Title: Variational problems for tree roots and branches
This paper studies two classes of variational problems introduced in Bressan and Sun (On the optimal shape of tree roots and branches. arXiv:1803.01042), related to the optimal shapes of tree roots and branches. Given a measure μ describing the distribution of leaves, a sunlight functional S(μ) computes the total amount of light captured by the leaves. For a measure μ describing the distribution of root hair cells, a harvest functional H(μ) computes the total amount of water and nutrients gathered by the roots. In both cases, we seek a measure μ that maximizes these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk or from the trunk to the leaves. Compared with Bressan and Sun, here we do not impose any a priori bound on the total mass of the optimal measure μ, and more careful a priori estimates are thus required. In the unconstrained optimization problem for branches, we prove that an optimal measure exists, with bounded support and bounded total mass. In the unconstrained problem for tree roots, we prove that an optimal measure exists, with bounded support but possibly unbounded total mass. The last section of the paper analyzes how the size of the optimal tree depends on the parameters defining the various functionals. more »« less
Bressan, Alberto; Sun, Qing(
, Mathematical Models and Methods in Applied Sciences)
null
(Ed.)
This paper introduces two classes of variational problems, determining optimal shapes for tree roots and branches. Given a measure [Formula: see text], describing the distribution of leaves, we introduce a sunlight functional [Formula: see text] computing the total amount of light captured by the leaves. On the other hand, given a measure [Formula: see text] describing the distribution of root hair cells, we consider a harvest functional [Formula: see text] computing the total amount of water and nutrients gathered by the roots. In both cases, we seek to maximize these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk and from the trunk to the leaves. The main results establish various properties of these functionals, and the existence of optimal distributions. In particular, we prove the upper semicontinuity of [Formula: see text] and [Formula: see text], together with a priori estimates on the support of optimal distributions.
Crous, P.W.; Osieck, E.R.; Jurjevi, Ž; Boers, J.; Van Iperen, A.L.; Starink-Willemse, M.; Dima, B.; Balashov, S.; Bulgakov, T.S.; Johnston, P.R.; et al(
, Persoonia - Molecular Phylogeny and Evolution of Fungi)
Novel species of fungi described in this study include those from various countries as follows: Antartica , Cladosporium austrolitorale from coastal sea sand. Australia , Austroboletus yourkae on soil, Crepidotus innuopurpureus on dead wood, Curvularia stenotaphri from roots and leaves of Stenotaphrum secundatum and Thecaphora stajsicii from capsules of Oxalis radicosa. Belgium , Paraxerochrysium coryli (incl. Paraxerochrysium gen. nov.) from Corylus avellana. Brazil , Calvatia nordestina on soil, Didymella tabebuiicola from leaf spots on Tabebuia aurea, Fusarium subflagellisporum from hypertrophied floral and vegetative branches of Mangifera indica and Microdochium maculosum from living leaves of Digitaria insularis. Canada , Cuphophyllus bondii fromagrassland. Croatia , Mollisia inferiseptata from a rotten Laurus nobilis trunk. Cyprus , Amanita exilis oncalcareoussoil. Czech Republic , Cytospora hippophaicola from wood of symptomatic Vaccinium corymbosum. Denmark , Lasiosphaeria deviata on pieces of wood and herbaceousdebris. Dominican Republic , Calocybella goethei among grass on a lawn. France (Corsica) , Inocybe corsica onwetground. France (French Guiana) , Trechispora patawaensis on decayed branch of unknown angiosperm tree and Trechispora subregularis on decayed log of unknown angiosperm tree. Germany , Paramicrothecium sambuci (incl. Paramicrothecium gen. nov.)ondeadstemsof Sambucus nigra. India , Aureobasidium microtermitis from the gut of a Microtermes sp. termite, Laccaria diospyricola on soil and Phylloporia tamilnadensis on branches of Catunaregam spinosa . Iran , Pythium serotinoosporum from soil under Prunus dulcis. Italy , Pluteus brunneovenosus on twigs of broad leaved trees on the ground. Japan , Heterophoma rehmanniae on leaves of Rehmannia glutinosa f. hueichingensis. Kazakhstan , Murispora kazachstanica from healthy roots of Triticum aestivum. Namibia , Caespitomonium euphorbiae (incl. Caespitomonium gen. nov.)from stems of an Euphorbia sp. Netherlands , Alfaria junci, Myrmecridium junci, Myrmecridium juncicola, Myrmecridium juncigenum, Ophioceras junci, Paradinemasporium junci (incl. Paradinemasporium gen. nov.), Phialoseptomonium junci, Sporidesmiella juncicola, Xenopyricularia junci and Zaanenomyces quadripartis (incl. Zaanenomyces gen. nov.), fromdeadculmsof Juncus effusus, Cylindromonium everniae and Rhodoveronaea everniae from Evernia prunastri, Cyphellophora sambuci and Myrmecridium sambuci from Sambucus nigra, Kiflimonium junci, Saro cladium junci, Zaanenomyces moderatricis academiae and Zaanenomyces versatilis from dead culms of Juncus inflexus, Microcera physciae from Physcia tenella, Myrmecridium dactylidis from dead culms of Dactylis glomerata, Neochalara spiraeae and Sporidesmium spiraeae from leaves of Spiraea japonica, Neofabraea salicina from Salix sp., Paradissoconium narthecii (incl. Paradissoconium gen. nov.)from dead leaves of Narthecium ossifragum, Polyscytalum vaccinii from Vaccinium myrtillus, Pseudosoloacrosporiella cryptomeriae (incl. Pseudosoloacrosporiella gen. nov.)fromleavesof Cryptomeria japonica, Ramularia pararhabdospora from Plantago lanceolata, Sporidesmiella pini from needles of Pinus sylvestris and Xenoacrodontium juglandis (incl. Xenoacrodontium gen. nov. and Xenoacrodontiaceae fam. nov.)from Juglans regia . New Zealand , Cryptometrion metrosideri from twigs of Metrosideros sp., Coccomyces pycnophyllocladi from dead leaves of Phyllocladus alpinus, Hypoderma aliforme from fallen leaves Fuscopora solandri and Hypoderma subiculatum from dead leaves Phormium tenax. Norway , Neodevriesia kalakoutskii from permafrost and Variabilispora viridis from driftwood of Picea abies. Portugal , Entomortierella hereditatis from abio film covering adeteriorated limestone wall. Russia , Colpoma junipericola from needles of Juniperus sabina, Entoloma cinnamomeum on soil in grasslands, Entoloma verae on soil in grasslands, Hyphodermella pallidostraminea on a dry dead branch of Actinidia sp., Lepiota sayanensis onlitterinamixedforest, Papiliotrema horticola from Malus communis , Paramacroventuria ribis (incl. Paramacroventuria gen. nov.)fromleaves of Ribes aureum and Paramyrothecium lathyri from leaves of Lathyrus tuberosus. South Africa , Harzia combreti from leaf litter of Combretum collinum ssp. sulvense, Penicillium xyleborini from Xyleborinus saxesenii , Phaeoisaria dalbergiae from bark of Dalbergia armata, Protocreopsis euphorbiae from leaf litter of Euphorbia ingens and Roigiella syzygii from twigs of Syzygium chordatum . Spain , Genea zamorana on sandy soil, Gymnopus nigrescens on Scleropodium touretii, Hesperomyces parexochomi on Parexochomus quadriplagiatus, Paraphoma variabilis from dung, Phaeococcomyces kinklidomatophilus from a blackened metal railing of an industrial warehouse and Tuber suaveolens in soil under Quercus faginea. Svalbard and Jan Mayen , Inocybe nivea associated with Salix polaris. Thailand , Biscogniauxia whalleyi oncorticatedwood. UK , Parasitella quercicola from Quercus robur. USA , Aspergillus arizonicus from indoor air in a hospital, Caeliomyces tampanus (incl. Caeliomyces gen. nov.)fromoffice dust, Cippumomyces mortalis (incl. Cippumomyces gen. nov.)fromatombstone, Cylindrium desperesense from air in a store, Tetracoccosporium pseudoaerium from air sample in house, Toxicocladosporium glendoranum from air in a brick room, Toxicocladosporium losalamitosense from air in a classroom, Valsonectria portsmouthensis from airinmen'slockerroomand Varicosporellopsis americana from sludge in a water reservoir. Vietnam , Entoloma kovalenkoi on rotten wood, Fusarium chuoi inside seed of Musa itinerans , Micropsalliota albofelina on soil in tropical evergreen mixed forest sand Phytophthora docyniae from soil and roots of Docynia indica. Morphological and culture characteristics are supported by DNA barcodes.
Abstract Wind-induced stress is the primary mechanical cause of tree failures. Among different factors, the branching mechanism plays a central role in the stress distribution and stability of trees in windstorms. A recent study showed that Leonardo da Vinci’s original observation, stating that the total cross section of branches conserved across branching nodes is the optimal configuration for resisting wind-induced damage in rigid trees, is correct. However, the breaking risk and the optimal branching pattern of trees are also a function of their reconfiguration capabilities and the processes they employ to mitigate high wind-induced stress hotspots. In this study, using a numerical model of rigid and flexible branched trees, we explore the role of flexibility and branching patterns of trees in their reconfiguration and stress mitigation capabilities. We identify the robust optimal branching mechanism for an extensive range of tree flexibility. Our results show that the probability of a tree breaking at each branching level from the stem to terminal foliage strongly depends on the cross section changes in the branching nodes, the overall tree geometry, and the level of tree flexibility. Three response categories have been identified: the stress concentration in the main trunk, the uniform stress level through the tree’s height, and substantial stress localization in the terminal branches. The reconfigurability of the tree determines the dominant response mode. The results suggest a very similar optimal branching law for both flexible and rigid trees wherein uniform stress distribution occurs throughout the tree’s height. An exception is the very flexible branched plants in which the optimal branching pattern deviates from this prediction and is strongly affected by the reconfigurability of the tree.
Czyzowicz, J.; Dobrev, S.; Killick, R.; Kranakis, E.; Krizanc, D.; Narayanan, L.; Opatrny, J; Pankratov, D.; Shende, S.(
, 28th International Colloquium on Structural Information and Communication Complexity (SIROCCO))
null
(Ed.)
We consider the problem of collective exploration of a known n-
node edge-weighted graph by k mobile agents that have limited energy but are
capable of energy transfers. The agents are initially placed at an arbitrary subset
of nodes in the graph, and each agent has an initial, possibly different, amount
of energy. The goal of the exploration problem is for every edge in the graph to
be traversed by at least one agent. The amount of energy used by an agent to
travel distance x is proportional to x. In our model, the agents can share energy
when co-located: when two agents meet, one can transfer part of its energy to
the other.
For an n-node path, we give an O(n+k) time algorithm that either nds an
exploration strategy, or reports that one does not exist. For an n-node tree with
l leaves, we give an O(n+lk^2) algorithm that finds an exploration strategy if one
exists. Finally, for the general graph case, we show that the problem of deciding
if exploration is possible by energy-sharing agents is NP-hard, even for 3-regular
graphs. In addition, we show that it is always possible to find an exploration
strategy if the total energy of the agents is at least twice the total weight of the
edges; moreover, this is asymptotically optimal.
Nutrient allocation is an important aspect of plant resource uptake and use, which is related to life‐history strategies. Although to date considerable attention has focused on plant allocation of nitrogen and phosphorus, comparatively little information is available on the allocation of various other nutrients and their up‐scaling from the species to community level.
We measured 10 nutrient elements in the leaves, branches and fine roots of 551 plant species growing in eight forest ecosystems in China, ranging from cold temperate to subtropical forests. We estimated the scaling relationship of multiple nutrients among plant organs at the species level and scaled‐up the relationship to the community level by combining this information with that of community structure.
Nutrient allocation among plant organs was conserved in different functional groups and biomes across broad environmental gradients. Nutrient partitioning between organs with similar function tended to be isometric, whereas partitioning between organs with distinct functions tended to be allometric. The scaling relationship between above‐ and below‐ground organs remained consistent, whereas the scaling relationship within above‐ground organs changed after scaling up from the species to the community level, with the relative change in nutrients being consistently smaller in the more active organs.
Synthesis. The pattern of multiple nutrient allocation among organs showed a degree of conservatism across plant functional groups and biomes, with disproportional changes in nutrient content between functionally distinct organs and a lower relative change in more active organs. This conservative strategy implies the existence of general rules that constrain plant nutrient allocation.
Bressan, Alberto, Palladino, Michele, and Sun, Qing. Variational problems for tree roots and branches. Retrieved from https://par.nsf.gov/biblio/10162554. Calculus of variations and partial differential equations 59.7 Web. doi:10.1007/s00526-019-1666-1.
Bressan, Alberto, Palladino, Michele, & Sun, Qing. Variational problems for tree roots and branches. Calculus of variations and partial differential equations, 59 (7). Retrieved from https://par.nsf.gov/biblio/10162554. https://doi.org/10.1007/s00526-019-1666-1
@article{osti_10162554,
place = {Country unknown/Code not available},
title = {Variational problems for tree roots and branches},
url = {https://par.nsf.gov/biblio/10162554},
DOI = {10.1007/s00526-019-1666-1},
abstractNote = {This paper studies two classes of variational problems introduced in Bressan and Sun (On the optimal shape of tree roots and branches. arXiv:1803.01042), related to the optimal shapes of tree roots and branches. Given a measure μ describing the distribution of leaves, a sunlight functional S(μ) computes the total amount of light captured by the leaves. For a measure μ describing the distribution of root hair cells, a harvest functional H(μ) computes the total amount of water and nutrients gathered by the roots. In both cases, we seek a measure μ that maximizes these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk or from the trunk to the leaves. Compared with Bressan and Sun, here we do not impose any a priori bound on the total mass of the optimal measure μ, and more careful a priori estimates are thus required. In the unconstrained optimization problem for branches, we prove that an optimal measure exists, with bounded support and bounded total mass. In the unconstrained problem for tree roots, we prove that an optimal measure exists, with bounded support but possibly unbounded total mass. The last section of the paper analyzes how the size of the optimal tree depends on the parameters defining the various functionals.},
journal = {Calculus of variations and partial differential equations},
volume = {59},
number = {7},
author = {Bressan, Alberto and Palladino, Michele and Sun, Qing},
}
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