpine river Enziwigger was chosen as an example for a small channelized river with artificial steps within the riverbed. Several methods were developed, tested and combined that capture the four dimensions (three spatial and one temporal) of the interactions between surface water, the hyporheic zone and groundwater, for individual river segments. The setup of a monitoring network as well as the realization of field-measurements provided data for groundwater flow models. Continuous time series of hydraulic data, temperature and electrical conductivity within the river and the riverbed, as well as within the riverine groundwater, allowed identifying zones with significant exchange of surface water and groundwater. Additionally, the data helped describe the transient character of groundwater flow-paths under various hydrological boundary conditions. Results of the field-measurements in combination with transient groundwater flow modeling and scenario analyses illustrate the relevance of dynamically changing infiltration and exfiltration patterns within the riverbed