Browsing by Subject "EQUATIONS"

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  • Hu, Man; Pitkanen, Timo P.; Minunno, Francesco; Tian, Xianglin; Lehtonen, Aleksi; Makela, Annikki (2021)
    Background and Aims Branch biomass and other attributes are important for estimating the carbon budget of forest stands and characterizing crown structure. As destructive measuring is time-consuming and labour-intensive, terrestrial laser scanning (TLS) as a solution has been used to estimate branch biomass quickly and non-destructively. However, branch information extraction from TLS data alone is challenging due to occlusion and other defects, especially for estimating individual branch attributes in coniferous trees. Methods This study presents a method, entitled TSMtls, to estimate individual branch biomass non-destructively and accurately by combining tree structure models and TLS data. The TSMtls method constructs the stem-taper curve from TLS data, then uses tree structure models to determine the number, basal area and biomass of individual branches at whorl level. We estimated the tree structural model parameters from 122 destructively measured Scots pine (Pinus sylvestris) trees and tested the method on six Scots pine trees that were first TLS-scanned and later destructively measured. Additionally, we estimated the branch biomass using other TLS-based approaches for comparison. Key Results Tree-level branch biomass estimates derived from TSMtls showed the best agreement with the destructive measurements [coefficient of variation of root mean square error (CV-RMSE) = 9.66 % and concordance correlation coefficient (CCC) = 0.99], outperforming the other TLS-based approaches (CV-RMSE 12.97-57.45 % and CCC 0.43-0.98 ). Whorl-level individual branch attributes estimates produced from TSMtls showed more accurate results than those produced from TLS data directly. Conclusions The results showed that the TSMtls method proposed in this study holds promise for extension to more species and larger areas.
  • Tanhuanpää, Topi; Kankare, Ville; Setälä, Heikki; Yli-Pelkonen, Vesa; Vastaranta, Mikko; Niemi, Mikko T.; Raisio, Juha; Holopainen, Markus (2017)
    Assessment of the amount of carbon sequestered and the value of ecosystem services provided by urban trees requires reliable data. Predicting the proportions and allometric relationships of individual urban trees with models developed for trees in rural forests may result in significant errors in biomass calculations. To better understand the differences in biomass accumulation and allocation between urban and rural trees, two existing biomass models for silver birch (Betula pendula Roth) were tested for their performance in assessing the above-ground biomass (AGB) of 12 urban trees. In addition, the performance of a volume-based method utilizing accurate terrestrial laser scanning (TLS) data and stem density was evaluated in assessing urban tree AGB. Both tested models underestimated the total AGB of single trees, which was mainly due to a substantial underestimation of branch biomass. The volume-based method produced the most accurate estimates of stem biomass. The results suggest that biomass models originally based on sample trees from rural forests should not be used for urban, open-grown trees, and that volume-based methods utilizing TLS data are a promising alternative for non-destructive assessment of urban tree AGB. (C) 2017 Elsevier GmbH. All rights reserved.
  • Pyorala, Jiri; Liang, Xinlian; Saarinen, Ninni; Kankare, Ville; Wang, Yunsheng; Holopainen, Markus; Hyyppa, Juha; Vastaranta, Mikko (2018)
    Terrestrial laser scanning (TLS) accompanied by quantitative tree-modeling algorithms can potentially acquire branching data non-destructively from a forest environment and aid the development and calibration of allometric crown biomass and wood quality equations for species and geographical regions with inadequate models. However, TLS's coverage in capturing individual branches still lacks evaluation. We acquired TLS data from 158 Scots pine (Pinus sylvestris L.) trees and investigated the performance of a quantitative branch detection and modeling approach for extracting key branching parameters, namely the number of branches, branch diameter (b(d)) and branch insertion angle (b) in various crown sections. We used manual point cloud measurements as references. The accuracy of quantitative branch detections decreased significantly above the live crown base height, principally due to the increasing scanner distance as opposed to occlusion effects caused by the foliage. b(d) was generally underestimated, when comparing to the manual reference, while b was estimated accurately: tree-specific biases were 0.89cm and 1.98 degrees, respectively. Our results indicate that full branching structure remains challenging to capture by TLS alone. Nevertheless, the retrievable branching parameters are potential inputs into allometric biomass and wood quality equations.
  • Harjulehto, Petteri; Hästö, Peter; Juusti, Jonne (2023)
    We study minimizers of non-autonomous functionalsinf u circumflex accent cc(x, |Vu|) dx Omega when cc has generalized Orlicz growth. We consider the case where the upper growth rate of cc is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function cc to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.
  • Chen, Linxiao; Turunen, Joonas (2020)
    We consider Boltzmann random triangulations coupled to the Ising model on their faces, under Dobrushin boundary conditions and at the critical point of the model. The first part of this paper computes explicitly the partition function of this model by solving its Tutte's equation, extending a previous result by Bernardi and Bousquet-Melou (J Combin Theory Ser B 101(5):315-377, 2011) to the model with Dobrushin boundary conditions. We show that the perimeter exponent of the model is 7/3 in contrast to the exponent 5/2 for uniform triangulations. In the second part, we show that the model has a local limit in distribution when the two components of the Dobrushin boundary tend to infinity one after the other. The local limit is constructed explicitly using the peeling process along an Ising interface. Moreover, we show that the main interface in the local limit touches the (infinite) boundary almost surely only finitely many times, a behavior opposite to that of the Bernoulli percolation on uniform maps. Some scaling limits closely related to the perimeters of finite clusters are also obtained.
  • Aalto, Juha; Niittynen, Pekka; Riihimaki, Henri; Luoto, Miska (2021)
    Tundra ecosystems have experienced changes in vegetation composition, distribution, and productivity over the past century due to climate warming. However, the increase in above-ground biomass may be constrained by cryogenic land surface processes that cause topsoil disturbance and variable microsite conditions. These effects have remained unaccounted for in tundra biomass models, although they can impact multiple opposing feedbacks between the biosphere and atmosphere, ecosystem functioning and biodiversity. Here, by using field-quantified data from northern Europe, remote sensing, and machine learning, we show that cryogenic land surface processes substantially constrain above-ground biomass in tundra. The three surveyed processes (cryoturbation, solifluction, and nivation) collectively reduced biomass by an average of 123.0 g m(-2) (-30.0%). This effect was significant over landscape positions and was especially pronounced in snowbed environments, where the mean reduction in biomass was 57.3%. Our results imply that cryogenic land surface processes are pivotal in shaping future patterns of tundra biomass, as long as cryogenic ground activity is retained by climate warming. Vegetation in tundra ecosystems is constrained by cryogenic land surface processes, despite the fact that models of future biomass changes rarely take these into account, according to field and remote sensing data from northern Europe.
  • Diekmann, Odo; Gyllenberg, Mats; Metz, J. A. J.; Nakaoka, Shinji; de Roos, Andre M. (2010)
  • Afonso, Marco Martins; Muratore-Ginanneschi, Paolo; Gama, Silvio M. A.; Mazzino, Andrea (2018)
    We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show howto compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.
  • Kauppi, P. E.; Birdsey, R. A.; Pan, Y.; Ihalainen, A.; Nöjd, P.; Lehtonen, A. (2015)
  • Diekmann, Odo; Gyllenberg, Mats; Metz, Johan A. J. (2020)
    In a physiologically structured population model (PSPM) individuals are characterised by continuous variables, like age and size, collectively called their i-state. The world in which these individuals live is characterised by another set of variables, collectively called the environmental condition. The model consists of submodels for (i) the dynamics of the i-state, e.g. growth and maturation, (ii) survival, (iii) reproduction, with the relevant rates described as a function of (i-state, environmental condition), (iv) functions of (i-state, environmental condition), like biomass or feeding rate, that integrated over the i-state distribution together produce the output of the population model. When the environmental condition is treated as a given function of time (input), the population model becomes linear in the state. Density dependence and interaction with other populations is captured by feedback via a shared environment, i.e., by letting the environmental condition be influenced by the populations' outputs. This yields a systematic methodology for formulating community models by coupling nonlinear input-output relations defined by state-linear population models. For some combinations of submodels an (infinite dimensional) PSPM can without loss of relevant information be replaced by a finite dimensional ODE. We then call the model ODE-reducible. The present paper provides (a) a test for checking whether a PSPM is ODE reducible, and (b) a catalogue of all possible ODE-reducible models given certain restrictions, to wit: (i) the i-state dynamics is deterministic, (ii) the i-state space is one-dimensional, (iii) the birth rate can be written as a finite sum of environment-dependent distributions over the birth states weighted by environment independent 'population outputs'. So under these restrictions our conditions for ODE-reducibility are not only sufficient but in fact necessary. Restriction (iii) has the desirable effect that it guarantees that the population trajectories are after a while fully determined by the solution of the ODE so that the latter gives a complete picture of the dynamics of the population and not just of its outputs.
  • Ylinen, Elisa; Merras-Salmio, Laura; Gunnar, Riikka; Jahnukainen, Timo; Pakarinen, Mikko P. (2018)
    Objective: Although impaired renal function has been a frequent finding among adults with intestinal failure (IF), the data on children is scarce. The aim of this study was to assess renal function in pediatric-onset IF. Methods: Medical records of 70 patients (38 boys) with pediatric-onset IF due to either short bowel syndrome (n = 59) or primary motility disorder (n = 11) and a history of parenteral nutrition (PN) dependency for >= 1 mo were evaluated. Renal function at the most recent follow-up was studied using plasma creatinine, cystatin C, and urea concentrations and estimated glomerular filtration rate (eGFR). Results: At a median age of 5.7 y and after PN duration of 3.2 y, 20 patients (29%) had decreased eGFR and higher cystatin C and urea concentrations. Patients with decreased renal function had significantly longer duration of PN (3.2 versus 0.9 y; P = 0.030) and shorter percentage of age adjusted small bowel length remaining (22 versus 32%; P = 0.041) compared with patients with preserved renal function. No other predisposing factors for decreased eGFR were identified. Conclusions: Patients with pediatric-onset IF are at significant risk for impaired renal function, which is associated with the duration of PN and the length of the remaining small bowel. In the present study, no other predisposing factors for decreased eGFR were found. Further studies using measured GFR are needed. (C) 2017 Elsevier Inc. All rights reserved.
  • Eirola, Timo; Koskela, Antti (2019)
    We consider Arnoldi-like processes to obtain symplectic subspaces for Hamiltonian systems. Large dimensional systems are locally approximated by ones living in low dimensional subspaces, and we especially consider Krylov subspaces and some of their extensions. These subspaces can be utilized in two ways: by solving numerically local small dimensional systems and then mapping back to the large dimension, or by using them for the approximation of necessary functions in exponential integrators applied to large dimensional systems. In the former case one can expect an excellent energy preservation and in the latter this is so for linear systems. We consider second order exponential integrators which solve linear systems exactly and for which these two approaches are in a certain sense equivalent. We also consider the time symmetry preservation properties of the integrators. In numerical experiments these methods combined with symplectic subspaces show promising behavior also when applied to nonlinear Hamiltonian problems.
  • Li, T.; Chen, M. Z.; Zhang, C. L.; Nazarewicz, W.; Kortelainen, M. (2020)
    Background: An electron localization function was originally introduced to visualize in positional space bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules, and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize cluster structures in light nuclei, formation of fragments in fission, and pasta phases appearing in the inner crust of neutron stars. Purpose: We use the NLF to study the nuclear response to fast rotation. Methods: We generalize the NLF to the case of nuclear rotation. The extended expressions involve both timeeven and time-odd local particle and spin densities and currents. Since the current density and density gradient contribute to the NLF primarily at the surface, we propose a simpler spatial measure given by the kinetic-energy density. Illustrative calculations for the superdeformed yrast band of Dy-152 were carried out by using the cranked Skyrme-Hartree-Fock method. We also employed the cranked harmonic-oscillator model to gain insights into spatial patterns revealed by the NLF at high angular momentum. Results: In the case of a deformed rotating nucleus, several NLFs can be introduced, depending on the definition of the spin-quantization axis, direction of the total angular momentum, and self-consistent symmetries of the system. Contributions to the NLF from the current density, spin-current tensor density, and density gradient terms are negligible in the nuclear interior. The oscillating pattern of the simplified NLF can be explained in terms of a constructive interference between kinetic-energy and particle densities. The characteristic nodal pattern seen in the NLF in the direction of major axis of a rotating nucleus comes from single-particle orbits carrying large aligned angular momentum. The variation of the NLF along the minor axis of the nucleus can be traced back to deformation-aligned orbits. Conclusions: The NLF allows a simple interpretation of the shell structure evolution in the rotating nucleus in terms of the angular-momentum alignment of individual nucleons. We expect that the NLF will be very useful for the characterization and visualization of other collective modes in nuclei and time-dependent processes.
  • Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther (2019)
    We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively. (C) 2019 Published by Elsevier Inc.
  • Beretta, Elena; Cavaterra, Cecilia; Ratti, Luca (2020)
    In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.
  • Moreno-Ibanez, Manuel; Gritsevich, Maria; Trigo-Rodriguez, Josep M.; Silber, Elizabeth A. (2020)
    Meteoroids impacting the Earth atmosphere are commonly classified using the PE criterion. This criterion was introduced to support the identification of the fireball type by empirically linking its orbital origin and composition characteristics. Additionally, it is used as an indicator of the meteoroid tensile strength and its ability to penetrate the atmosphere. However, the level of classification accuracy of the PE criterion depends on the ability to constrain the value of the input data, retrieved from the fireball observation, required to derive the PE value. To overcome these uncertainties and achieve a greater classification detail, we propose a new formulation using scaling laws and dimensionless variables that groups all the input variables into two parameters that are directly obtained from the fireball observations. These two parameters, alpha and beta, represent the drag and the mass-loss rates along the luminous part of the trajectory, respectively, and are linked to the shape, strength, ablation efficiency, mineralogical nature of the projectile, and duration of the fireball. Thus, the new formulation relies on a physical basis. This work shows the mathematical equivalence between the PE criterion and the logarithm of 2 alpha beta under the same PE criterion assumptions. We demonstrate that log(2 alpha beta) offers a more general formulation that does not require any preliminary constraint on the meteor flight scenario and discuss the suitability of the new formulation for expanding the classification beyond fully disintegrating fireballs to larger impactors including meteorite-dropping fireballs. The reliability of the new formulation is validated using the Prairie Network meteor observations.
  • Väisänen, Timo; Markkanen, Johannes; Penttilä, Antti; Muinonen, Karri (2019)
    We present a numerical method for solving electromagnetic scattering by dense discrete random media entitled radiative transfer with reciprocal transactions ((RT2)-T-2). The (RT2)-T-2 is a combination of the Monte Carlo radiative-transfer, coherent-backscattering, and superposition T-matrix methods. The applicability of the radiative transfer is extended to dense random media by incorporating incoherent volume elements containing multiple particles. We analyze the (RT2)-T-2 by comparing the results with the asymptotically exact superposition T-matrix method, and show that the (RT2)-T-2 removes the caveats of radiative-transfer methods by comparing it to the RT-CB. We study various implementation choices that result in an accurate and efficient numerical algorithm. In particular, we focus on the properties of the incoherent volume elements and their effects on the final solution.
  • Rundell, William; Zhang, Zhidong (2018)
    Abstract A standard inverse problem is to determine a source which is supported in an unknown domain D from external boundary measurements. Here we consider the case of a time-independent situation where the source is equal to unity in an unknown subdomain D of a larger given domain Ω and the boundary of D has the star-like shape, i.e. ∂ D = { q ( θ ) ( cos ⁡ θ , sin ⁡ θ ) ⊤ : θ ∈ [ 0 , 2 π ] } . Overposed measurements consist of time traces of the solution or its flux values on a set of discrete points on the boundary ∂Ω. The case of a parabolic equation was considered in [6]. In our situation we extend this to cover the subdiffusion case based on an anomalous diffusion model and leading to a fractional order differential operator. We will show a uniqueness result and examine a reconstruction algorithm. One of the main motives for this work is to examine the dependence of the reconstructions on the parameter α, the exponent of the fractional operator which controls the degree of anomalous behaviour of the process. Some previous inverse problems based on fractional diffusion models have shown considerable differences between classical Brownian diffusion and the anomalous case.
  • Kuusi, Tuomo; Misawa, Masashi; Nakamura, Kenta (2020)
    We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the special case . In this article we establish a priori estimates and regularity results for the p-Sobolev type flow, which are necessary for further analysis and classification of limits as time tends to infinity.
  • Kivelä, Jesper M.; Lempinen, Marko; Holmberg, Christer; Jalanko, Hannu; Pakarinen, Mikko P.; Isoniemi, Helena; Lauronen, Jouni (2019)
    It has been proposed that the liver protects the kidney in CLKT. However, few studies have examined long-term renal function after CLKT and contrasted renal function of CLKT patients to KT patients beyond one year after transplantation. We studied long-term renal function of CLKT patients and compared renal function of CLKT patients to KT patients between one and five years after transplantation. Patients who underwent CLKT between 1993 and 2011 were included (n = 34; 11 children and 23 adults). Ninety-six (27 children and 69 adults) KT patients were selected as controls. GFR was estimated (eGFR) and measured (mGFR) with Cr-51-EDTA clearance. Mean mGFR was 63 at one and 70 at ten years after pediatric CLKT. Mean eGFR was 75 at one and 50 at ten years after adult CLKT. Difference in mean mGFR between pediatric CLKT and KT patients was 8 (95% CI -7 to 23) and 11 (95% CI -4 to 26) at one and five years after transplantation, respectively. Difference in mean eGFR between adult CLKT and KT patients was 8 (95% CI -5 to 20) and 1 (95% CI -10 to 12) at one and five years after transplantation, respectively. Longitudinal changes in GFRs were somewhat similar in CLKT and KT patients in both age-groups but pediatric CLKT patients had on average higher GFRs than pediatric KT patients. In long-term follow-up, renal function remains stable in pediatric CLKT patients but declines in adult CLKT patients.