2,396 research outputs found
A two-scale Stefan problem arising in a model for tree sap exudation
The study of tree sap exudation, in which a (leafless) tree generates
elevated stem pressure in response to repeated daily freeze-thaw cycles, gives
rise to an interesting multi-scale problem involving heat and multiphase
liquid/gas transport. The pressure generation mechanism is a cellular-level
process that is governed by differential equations for sap transport through
porous cell membranes, phase change, heat transport, and generation of osmotic
pressure. By assuming a periodic cellular structure based on an appropriate
reference cell, we derive an homogenized heat equation governing the global
temperature on the scale of the tree stem, with all the remaining physics
relegated to equations defined on the reference cell. We derive a corresponding
strong formulation of the limit problem and use it to design an efficient
numerical solution algorithm. Numerical simulations are then performed to
validate the results and draw conclusions regarding the phenomenon of sap
exudation, which is of great importance in trees such as sugar maple and a few
other related species. The particular form of our homogenized temperature
equation is obtained using periodic homogenization techniques with two-scale
convergence, which we investigate theoretically in the context of a simpler
two-phase Stefan-type problem corresponding to a periodic array of melting
cylindrical ice bars with a constant thermal diffusion coefficient. For this
reduced model, we prove results on existence, uniqueness and convergence of the
two-scale limit solution in the weak form, clearly identifying the missing
pieces required to extend the proofs to the fully nonlinear sap exudation
model. Numerical simulations of the reduced equations are then compared with
results from the complete sap exudation model.Comment: 35 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1411.303
Analysis and homogenisation of a linear Cahn–Larché system with phase separation on the microscale
Identification of microstructural information from macroscopic boundary measurements in steady‐state linear elasticity
Infinite depth interaction theory for arbitrary bodies with application to wave forcing of many ice floes
Bosonic behavior of entangled fermions
Two bound, entangled fermions form a composite boson, which can be treated as
an elementary boson as long as the Pauli principle does not affect the behavior
of many such composite bosons. The departure of ideal bosonic behavior is
quantified by the normalization ratio of multi-composite-boson states. We
derive the two-fermion-states that extremize the normalization ratio for a
fixed single-fermion purity P, and establish general tight bounds for this
indicator. For very small purities, P<1/N^2, the upper and lower bounds
converge, which allows to quantify accurately the departure from perfectly
bosonic behavior, for any state of many composite bosons.Comment: 9 pages, 5 figures, accepted by PR
Computation and Palaeography: Potentials and Limits
This manifesto documents the program and outcomes of Dagstuhl Seminar 12382 ‘Perspectives Workshop: Computation and Palaeography: Potentials and Limits’. The workshop focused on the interaction of palaeography, the study of ancient and me- dieval documents, with computerised tools, particularly those developed for analysis of digital images and text mining. The goal of this marriage of disciplines is to provide e cient solutions to time and labor consuming palaeographic tasks. It furthermore attempts to provide scholars with quantitative evidence to palaeographical arguments, consequently facilitating a better understanding of our cultural heritage through the unique perspective of ancient and medieval documents. The workshop provided a vital opportunity for palaeographers to interact and discuss the potential of digital methods with computer scientists specialising in machine vision and statistical data analysis. This was essential not only in suggesting new directions and ideas for improving palaeographic research, but also in identifying questions which scholars working individually, in their respective elds, would not have asked without directly communicating with colleagues from outside their research community
Computational polyconvexification of isotropic functions
Based on the characterization of the polyconvex envelope of isotropic
functions by their signed singular value representations, we propose a simple
algorithm for the numerical approximation of the polyconvex envelope. Instead
of operating on the -dimensional space of matrices, the algorithm requires
only the computation of the convex envelope of a function on a -dimensional
manifold, which is easily realized by standard algorithms. The significant
speedup associated with the dimensional reduction from to is
demonstrated in a series of numerical experiments.Comment: 17 pages, 7 figure
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