A Matlab Implementation of a Flat Norm Motivated Polygonal Edge Matching Method using a Decomposition of Boundary into Four 1-Dimensional Currents

We describe and provide code and examples for a polygonal edge matching method.Comment: Contains Matlab code and 4 figure

Mechanistic Modeling of Microtopographic Impacts on CO2 and CH4 Fluxes in an Alaskan Tundra Ecosystem Using the CLM-Microbe Model

Spatial heterogeneities in soil hydrology have been confirmed as a key control on CO2 and CH4 fluxes in the Arctic tundra ecosystem. In this study, we applied a mechanistic ecosystem model, CLM-Microbe, to examine the microtopographic impacts on CO2 and CH4 fluxes across seven landscape types in Utqiaġvik, Alaska: trough, low-centered polygon (LCP) center, LCP transition, LCP rim, high-centered polygon (HCP) center, HCP transition, and HCP rim. We first validated the CLM-Microbe model against static-chamber measured CO2 and CH4 fluxes in 2013 for three landscape types: trough, LCP center, and LCP rim. Model application showed that low-elevation and thus wetter landscape types (i.e., trough, transitions, and LCP center) had larger CH4 emissions rates with greater seasonal variations than high-elevation and drier landscape types (rims and HCP center). Sensitivity analysis indicated that substrate availability for methanogenesis (acetate, CO2 + H2) is the most important factor determining CH4 emission, and vegetation physiological properties largely affect the net ecosystem carbon exchange and ecosystem respiration in Arctic tundra ecosystems. Modeled CH4 emissions for different microtopographic features were upscaled to the eddy covariance (EC) domain with an area-weighted approach before validation against EC-measured CH4 fluxes. The model underestimated the EC-measured CH4 flux by 20% and 25% at daily and hourly time steps, suggesting the importance of the time step in reporting CH4 flux. The strong microtopographic impacts on CO2 and CH4 fluxes call for a model-data integration framework for better understanding and predicting carbon flux in the highly heterogeneous Arctic landscape

Minimal surfaces from circle patterns: Geometry from combinatorics

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal surfaces. The data used for the construction are purely combinatorial--the combinatorics of the curvature line pattern. A Weierstrass-type representation and an associated family are derived. We show the convergence to continuous minimal surfaces.Comment: 30 pages, many figures, some in reduced resolution. v2: Extended introduction. Minor changes in presentation. v3: revision according to the referee's suggestions, improved & expanded exposition, references added, minor mistakes correcte

Rectification of energy and motion in non-equilibrium parity violating metamaterials

Uncovering new mechanisms for rectification of stochastic fluctuations has been a longstanding problem in non-equilibrium statistical mechanics. Here, using a model parity violating metamaterial that is allowed to interact with a bath of active energy consuming particles, we uncover new mechanisms for rectification of energy and motion. Our model active metamaterial can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and inter-particle interactions of the parity violating material can couple with the non-equilibrium fluctuations of an active bath and enable rectification of energy and motion.Comment: 9 Pages + S

3-D facial expression representation using B-spline statistical shape model

Effective representation and recognition of human faces are essential in a number of applications including human-computer interaction (HCI), bio-metrics or video conferencing. This paper presents initial results obtained for a novel method of 3-D facial expressions representation based on the shape space vector of the statistical shape model. The statistical shape model is constructed based on the control points of the B-spline surfaces of the train-ing data set. The model fitting for the data is achieved by a modified iterative closest point (ICP) method with the surface deformations restricted to the es-timated shape space. The proposed method is fully automated and tested on the synthetic 3-D facial data with various facial expressions. Experimental results show that the proposed 3-D facial expression representation can be potentially used for practical applications