Mathematical model for silicon electrode - Part I. 2-d model
NASA Astrophysics Data System (ADS)
Sikha, Godfrey; De, Sumitava; Gordon, Joseph
2014-09-01
This paper presents a 2-dimensional transient numerical model to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strains, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are presented and discussed. The effect of radius of Si NW and lithiation rate, on the maximum stresses developed in the Si NW are also discussed.
A mathematical model for foreign body reactions in 2D
Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping
2010-01-01
The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general. PMID:21532988
A mathematical model incorporating the effects of detector width in 2D PET
NASA Astrophysics Data System (ADS)
Mair, B. A.
2000-02-01
For decades, the Radon transform has been used as an approximate model for two-dimensional (2D) positron emission tomography (PET). Since this model assumes that detector tubes are represented by lines (hence have no area), PET reconstruction algorithms need to be modified to account for the nonzero width of detectors. To date, these modifications have been obtained by computational methods, so fail to exhibit any inherent mathematical structure of the PET transform which takes emission intensity to detector tube means. This paper contains a precise mathematical representation of this PET transform and exploits this representation to propose a new method for reconstructing PET images. This representation is achieved by expressing the probability that an emission at a point is detected in a detector tube, in terms of the Green function and Poisson kernel for Laplace's equation on the unit disc. This new PET transform involves four weighted line integrals of the emission intensity function, instead of the single unweighted line integral defining the 2D Radon transform. Despite the complexity of this model, a reconstruction method is obtained by using classical orthogonal series representations of the emission intensity and detection means in terms of circular harmonics, Bessel functions and Chebyshev polynomials.
NASA Astrophysics Data System (ADS)
Duxbury, N. S.; Romanovsky, V. E.; Romanovskii, N. N.; Garagulya, L. S.; Brouchkov, A. V.; Komarov, I. A.; Roman, L. T.; Tipenko, G. S.; Buldovich, S. N.; Maximova, L. N.
2012-12-01
We have developed coupled permafrost - carbon physical and numerical models, where carbon is in the form of methane clathrate hydrate ( CH4*6H2O ) in a porous subsurface environment. The driving force for the subsurface temperature field dynamics is climate variations on the Earth's surface. This is an upper boundary condition for the nonlinear evolutionary system of partial differential equations (PDEs) describing subsurface heat transfer (parabolic PDEs) in a generalized Stefan formulation. The developed numerical model is a valuable computational tool to quantitatively study nonlinear dynamical thermal processes with phase transitions in terrestrial and Martian subsurfaces. Our model is multifrontal and therefore allows one to perform computations for a problem with any number of emerging/vanishing phase transition interfaces (both in methane gas hydrate deposits and in permafrost), since the model treats these fronts implicitly in an enthalpy formulation and in corresponding finite-difference scheme. This model takes into account the pressure (and therefore the depth) dependence of the phase transition temperature for methane clathrate hydrate. We have performed model computations using the thermophysical characteristics (heat capacity, density/porosity, thermal conductivity) for the Siberian subsurface. It can be used as a terrestrial analog for the Martian subsurface (e.g., Duxbury et al., 2001). Also, thermophysical coefficients from laboratory experiments for methane clathrate hydrate were used in our model. In addition, our model takes into account the dependence of subsurface thermophysical characteristics on temperature and spatial coordinates. The results of our computations and their interpretation will be presented. References. N. S. Duxbury, I. A. Zotikov, K. H. Nealson, V. E. Romanovsky, F. D. Carsey (2001). A numerical model for an alternative origin of Lake Vostok and its exobiological implications for Mars, Journal of Geophysical Research
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Exact Solution of Ising Model in 2d Shortcut Network
NASA Astrophysics Data System (ADS)
Shanker, O.
We give the exact solution to the Ising model in the shortcut network in the 2D limit. The solution is found by mapping the model to the square lattice model with Brascamp and Kunz boundary conditions.
Studying Zeolite Catalysts with a 2D Model System
Boscoboinik, Anibal
2016-12-07
Anibal Boscoboinik, a materials scientist at Brookhaven’s Center for Functional Nanomaterials, discusses the surface-science tools and 2D model system he uses to study catalysis in nanoporous zeolites, which catalyze reactions in many industrial processes.
Technical Review of the UNET2D Hydraulic Model
Perkins, William A.; Richmond, Marshall C.
2009-05-18
The Kansas City District of the US Army Corps of Engineers is engaged in a broad range of river management projects that require knowledge of spatially-varied hydraulic conditions such as velocities and water surface elevations. This information is needed to design new structures, improve existing operations, and assess aquatic habitat. Two-dimensional (2D) depth-averaged numerical hydraulic models are a common tool that can be used to provide velocity and depth information. Kansas City District is currently using a specific 2D model, UNET2D, that has been developed to meet the needs of their river engineering applications. This report documents a tech- nical review of UNET2D.
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
2D microscopic model of graphene fracture properties
NASA Astrophysics Data System (ADS)
Hess, Peter
2015-05-01
An analytical two-dimensional (2D) microscopic fracture model based on Morse-type interaction is derived containing no adjustable parameter. From the 2D Young’s moduli and 2D intrinsic strengths of graphene measured by nanoindentation based on biaxial tension and calculated by density functional theory for uniaxial tension the widely unknown breaking force, line or edge energy, surface energy, fracture toughness, and strain energy release rate were determined. The simulated line energy agrees well with ab initio calculations and the fracture toughness of perfect graphene sheets is in good agreement with molecular dynamics simulations and the fracture toughness evaluated for defective graphene using the Griffith relation. Similarly, the estimated critical strain energy release rate agrees well with result of various theoretical approaches based on the J-integral and surface energy. The 2D microscopic model, connecting 2D and three-dimensional mechanical properties in a consistent way, provides a versatile relationship to easily access all relevant fracture properties of pristine 2D solids.
An Intercomparison of 2-D Models Within a Common Framework
NASA Technical Reports Server (NTRS)
Weisenstein, Debra K.; Ko, Malcolm K. W.; Scott, Courtney J.; Jackman, Charles H.; Fleming, Eric L.; Considine, David B.; Kinnison, Douglas E.; Connell, Peter S.; Rotman, Douglas A.; Bhartia, P. K. (Technical Monitor)
2002-01-01
A model intercomparison among the Atmospheric and Environmental Research (AER) 2-D model, the Goddard Space Flight Center (GSFC) 2-D model, and the Lawrence Livermore National Laboratory 2-D model allows us to separate differences due to model transport from those due to the model's chemical formulation. This is accomplished by constructing two hybrid models incorporating the transport parameters of the GSFC and LLNL models within the AER model framework. By comparing the results from the native models (AER and e.g. GSFC) with those from the hybrid model (e.g. AER chemistry with GSFC transport), differences due to chemistry and transport can be identified. For the analysis, we examined an inert tracer whose emission pattern is based on emission from a High Speed Civil Transport (HSCT) fleet; distributions of trace species in the 2015 atmosphere; and the response of stratospheric ozone to an HSCT fleet. Differences in NO(y) in the upper stratosphere are found between models with identical transport, implying different model representations of atmospheric chemical processes. The response of O3 concentration to HSCT aircraft emissions differs in the models from both transport-dominated differences in the HSCT-induced perturbations of H2O and NO(y) as well as from differences in the model represent at ions of O3 chemical processes. The model formulations of cold polar processes are found to be the most significant factor in creating large differences in the calculated ozone perturbations
Studying Zeolite Catalysts with a 2D Model System
Boscoboinik, Anibal
2016-12-14
Anibal Boscoboinik, a materials scientist at Brookhavenâs Center for Functional Nanomaterials, discusses the surface-science tools and 2D model system he uses to study catalysis in nanoporous zeolites, which catalyze reactions in many industrial processes.
Gold-standard performance for 2D hydrodynamic modeling
NASA Astrophysics Data System (ADS)
Pasternack, G. B.; MacVicar, B. J.
2013-12-01
Two-dimensional, depth-averaged hydrodynamic (2D) models are emerging as an increasingly useful tool for environmental water resources engineering. One of the remaining technical hurdles to the wider adoption and acceptance of 2D modeling is the lack of standards for 2D model performance evaluation when the riverbed undulates, causing lateral flow divergence and convergence. The goal of this study was to establish a gold-standard that quantifies the upper limit of model performance for 2D models of undulating riverbeds when topography is perfectly known and surface roughness is well constrained. A review was conducted of published model performance metrics and the value ranges exhibited by models thus far for each one. Typically predicted velocity differs from observed by 20 to 30 % and the coefficient of determination between the two ranges from 0.5 to 0.8, though there tends to be a bias toward overpredicting low velocity and underpredicting high velocity. To establish a gold standard as to the best performance possible for a 2D model of an undulating bed, two straight, rectangular-walled flume experiments were done with no bed slope and only different bed undulations and water surface slopes. One flume tested model performance in the presence of a porous, homogenous gravel bed with a long flat section, then a linear slope down to a flat pool bottom, and then the same linear slope back up to the flat bed. The other flume had a PVC plastic solid bed with a long flat section followed by a sequence of five identical riffle-pool pairs in close proximity, so it tested model performance given frequent undulations. Detailed water surface elevation and velocity measurements were made for both flumes. Comparing predicted versus observed velocity magnitude for 3 discharges with the gravel-bed flume and 1 discharge for the PVC-bed flume, the coefficient of determination ranged from 0.952 to 0.987 and the slope for the regression line was 0.957 to 1.02. Unsigned velocity
Teaching Mathematical Modelling.
ERIC Educational Resources Information Center
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Instantons in 2D U(1) Higgs model and 2D CP(N-1) sigma models
NASA Astrophysics Data System (ADS)
Lian, Yaogang
2007-12-01
In this thesis I present the results of a study of the topological structures of 2D U(1) Higgs model and 2D CP N-1 sigma models. Both models have been studied using the overlap Dirac operator construction of topological charge density. The overlap operator provides a more incisive probe into the local topological structure of gauge field configurations than the traditional plaquette-based operator. In the 2D U(1) Higgs model, we show that classical instantons with finite sizes violate the negativity of topological charge correlator by giving a positive contribution to the correlator at non-zero separation. We argue that instantons in 2D U(1) Higgs model must be accompanied by large quantum fluctuations in order to solve this contradiction. In 2D CPN-1 sigma models, we observe the anomalous scaling behavior of the topological susceptibility chi t for N ≤ 3. The divergence of chi t in these models is traced to the presence of small instantons with a radius of order a (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Luscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in CP1 and CP 2, leading to a divergent topological susceptibility in the continuum limit. For the CPN-1 models with N > 3 the topological susceptibility is observed to scale properly with the mass gap. Another topic presented in this thesis is an implementation of the Zolotarev optimal rational approximation for the overlap Dirac operator. This new implementation has reduced the time complexity of the overlap routine from O(N3 ) to O(N), where N is the total number of sites on the lattice. This opens up a door to more accurate lattice measurements in the future.
2-D Magnetohydrodynamic Modeling of A Pulsed Plasma Thruster
NASA Technical Reports Server (NTRS)
Thio, Y. C. Francis; Cassibry, J. T.; Wu, S. T.; Rodgers, Stephen L. (Technical Monitor)
2002-01-01
Experiments are being performed on the NASA Marshall Space Flight Center (MSFC) MK-1 pulsed plasma thruster. Data produced from the experiments provide an opportunity to further understand the plasma dynamics in these thrusters via detailed computational modeling. The detailed and accurate understanding of the plasma dynamics in these devices holds the key towards extending their capabilities in a number of applications, including their applications as high power (greater than 1 MW) thrusters, and their use for producing high-velocity, uniform plasma jets for experimental purposes. For this study, the 2-D MHD modeling code, MACH2, is used to provide detailed interpretation of the experimental data. At the same time, a 0-D physics model of the plasma initial phase is developed to guide our 2-D modeling studies.
Mathematical modeling in neuroendocrinology.
Bertram, Richard
2015-04-01
Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
Flow transitions in a 2D directional solidification model
NASA Technical Reports Server (NTRS)
Larroude, Philippe; Ouazzani, Jalil; Alexander, J. Iwan D.
1992-01-01
Flow transitions in a Two Dimensional (2D) model of crystal growth were examined using the Bridgman-Stockbarger me thod. Using a pseudo-spectral Chebyshev collocation method, the governing equations yield solutions which exhibit a symmetry breaking flow tansition and oscillatory behavior indicative of a Hopf bifurcation at higher values of Ra. The results are discussed from fluid dynamic viewpoint, and broader implications for process models are also addressed.
Modeling of lamps through a diffuser with 2D and 3D picket-fence backlight models
NASA Astrophysics Data System (ADS)
Belshaw, Richard J.; Wilmott, Roger; Thomas, John T.
2002-08-01
Laboratory photometric measurements are taken of a display backlight one metre away from the emission surface (diffuser) with a whole acceptance angle on the photometer of about 0.125 degrees (2.182mm spot size at emission surface). A simulation method was sought to be able to obtain the brightness uniformity (luminance peak to trough ratio from above one lamp to the null between lamps in a picket-fence backlight). A 3D raytrace BackLight model in TracePro and a 2D Mathematical model in Matlab have been developed. With a specimen backlight in the laboratory, a smooth luminance profile was measured by the photometer on the diffuser surface. Ray Trace models in both 3D and 2D take too long to produce smooth 'continuous filled' distributions. The Mathematical 2D approach, although with limitations, yielded smooth solutions in a very reasonable time frame.
Numerical modelling of spallation in 2D hydrodynamics codes
NASA Astrophysics Data System (ADS)
Maw, J. R.; Giles, A. R.
1996-05-01
A model for spallation based on the void growth model of Johnson has been implemented in 2D Lagrangian and Eulerian hydrocodes. The model has been extended to treat complete separation of material when voids coalesce and to describe the effects of elevated temperatures and melting. The capabilities of the model are illustrated by comparison with data from explosively generated spall experiments. Particular emphasis is placed on the prediction of multiple spall effects in weak, low melting point, materials such as lead. The correlation between the model predictions and observations on the strain rate dependence of spall strength is discussed.
NGMIX: Gaussian mixture models for 2D images
NASA Astrophysics Data System (ADS)
Sheldon, Erin
2015-08-01
NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.
Numerical 2D-modeling of multiroll leveling
NASA Astrophysics Data System (ADS)
Mathieu, N.; Potier-Ferry, M.; Zahrouni, H.
2016-10-01
Multiroll leveling is a forming process used in the metals industries (aluminum, steel, …) in order to correct flatness defects and minimize residual stresses in strips thanks to alternating bending. This work proposes a Finite Element 2D model to simulate the metal sheet conveying through the machine. Obtained results (plastic strain and residual stress distributions through thickness) are analysed. Strip deformation, after elastic springback and potential buckling, is also predicted (residual curvatures).
Wang, Bin; Gao, Yongsheng
2016-12-01
In this paper, we present a novel mathematical tool, Structure Integral Transform (SIT), for invariant shape description and recognition. Different from the Radon Transform (RT), which integrates the shape image function over a 1D line in the image plane, the proposed SIT builds upon two orthogonal integrals over a 2D K -cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral. The proposed SIT brings the following advantages over the RT: 1) it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition; 2) the shape regions are dissected by the K -cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery; and 3) it is easier to build a completely invariant shape descriptor. The experimental results of applying SIT to shape recognition demonstrate its superior performance over the well-known Radon transform, and the well-known shape contexts and the polar harmonic transforms.
Influence of Elevation Data Source on 2D Hydraulic Modelling
NASA Astrophysics Data System (ADS)
Bakuła, Krzysztof; StĘpnik, Mateusz; Kurczyński, Zdzisław
2016-08-01
The aim of this paper is to analyse the influence of the source of various elevation data on hydraulic modelling in open channels. In the research, digital terrain models from different datasets were evaluated and used in two-dimensional hydraulic models. The following aerial and satellite elevation data were used to create the representation of terrain-digital terrain model: airborne laser scanning, image matching, elevation data collected in the LPIS, EuroDEM, and ASTER GDEM. From the results of five 2D hydrodynamic models with different input elevation data, the maximum depth and flow velocity of water were derived and compared with the results of the most accurate ALS data. For such an analysis a statistical evaluation and differences between hydraulic modelling results were prepared. The presented research proved the importance of the quality of elevation data in hydraulic modelling and showed that only ALS and photogrammetric data can be the most reliable elevation data source in accurate 2D hydraulic modelling.
Fracture surfaces of heterogeneous materials: A 2D solvable model
NASA Astrophysics Data System (ADS)
Katzav, E.; Adda-Bedia, M.; Derrida, B.
2007-05-01
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.
Towards more realistic 2D & 3D numerical models of Earth's mantle
NASA Astrophysics Data System (ADS)
Ghias, Sanaz
2011-12-01
There are a number of simplifying assumptions in modeling Earth's deep interior. These are mostly simplifying assumptions that make the mathematics simpler either for less complicated modeling or for numerical efficiency purposes. The aim of this study is to investigate the effects of some of these simplifying assumptions on 2D and 3D mantle convection models. In particular, the cases with variable coefficients of thermal expansion, alpha, and the inclusion of mineral phase transitions and viscosity stratification have been studied. The coefficient of thermal expansion is temperature- and depth-dependent in Earth. But for simplicity, it has been considered as constant in most mantle convection models and only depth-dependent in others. 2D mantle convection models (2D Cartesian and 2D cylindrical) have been created based on an existing model from Jarvis [1992] to investigate the effects of temperature- and depth-dependent alpha on mantle convection compared with the simplified cases. Also an existing version of a 3D parallel mantle convection model, MC3D, from Lowman et al. [2001] have been modified to include the temperature- and depth-dependent alpha. In the 3D study it has also been investigated that how the effects of temperature- and depth-dependent alpha vary with or without lithospheric plates. There are at least two mineral phase transitions in Earth. There is an exothermic phase boundary at 410km below the surface and an endothermic phase boundary at 660km below the surface. For simplicity, most mantle convection models do not consider any of the phase boundaries. Some consider only the endothermic phase boundary. A 2D cylindrical model from Shahnas and Jarvas [2005] has been employed to investigate the effects of considering both phase boundaries compared to models with either no, or one, phase boundary. Different viscosity stratifications have been used in addition to the phase boundaries.
2D Quantum Transport Modeling in Nanoscale MOSFETs
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, B.
2001-01-01
We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on an equal footing. Electron bandstructure is treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are consistent with 1D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller leakage current than the longer gate length device without a significant trade-off in on-current.
Model dielectric function for 2D semiconductors including substrate screening
Trolle, Mads L.; Pedersen, Thomas G.; Véniard, Valerie
2017-01-01
Dielectric screening of excitons in 2D semiconductors is known to be a highly non-local effect, which in reciprocal space translates to a strong dependence on momentum transfer q. We present an analytical model dielectric function, including the full non-linear q-dependency, which may be used as an alternative to more numerically taxing ab initio screening functions. By verifying the good agreement between excitonic optical properties calculated using our model dielectric function, and those derived from ab initio methods, we demonstrate the versatility of this approach. Our test systems include: Monolayer hBN, monolayer MoS2, and the surface exciton of a 2 × 1 reconstructed Si(111) surface. Additionally, using our model, we easily take substrate screening effects into account. Hence, we include also a systematic study of the effects of substrate media on the excitonic optical properties of MoS2 and hBN. PMID:28117326
2D Numerical MHD Models of Solar Explosive Events
NASA Astrophysics Data System (ADS)
Roussev, I.
2001-10-01
Observations of the Sun reveal a great variety of dynamic phenomena interpretable as a manifestation of magnetic reconnection. These range from small-scale 'Explosive events' seen in the 'quiet' Sun, through violent flares observed in active regions. The high degree of complexity of the magnetic field inferred from observations may locally produce a fruitful environment for the process of magnetic reconnection to take place. Explosive events are associated with regions undergoing magnetic flux cancellation. This thesis presents a 2-dimensional (2D) numerical study devoted to explore the idea that the salient spectral signatures seen in explosive events are most probably caused by bi-directional outflow jets as a results of an ongoing magnetic reconnection. In order to provide qualitative results needed for the better physical interpretation of solar explosive events, several models intended to represent a 'quiet' Sun transition of solar explosive events, several models intended to represent a 'quiet' Sun transition region undergoing magnetic reconnection are examined, in both unstratified and gravitationally stratified atmospheres. The magnetic reconnection is initiated in an ad hoc manner, and the dynamic evolution is followed by numerically solving the equations of 2D dissipative magnetohydrodynamics (MHD), including the effects of field-aligned thermal conduction, radiative losses, volumetric heating, and anomalous resistivity.
2D Quantum Transport Modeling in Nanoscale MOSFETs
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density- gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Quantum simulations are focused on MIT 25, 50 and 90 nm "well- tempered" MOSFETs and compared to classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are quantitatively consistent with I D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and sub-threshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.
Mass loss in 2D rotating stellar models
Lovekin, Caterine; Deupree, Bob
2010-10-05
Radiatively driven mass loss is an important factor in the evolution of massive stars . The mass loss rates depend on a number of stellar parameters, including the effective temperature and luminosity. Massive stars are also often rapidly rotating, which affects their structure and evolution. In sufficiently rapidly rotating stars, both the effective temperature and radius vary significantly as a function of latitude, and hence mass loss rates can vary appreciably between the poles and the equator. In this work, we discuss the addition of mass loss to a 2D stellar evolution code (ROTORC) and compare evolution sequences with and without mass loss. Preliminary results indicate that a full 2D calculation of mass loss using the local effective temperature and luminosity can significantly affect the distribution of mass loss in rotating main sequence stars. More mass is lost from the pole than predicted by 1D models, while less mass is lost at the equator. This change in the distribution of mass loss will affect the angular momentum loss, the surface temperature and luminosity, and even the interior structure of the star. After a single mass loss event, these effects are small, but can be expected to accumulate over the course of the main sequence evolution.
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Generalization Technique for 2D+SCALE Dhe Data Model
NASA Astrophysics Data System (ADS)
Karim, Hairi; Rahman, Alias Abdul; Boguslawski, Pawel
2016-10-01
Different users or applications need different scale model especially in computer application such as game visualization and GIS modelling. Some issues has been raised on fulfilling GIS requirement of retaining the details while minimizing the redundancy of the scale datasets. Previous researchers suggested and attempted to add another dimension such as scale or/and time into a 3D model, but the implementation of scale dimension faces some problems due to the limitations and availability of data structures and data models. Nowadays, various data structures and data models have been proposed to support variety of applications and dimensionality but lack research works has been conducted in terms of supporting scale dimension. Generally, the Dual Half Edge (DHE) data structure was designed to work with any perfect 3D spatial object such as buildings. In this paper, we attempt to expand the capability of the DHE data structure toward integration with scale dimension. The description of the concept and implementation of generating 3D-scale (2D spatial + scale dimension) for the DHE data structure forms the major discussion of this paper. We strongly believed some advantages such as local modification and topological element (navigation, query and semantic information) in scale dimension could be used for the future 3D-scale applications.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Effects of Agent's Repulsion in 2d Flocking Models
NASA Astrophysics Data System (ADS)
Moussa, Najem; Tarras, Iliass; Mazroui, M'hammed; Boughaleb, Yahya
In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R1), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R1) are found. Implications of these findings are discussed.
2-D Model for Normal and Sickle Cell Blood Microcirculation
NASA Astrophysics Data System (ADS)
Tekleab, Yonatan; Harris, Wesley
2011-11-01
Sickle cell disease (SCD) is a genetic disorder that alters the red blood cell (RBC) structure and function such that hemoglobin (Hb) cannot effectively bind and release oxygen. Previous computational models have been designed to study the microcirculation for insight into blood disorders such as SCD. Our novel 2-D computational model represents a fast, time efficient method developed to analyze flow dynamics, O2 diffusion, and cell deformation in the microcirculation. The model uses a finite difference, Crank-Nicholson scheme to compute the flow and O2 concentration, and the level set computational method to advect the RBC membrane on a staggered grid. Several sets of initial and boundary conditions were tested. Simulation data indicate a few parameters to be significant in the perturbation of the blood flow and O2 concentration profiles. Specifically, the Hill coefficient, arterial O2 partial pressure, O2 partial pressure at 50% Hb saturation, and cell membrane stiffness are significant factors. Results were found to be consistent with those of Le Floch [2010] and Secomb [2006].
[Mathematical models of hysteresis
Mayergoyz, I.D.
1991-01-01
The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.
Ab initio modeling of 2D layered organohalide lead perovskites
NASA Astrophysics Data System (ADS)
Fraccarollo, Alberto; Cantatore, Valentina; Boschetto, Gabriele; Marchese, Leonardo; Cossi, Maurizio
2016-04-01
A number of 2D layered perovskites A2PbI4 and BPbI4, with A and B mono- and divalent ammonium and imidazolium cations, have been modeled with different theoretical methods. The periodic structures have been optimized (both in monoclinic and in triclinic systems, corresponding to eclipsed and staggered arrangements of the inorganic layers) at the DFT level, with hybrid functionals, Gaussian-type orbitals and dispersion energy corrections. With the same methods, the various contributions to the solid stabilization energy have been discussed, separating electrostatic and dispersion energies, organic-organic intralayer interactions and H-bonding effects, when applicable. Then the electronic band gaps have been computed with plane waves, at the DFT level with scalar and full relativistic potentials, and including the correlation energy through the GW approximation. Spin orbit coupling and GW effects have been combined in an additive scheme, validated by comparing the computed gap with well known experimental and theoretical results for a model system. Finally, various contributions to the computed band gaps have been discussed on some of the studied systems, by varying some geometrical parameters and by substituting one cation in another's place.
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Richardson, mathematical modeller
NASA Astrophysics Data System (ADS)
Vreugdenhil, C. B.
1994-03-01
On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.
2D modeling of electromagnetic waves in cold plasmas
Crombé, K.; Van Eester, D.; Koch, R.; Kyrytsya, V.
2014-02-12
The consequences of sheath (rectified) electric fields, resulting from the different mobility of electrons and ions as a response to radio frequency (RF) fields, are a concern for RF antenna design as it can cause damage to antenna parts, limiters and other in-vessel components. As a first step to a more complete description, the usual cold plasma dielectric description has been adopted, and the density profile was assumed to be known as input. Ultimately, the relevant equations describing the wave-particle interaction both on the fast and slow timescale will need to be tackled but prior to doing so was felt as a necessity to get a feeling of the wave dynamics involved. Maxwell's equations are solved for a cold plasma in a 2D antenna box with strongly varying density profiles crossing also lower hybrid and ion-ion hybrid resonance layers. Numerical modelling quickly becomes demanding on computer power, since a fine grid spacing is required to capture the small wavelengths effects of strongly evanescent modes.
ERIC Educational Resources Information Center
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Imbert-Gérard, Lise-Marie
2015-12-15
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
Analysis of stochastic phenomena in 2D Hindmarsh-Rose neuron model
NASA Astrophysics Data System (ADS)
Bashkirtseva, I.; Ryashko, L.; Slepukhina, E.
2016-10-01
In mathematical research of neuronal activity, conceptual models play an important role. We consider 2D Hindmarsh-Rose model, which exhibits the fundamental property of neuron, the excitability. We study how random disturbances affect this property. The effects of noise are analysed in the parametric zone where the deterministic model is characterized by the coexistence of two stable equilibria. We show that under random disturbances, noise-induced transitions between the attractors occur, forming a new complex dynamic regime of stochastic bursting. It is confirmed by changes of distribution of random trajectories and interspike intervals. For the analysis of this noise-induced phenomenon, we apply the stochastic sensitivity technique and confidence domains method. We suggest a method for estimation of threshold noise intensity corresponding to the onset of noise-induced bursting. We show that the obtained values are in a good agreement with direct numerical simulations.
2D DEM model of sand transport with wind interaction
NASA Astrophysics Data System (ADS)
Oger, L.; Valance, A.
2013-06-01
The advance of the dunes in the desert is a threat to the life of the local people. The dunes invade houses, agricultural land and perturb the circulation on the roads. It is therefore very important to understand the mechanism of sand transport in order to fight against desertification. Saltation in which sand grains are propelled by the wind along the surface in short hops, is the primary mode of blown sand movement [1]. The saltating grains are very energetic and when impact a sand surface, they rebound and consequently eject other particles from the sand bed. The ejected grains, called reptating grains, contribute to the augmentation of the sand flux. Some of them can be promoted to the saltation motion. We use a mechanical model based on the Discrete Element Method to study successive collisions of incident energetic beads with granular packing in the context of Aeolian saltation transport. We investigate the collision process for the case where the incident bead and those from the packing have identical mechanical properties. We analyze the features of the consecutive collision processes made by the transport of the saltating disks by a wind in which its profile is obtained from the counter-interaction between air flow and grain flows. We used a molecular dynamics method known as DEM (soft Discrete Element Method) with a initial static packing of 20000 2D particles. The dilation of the upper surface due to the consecutive collisions is responsible for maintaining the flow at a given energy input due to the wind.
Mathematical Modelling in European Education
ERIC Educational Resources Information Center
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
A Primer for Mathematical Modeling
ERIC Educational Resources Information Center
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Mathematical Modeling: Convoying Merchant Ships
ERIC Educational Resources Information Center
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…
Evaluation of Hydrus-2D model for solute distribution in subsurface drip
NASA Astrophysics Data System (ADS)
Souza, Claudinei; Bizari, Douglas; Grecco, Katarina
2015-04-01
The competition for water use between agriculture, industry and population has become intense over the years, requiring a rational use of this resource for food production. The subsurface drip irrigation can help producers with the optimization of operating parameters such as frequency and duration of irrigation, flow, spacing and depth of the dripper installation. This information can be obtained by numerical simulations using mathematical models, thus the aim of this study was to evaluate the HYDRUS-2D model from experimental data to predict the size of the wet bulbs generated by emitters of different application rates (1.0 and 1.6 L h-1). The results showed that horizontal displacement (bulb diameter) remained the largest in all the bulbs, observed both in experimental trials and estimated by the model and the correlation between them was high, above 0.90 to below 16% error. We conclude that the HYDRUS-2D model can be used to estimate the dimensions of the wet bulb getting new information on the sizing of the irrigation system.
Mathematical models of vaccination.
Scherer, Almut; McLean, Angela
2002-01-01
Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation models of mass vaccination that can be used to address important questions about the predicted impact of vaccination programmes. We show how to calculate the threshold vaccination coverage rate that will eradicate an infection, explore the impact of vaccine-induced immunity that wanes through time, and study the competitive interactions between vaccine susceptible and vaccine resistant strains of infectious agent.
A 2D simulation model for urban flood management
NASA Astrophysics Data System (ADS)
Price, Roland; van der Wielen, Jonathan; Velickov, Slavco; Galvao, Diogo
2014-05-01
The European Floods Directive, which came into force on 26 November 2007, requires member states to assess all their water courses and coast lines for risk of flooding, to map flood extents and assets and humans at risk, and to take adequate and coordinated measures to reduce the flood risk in consultation with the public. Flood Risk Management Plans are to be in place by 2015. There are a number of reasons for the promotion of this Directive, not least because there has been much urban and other infrastructural development in flood plains, which puts many at risk of flooding along with vital societal assets. In addition there is growing awareness that the changing climate appears to be inducing more frequent extremes of rainfall with a consequent increases in the frequency of flooding. Thirdly, the growing urban populations in Europe, and especially in the developing countries, means that more people are being put at risk from a greater frequency of urban flooding in particular. There are urgent needs therefore to assess flood risk accurately and consistently, to reduce this risk where it is important to do so or where the benefit is greater than the damage cost, to improve flood forecasting and warning, to provide where necessary (and possible) flood insurance cover, and to involve all stakeholders in decision making affecting flood protection and flood risk management plans. Key data for assessing risk are water levels achieved or forecasted during a flood. Such levels should of course be monitored, but they also need to be predicted, whether for design or simulation. A 2D simulation model (PriceXD) solving the shallow water wave equations is presented specifically for determining flood risk, assessing flood defense schemes and generating flood forecasts and warnings. The simulation model is required to have a number of important properties: -Solve the full shallow water wave equations using a range of possible solutions; -Automatically adjust the time step and
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Teaching and Assessing Mathematical Modelling.
ERIC Educational Resources Information Center
Lingefjard, T.
2002-01-01
Reports on the observed actions of prospective Swedish secondary mathematics teachers as they were working in a modeling situation. Discusses the way the students tackled the modeling situation and their strategies and attitudes as well as the difficulties in assessing mathematical modeling performance. (KHR)
The Implementation of C-ID, R2D2 Model on Learning Reading Comprehension
ERIC Educational Resources Information Center
Rayanto, Yudi Hari; Rusmawan, Putu Ngurah
2016-01-01
The purposes of this research are to find out, (1) whether C-ID, R2D2 model is effective to be implemented on learning Reading comprehension, (2) college students' activity during the implementation of C-ID, R2D2 model on learning Reading comprehension, and 3) college students' learning achievement during the implementation of C-ID, R2D2 model on…
Explorations in Elementary Mathematical Modeling
ERIC Educational Resources Information Center
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Completeness of the classical 2D Ising model and universal quantum computation.
Van den Nest, M; Dür, W; Briegel, H J
2008-03-21
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.
An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh
2011-01-01
Hanson, H.; Wamsley, T., and Zundel, A. K., 2006. Two-dimensional depth-averaged circulation model CMS- M2D : Version 3.0, Report 2: Sediment...Militello, A.; Reed, C.W.; Zundel, A.K. and Kraus, N.C., 2004. Two-dimensional depth-averaged circulation model M2D : Version 2.0, Report 1, Technical
Mathematical modelling in developmental biology.
Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier
2013-06-01
In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.
Mathematical Modeling of Diverse Phenomena
NASA Technical Reports Server (NTRS)
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Improvement of a 2D numerical model of lava flows
NASA Astrophysics Data System (ADS)
Ishimine, Y.
2013-12-01
I propose an improved procedure that reduces an improper dependence of lava flow directions on the orientation of Digital Elevation Model (DEM) in two-dimensional simulations based on Ishihara et al. (in Lava Flows and Domes, Fink, JH eds., 1990). The numerical model for lava flow simulations proposed by Ishihara et al. (1990) is based on two-dimensional shallow water model combined with a constitutive equation for a Bingham fluid. It is simple but useful because it properly reproduces distributions of actual lava flows. Thus, it has been regarded as one of pioneer work of numerical simulations of lava flows and it is still now widely used in practical hazard prediction map for civil defense officials in Japan. However, the model include an improper dependence of lava flow directions on the orientation of DEM because the model separately assigns the condition for the lava flow to stop due to yield stress for each of two orthogonal axes of rectangular calculating grid based on DEM. This procedure brings a diamond-shaped distribution as shown in Fig. 1 when calculating a lava flow supplied from a point source on a virtual flat plane although the distribution should be circle-shaped. To improve the drawback, I proposed a modified procedure that uses the absolute value of yield stress derived from both components of two orthogonal directions of the slope steepness to assign the condition for lava flows to stop. This brings a better result as shown in Fig. 2. Fig. 1. (a) Contour plots calculated with the original model of Ishihara et al. (1990). (b) Contour plots calculated with a proposed model.
Anomalous invasion in a 2d model of chemotactic predation
NASA Astrophysics Data System (ADS)
Willemsen, Jorge F.
2010-09-01
It has been hypothesized that plankton predators sense the presence of their prey through detection of chemical signals exuded by the prey. This process is formulated using elements of existing models, tailored to correspond to the specific process under investigation. The motivation for the resulting model is discussed in detail. Numerical results are then presented. It is found that the front representing the advance of the predator into the prey is irregular in a novel way, and the reasons for this anomalous invasion are discussed. It is recognized that reaction-diffusion models, starting perhaps with Turing, can lead to what might have been thought of as anomalous patterns - yet the “flicker” front advance discovered here is indeed novel.
Implementation of Minimal Representations in 2d Ising Model Calculations
1992-05-01
Re r’ u. 60:252-262.263-276. 1941. [Ons44] Lars Onsager . Crystal statistics I. A two-dimensional model with an order-disorder transition. Physical Re...ID lattices but the subject really came to life in 1944 when Onsager [Ons44] derived an exact closed form expression for the partition function (see
Development of CCHE2D embankment break model
Technology Transfer Automated Retrieval System (TEKTRAN)
Earthen embankment breach often results in detrimental impact on downstream residents and infrastructure, especially those located in the flooding zone. Embankment failures are most commonly caused by overtopping or internal erosion. This study is to develop a practical numerical model for simulat...
Conservation laws and LETKF with 2D Shallow Water Model
NASA Astrophysics Data System (ADS)
Zeng, Yuefei; Janjic, Tijana
2016-04-01
Numerous approaches have been proposed to maintain physical conservation laws in the numerical weather prediction models. However, to achieve a reliable prediction, adequate initial conditions are also necessary, which are produced by a data assimilation algorithm. If an ensemble Kalman filters (EnKF) is used for this purpose, it has been shown that it could yield unphysical analysis ensemble that for example violates principles of mass conservation and positivity preservation (e.g. Janjic et al 2014) . In this presentation, we discuss the selection of conservation criteria for the analysis step, and start with testing the conservation of mass, energy and enstrophy. The simple experiments deal with nonlinear shallow water equations and simulated observations that are assimilated with LETKF (Localized Ensemble Transform Kalman Filter, Hunt et al. 2007). The model is discretized in a specific way to conserve mass, angular momentum, energy and enstrophy. The effects of the data assimilation on the conserved quantities (of mass, energy and enstrophy) depend on observation covarage, localization radius, observed variable and observation operator. Having in mind that Arakawa (1966) and Arakawa and Lamb (1977) showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of nondivergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, a cause of excessive numerical noise and possible eventual nonlinear instability, we test the effects on prediction depending on the type of errors in the initial condition. The performance with respect to nonlinear energy cascade is assessed as well.
A Model of the Effect of Uncertainty on the C elegans L2/L2d Decision
Avery, Leon
2014-01-01
At the end of the first larval stage, the C elegans larva chooses between two developmental pathways, an L2 committed to reproductive development and an L2d, which has the option of undergoing reproductive development or entering the dauer diapause. I develop a quantitative model of this choice using mathematical tools developed for pricing financial options. The model predicts that the optimal decision must take into account not only the expected potential for reproductive growth, but also the uncertainty in that expected potential. Because the L2d has more flexibility than the L2, it is favored in unpredictable environments. I estimate that the ability to take uncertainty into account may increase reproductive value by as much as 5%, and discuss possible experimental tests for this ability. PMID:25029446
Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model
NASA Astrophysics Data System (ADS)
Jung, Joon-Hee; Arakawa, Akio
2016-03-01
By explicitly resolving cloud-scale processes with embedded two-dimensional (2-D) cloud-resolving models (CRMs), superparameterized global atmospheric models have successfully simulated various atmospheric events over a wide range of time scales. Up to now, however, such models have not included the effects of topography on the CRM grid scale. We have used both 3-D and 2-D CRMs to simulate the effects of topography with prescribed "large-scale" winds. The 3-D CRM is used as a benchmark. The results show that the mean precipitation can be simulated reasonably well by using a 2-D representation of topography as long as the statistics of the topography such as the mean and standard deviation are closely represented. It is also shown that the use of a set of two perpendicular 2-D grids can significantly reduce the error due to a 2-D representation of topography.
Mathematical Models for Doppler Measurements
NASA Technical Reports Server (NTRS)
Lear, William M.
1987-01-01
Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.
Approaches to numerical solution of 2D Ising model
NASA Astrophysics Data System (ADS)
Soldatov, K. S.; Nefedev, K. V.; Kapitan, V. Yu; Andriushchenko, P. D.
2016-08-01
Parallel algorithm of partition function calculation of two-dimensional Ising model for systems with a finite number of spins was developed. Within a method of complete enumeration by using MPI technology with subsequent optimization of a parallel code time of calculations was reduced considerably. Partition function was calculated for systems of 16, 25, 36 Ising spins. Based on the obtained results, main thermodynamic and magnetic values dependences (such as heat capacity, magnetic susceptibility, mean square magnetization) for ferromagnetic and antiferromagnetic interactions was investigated. The analysis of a different configurations contribution showed, that states with the minimum energy have essential influence on dependences of thermodynamic values. Comparison with the results obtained by the Wang Landau algorithm was performed.
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
ERIC Educational Resources Information Center
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Bond Order Correlations in the 2D Hubbard Model
NASA Astrophysics Data System (ADS)
Moore, Conrad; Abu Asal, Sameer; Yang, Shuxiang; Moreno, Juana; Jarrell, Mark
We use the dynamical cluster approximation to study the bond correlations in the Hubbard model with next nearest neighbor (nnn) hopping to explore the region of the phase diagram where the Fermi liquid phase is separated from the pseudogap phase by the Lifshitz line at zero temperature. We implement the Hirsch-Fye cluster solver that has the advantage of providing direct access to the computation of the bond operators via the decoupling field. In the pseudogap phase, the parallel bond order susceptibility is shown to persist at zero temperature while it vanishes for the Fermi liquid phase which allows the shape of the Lifshitz line to be mapped as a function of filling and nnn hopping. Our cluster solver implements NVIDIA's CUDA language to accelerate the linear algebra of the Quantum Monte Carlo to help alleviate the sign problem by allowing for more Monte Carlo updates to be performed in a reasonable amount of computation time. Work supported by the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.
A 2D model to design MHD induction pumps
NASA Astrophysics Data System (ADS)
Stieglitz, R.; Zeininger, J.
2006-09-01
Technical liquid metal systems accompanied by a thermal transfer of energy such as reactor systems, metallurgical processes, metal refinement, casting, etc., require a forced convection of the fluid. The increased temperatures and more often the environmental conditions as, e.g., in a nuclear environment, pumping principles are required, in which rotating parts are absent. Additionally, in many applications a controlled atmosphere is indispensable, in order to ensure the structural integrity of the duct walls. An interesting option to overcome the sealing problem of a mechanical pump towards the surrounding is offered by induction systems. Although their efficiency compared to that of turbo machines is quite low, they have several advantages, which are attractive to the specific requirements in liquid metal applications such as: - low maintenance costs due to the absence of sealings, bearings and moving parts; - low degradation rate of the structural material; - simple replacement of the inductor without cut of the piping system; - fine regulation of flow rate by different inductor connections; - change of pump characteristics without change of the mechanical set-up. Within the article, general design requirements of electromagnetic pumps (EMP) are elaborated. The design of two annular linear induction pumps operating with sodium and lead-bismuth are presented and the calculated pump characteristics and experimentally obtained data are compared. In this context, physical effects leading to deviations between the model and the real data are addressed. Finally, the main results are summarized. Tables 4, Figs 4, Refs 12.
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
ERIC Educational Resources Information Center
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
NASA Astrophysics Data System (ADS)
Guo, Y. G.; Zhu, J. G.; Zhong, J. J.
2006-07-01
This paper reports the measurement and modelling of magnetic properties of SOMALOY TM 500, a soft magnetic composite (SMC) material, under different 2D vector magnetisations, such as alternating along one direction, circularly and elliptically rotating in a 2D plane. By using a 2D magnetic property tester, the B- H curves and core losses of the SMC material have been measured with different flux density patterns on a single sheet square sample. The measurements can provide useful information for modelling of the magnetic properties, such as core losses. The core loss models have been successfully applied in the design of rotating electrical machines with SMC core.
Hintermann, Edith; Holdener, Martin; Bayer, Monika; Loges, Stephanie; Pfeilschifter, Josef M; Granier, Claude; Manns, Michael P; Christen, Urs
2011-11-01
Autoimmune hepatitis (AIH) is a serious chronic inflammatory disease of the liver with yet unknown etiology and largely uncertain immunopathology. The hallmark of type 2 AIH is the generation of liver kidney microsomal-1 (LKM-1) autoantibodies, which predominantly react to cytochrome P450 2D6 (CYP2D6). The identification of disease initiating factors has been hampered in the past, since antibody epitope mapping was mostly performed using serum samples collected late during disease resulting in the identification of immunodominant epitopes not necessarily representing those involved in disease initiation. In order to identify possible environmental triggers for AIH, we analyzed for the first time the spreading of the anti-CYP2D6 antibody response over a prolonged period of time in AIH patients and in the CYP2D6 mouse model, in which mice infected with Adenovirus-human CYP2D6 (Ad-h2D6) develop antibodies with a similar specificity than AIH patients. Epitope spreading was analyzed in six AIH-2-patients and in the CYP2D6 mouse model using SPOTs membranes containing peptides covering the entire CYP2D6 protein. Despite of a considerable variation, both mice and AIH patients largely focus their humoral immune response on an immunodominant epitope early after infection (mice) or diagnosis (patients). The CYP2D6 mouse model revealed that epitope spreading is initiated at the immunodominant epitope and later expands to neighboring and remote regions. Sequence homologies to human pathogens have been detected for all identified epitopes. Our study demonstrates that epitope spreading does indeed occur during the pathogenesis of AIH and supports the concept of molecular mimicry as a possible initiating mechanism for AIH.
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
ERIC Educational Resources Information Center
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model
NASA Astrophysics Data System (ADS)
Procacci, Aldo; Scoppola, Benedetto; Scoppola, Elisabetta
2016-12-01
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the 2-d low-temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type contours.
The immunoreceptor NKG2D promotes tumour growth in a model of hepatocellular carcinoma
Sheppard, Sam; Guedes, Joana; Mroz, Anna; Zavitsanou, Anastasia-Maria; Kudo, Hiromi; Rothery, Stephen M.; Angelopoulos, Panagiotis; Goldin, Robert; Guerra, Nadia
2017-01-01
Inflammation is recognized as one of the drivers of cancer. Yet, the individual immune components that possess pro- and anti-tumorigenic functions in individual cancers remain largely unknown. NKG2D is a potent activating immunoreceptor that has emerged as an important player in inflammatory disorders besides its well-established function as tumour suppressor. Here, we provide genetic evidence of an unexpected tumour-promoting effect of NKG2D in a model of inflammation-driven liver cancer. Compared to NKG2D-deficient mice, NKG2D-sufficient mice display accelerated tumour growth associated with, an increased recruitment of memory CD8+T cells to the liver and exacerbated pro-inflammatory milieu. In addition, we show that NKG2D contributes to liver damage and consequent hepatocyte proliferation known to favour tumorigenesis. Thus, the NKG2D/NKG2D-ligand pathway provides an additional mechanism linking chronic inflammation to tumour development in hepatocellular carcinoma. Our findings expose the need to selectively target the types of cancer that could benefit from NKG2D-based immunotherapy. PMID:28128200
GEO2D - Two-Dimensional Computer Model of a Ground Source Heat Pump System
James Menart
2013-06-07
This file contains a zipped file that contains many files required to run GEO2D. GEO2D is a computer code for simulating ground source heat pump (GSHP) systems in two-dimensions. GEO2D performs a detailed finite difference simulation of the heat transfer occurring within the working fluid, the tube wall, the grout, and the ground. Both horizontal and vertical wells can be simulated with this program, but it should be noted that the vertical wall is modeled as a single tube. This program also models the heat pump in conjunction with the heat transfer occurring. GEO2D simulates the heat pump and ground loop as a system. Many results are produced by GEO2D as a function of time and position, such as heat transfer rates, temperatures and heat pump performance. On top of this information from an economic comparison between the geothermal system simulated and a comparable air heat pump systems or a comparable gas, oil or propane heating systems with a vapor compression air conditioner. The version of GEO2D in the attached file has been coupled to the DOE heating and cooling load software called ENERGYPLUS. This is a great convenience for the user because heating and cooling loads are an input to GEO2D. GEO2D is a user friendly program that uses a graphical user interface for inputs and outputs. These make entering data simple and they produce many plotted results that are easy to understand. In order to run GEO2D access to MATLAB is required. If this program is not available on your computer you can download the program MCRInstaller.exe, the 64 bit version, from the MATLAB website or from this geothermal depository. This is a free download which will enable you to run GEO2D..
CAST2D: A finite element computer code for casting process modeling
Shapiro, A.B.; Hallquist, J.O.
1991-10-01
CAST2D is a coupled thermal-stress finite element computer code for casting process modeling. This code can be used to predict the final shape and stress state of cast parts. CAST2D couples the heat transfer code TOPAZ2D and solid mechanics code NIKE2D. CAST2D has the following features in addition to all the features contained in the TOPAZ2D and NIKE2D codes: (1) a general purpose thermal-mechanical interface algorithm (i.e., slide line) that calculates the thermal contact resistance across the part-mold interface as a function of interface pressure and gap opening; (2) a new phase change algorithm, the delta function method, that is a robust method for materials undergoing isothermal phase change; (3) a constitutive model that transitions between fluid behavior and solid behavior, and accounts for material volume change on phase change; and (4) a modified plot file data base that allows plotting of thermal variables (e.g., temperature, heat flux) on the deformed geometry. Although the code is specialized for casting modeling, it can be used for other thermal stress problems (e.g., metal forming).
Mathematical Models of Gene Regulation
NASA Astrophysics Data System (ADS)
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Using Covariation Reasoning to Support Mathematical Modeling
ERIC Educational Resources Information Center
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
ASTP ranging system mathematical model
NASA Technical Reports Server (NTRS)
Ellis, M. R.; Robinson, L. H.
1973-01-01
A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.
Representativeness of 2D models to simulate 3D unstable variable density flow in porous media
NASA Astrophysics Data System (ADS)
Knorr, Bastian; Xie, Yueqing; Stumpp, Christine; Maloszewski, Piotr; Simmons, Craig T.
2016-11-01
Variable density flow in porous media has been studied primarily using numerical models because it is a semi-chaotic and transient process. Most of these studies have been 2D, owing to the computational restrictions on 3D simulations, and the ability to observe variable density flow in 2D experimentation. However, it is recognised that variable density flow is a three-dimensional process. A 3D system may cause weaker variable density flow than a 2D system due to stronger dispersion, but may also result in bigger fingers and hence stronger variable density flow because of more space for fingers to coalesce. This study aimed to determine the representativeness of 2D modelling to simulate 3D variable density flow. 3D homogeneous sand column experiments were conducted at three different water flow velocities with three different bromide tracer solutions mixed with methanol resulting in different density ratios. Both 2D axisymmetric and 3D numerical simulations were performed to reproduce experimental data. Experimental results showed that the magnitude of variable density flow increases with decreasing flow rates and decreasing density ratios. The shapes of the observed breakthrough curves differed significantly from those produced by 2D axisymmetric and 3D simulations. Compared to 2D simulations, the onset of instabilities was delayed but the growth was more pronounced in 3D simulations. Despite this difference, both 2D axisymmetric and 3D models successfully simulated mass recovery with high efficiency (between 77% and 99%). This study indicates that 2D simulations are sufficient to understand integrated features of variable density flow in homogeneous sand column experiments.
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters
NASA Astrophysics Data System (ADS)
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-02-01
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model.
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-01-01
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model. PMID:28181514
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters.
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-02-09
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model.
Mathematical Modeling: A Bridge to STEM Education
ERIC Educational Resources Information Center
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
The 24-Hour Mathematical Modeling Challenge
ERIC Educational Resources Information Center
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
Mathematical circulatory system model
NASA Technical Reports Server (NTRS)
Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)
2010-01-01
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
Multi-Scale Modeling, Design Strategies and Physical Properties of 2D Composite Sheets
2015-01-15
of Pennsylvania. The breakthrough results obtained are 1) prediction and subsequent experimental observation of strain induced changes in electronic...structure of TMD materials 2) Prediction and experimental observation of using defects in 2D materials to enhance charge storage capacity and 3...221 Philadelphia , PA 19104 -6205 4-Mar-2014 ABSTRACT Final Report: 9.4: Multi-scale modeling, design strategies and physical properties of 2D
On the assimilation of SWOT type data into 2D shallow-water models
NASA Astrophysics Data System (ADS)
Frédéric, Couderc; Denis, Dartus; Pierre-André, Garambois; Ronan, Madec; Jérôme, Monnier; Jean-Paul, Villa
2013-04-01
In river hydraulics, assimilation of water level measurements at gauging stations is well controlled, while assimilation of images is still delicate. In the present talk, we address the richness of satellite mapped information to constrain a 2D shallow-water model, but also related difficulties. 2D shallow models may be necessary for small scale modelling in particular for low-water and flood plain flows. Since in both cases, the dynamics of the wet-dry front is essential, one has to elaborate robust and accurate solvers. In this contribution we introduce robust second order, stable finite volume scheme [CoMaMoViDaLa]. Comparisons of real like tests cases with more classical solvers highlight the importance of an accurate flood plain modelling. A preliminary inverse study is presented in a flood plain flow case, [LaMo] [HoLaMoPu]. As a first step, a 0th order data processing model improves observation operator and produces more reliable water level derived from rough measurements [PuRa]. Then, both model and flow behaviours can be better understood thanks to variational sensitivities based on a gradient computation and adjoint equations. It can reveal several difficulties that a model designer has to tackle. Next, a 4D-Var data assimilation algorithm used with spatialized data leads to improved model calibration and potentially leads to identify river discharges. All the algorithms are implemented into DassFlow software (Fortran, MPI, adjoint) [Da]. All these results and experiments (accurate wet-dry front dynamics, sensitivities analysis, identification of discharges and calibration of model) are currently performed in view to use data from the future SWOT mission. [CoMaMoViDaLa] F. Couderc, R. Madec, J. Monnier, J.-P. Vila, D. Dartus, K. Larnier. "Sensitivity analysis and variational data assimilation for geophysical shallow water flows". Submitted. [Da] DassFlow - Data Assimilation for Free Surface Flows. Computational software http
Combining multitracing and 2D-modelling to identify the dynamic of heavy metals during flooding.
NASA Astrophysics Data System (ADS)
Hissler, C.; Hostache, R.; Matgen, P.; Tosheva, Z.; David, E.; Bates, P.; Stille, P.
2012-04-01
to assess the risk of floodplain contamination in heavy metal due to river sediment deposition and to heavy metal partitioning between particulate and dissolved phases. We focus on a multidisciplinary approach combining environmental geochemistry (multitracing) and hydraulic modelling (using TELEMAC-2D). One important single flood event was selected to illustrate this innovative approach. During the entire flood, the river water was sampled every hour in order to collect the particulate and the dissolved fractions. All the tracers were analyzed in both fractions. An important set of hydrological and sedimentological data are used to reach a more efficient calibration of the TELEMAC modelling system. In addition to standard techniques of hydrochemistry, new approaches of in situ suspended sediment transport monitoring will help getting new insights on the hydraulic system behaviour.
Analysis of vegetation effect on waves using a vertical 2-D RANS model
Technology Transfer Automated Retrieval System (TEKTRAN)
A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...
Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model
Balakrishnan, Minimol; Chakravarthy, V. Srinivasa; Guhathakurta, Soma
2015-01-01
Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias. PMID:26733873
Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model.
Balakrishnan, Minimol; Chakravarthy, V Srinivasa; Guhathakurta, Soma
2015-01-01
Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias.
Mathematical Modeling in the Undergraduate Curriculum
ERIC Educational Resources Information Center
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Teachers' Conceptions of Mathematical Modeling
ERIC Educational Resources Information Center
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical Modelling with Young Children
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2004-01-01
This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…
Mathematical modeling of biological ensembles
Harlow, F.H.; Sandoval, D.L.; Ruppel, H.M.
1986-07-01
Mathematical models are proposed for three distinctly different aspects of biophysical dynamics: mental dynamics, mob dynamics, and the evolution of species. Each section is self-contained, but the approaches are unified by the employment of stochastic equations for the interactive dynamics of numerous discrete entities.
MODELING THE TRANSVERSE THERMAL CONDUCTIVITY OF 2D-SICF/SIC COMPOSITES
Youngblood, Gerald E.; Senor, David J.; Jones, Russell H.
2002-09-01
A hierarchical model was developed to describe the effective transverse thermal conductivity, K effective, of a 2D-SiC/SiC composite made from stacked and infiltrated woven fabric layers in terms of constituent properties and microstructural and architectural variables. The model includes the expected effects of fiber-matrix interfacial conductance as well as the effects of high fiber packing fractions within individual tows and the non-uniform nature of 2D-fabric layers that include a significant amount of interlayer porosity. Model predictions were obtained for two versions of DuPont 2D-Hi Nicalon(Trademark)/PyC/ICVI-SiC composite, one with a thin (0.110 micron) and the other with a thick (1.040 micron) PyC fiber coating. The model predicts that the matrix porosity content and porosity shape factor have a major influence on K effective(T) for such a composite.
Seepage and Piping through Levees and Dikes using 2D and 3D Modeling Codes
2016-06-01
Modeling Codes Co as ta l a nd H yd ra ul ic s La bo ra to ry Hwai-Ping Cheng, Stephen M. England, and Clarissa M. Murray June 2016...Flood & Coastal Storm Damage Reduction Program ERDC/CHL TR-16-6 June 2016 Seepage and Piping through Levees and Dikes Using 2D and 3D Modeling Codes ...TYPE Final Report 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE Seepage and Piping through Levees and Dikes using 2D and 3D Modeling Codes
ERIC Educational Resources Information Center
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
A simple 2-D inundation model for incorporating flood damage in urban drainage planning
NASA Astrophysics Data System (ADS)
Pathirana, A.; Tsegaye, S.; Gersonius, B.; Vairavamoorthy, K.
2011-08-01
An urban inundation model was developed and coupled with 1-D drainage network model (EPA-SWMM5). The objective was to achieve a 1-D/2-D coupled model that is simple and fast enough to be consistently used in planning stages of urban drainage projects. The 2-D inundation model is based on a non-standard simplification of the shallow water equation, lays between diffusion-wave and full dynamic models. Simplifications were made in the process representation and numerical solving mechanisms and a depth scaled Manning coefficient was introduced to achieve stability in the cell wetting-drying process. The 2-D model is coupled with SWMM for simulation of both network flow and surcharge induced inundation. The coupling is archived by mass transfer from the network system to the 2-D system. A damage calculation block is integrated within the model code for assessing flood damage costs in optimal planning of urban drainage networks. The model is stable in dealing with complex flow conditions, and cell wetting/drying processes, as demonstrated by a number of idealised experiments. The model application is demonstrated by applying to a case study in Brazil.
NASA Astrophysics Data System (ADS)
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
On Limits of Embedding in 3D Images Based on 2D Watson's Model
NASA Astrophysics Data System (ADS)
Kavehvash, Zahra; Ghaemmaghami, Shahrokh
We extend the Watson image quality metric to 3D images through the concept of integral imaging. In the Watson's model, perceptual thresholds for changes to the DCT coefficients of a 2D image are given for information hiding. These thresholds are estimated in a way that the resulting distortion in the 2D image remains undetectable by the human eyes. In this paper, the same perceptual thresholds are estimated for a 3D scene in the integral imaging method. These thresholds are obtained based on the Watson's model using the relation between 2D elemental images and resulting 3D image. The proposed model is evaluated through subjective tests in a typical image steganography scheme.
Modeling Tear Film Dynamics on a 2-D Eye-shaped Domain
NASA Astrophysics Data System (ADS)
Li, Longfei; Braun, Richard; Maki, Kara; Henshaw, William
2012-11-01
We study tear film dynamics on a 2-D eye-shaped domain using a lubrication model. Time dependent flux boundary conditions that model the lacrimal gland tear supply and punctal drainage are imposed. We solved the model equations with Overture computational framework. Results reveals our model captures the hydraulic connectivity and other key physics of human tear film observed in vivo. Comparisons are made with existing models and experiments. Should time permit, osmolarity dynamics (salt ion concentration) will be included.
Integrated Navigation, Guidance, and Control of Missile Systems: 2-D Dynamic Models
2012-05-01
Plane Simulation Model Block Diagram .......................................................... 21 Figure A.1. Aerodynamic variables for a missile ...Figure A.1. Aerodynamic variables for a missile Page classification: UNCLASSIFIED DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION DOCUMENT...UNCLASSIFIED Integrated Navigation, Guidance, and Control of Missile Systems: 2-D Dynamic Models Farhan A. Faruqi Weapons
Evaluation of 2D shallow-water model for spillway flow with a complex geometry
Technology Transfer Automated Retrieval System (TEKTRAN)
Although the two-dimensional (2D) shallow water model is formulated based on several assumptions such as hydrostatic pressure distribution and vertical velocity is negligible, as a simple alternative to the complex 3D model, it has been used to compute water flows in which these assumptions may be ...
Disorder and interaction in 2D: exact diagonalization study of the Anderson-Hubbard-Mott model.
Kotlyar, R; Das Sarma, S
2001-03-12
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite-size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is unlikely that there is a 2D metal-insulator quantum phase transition, although the effect of interaction in some range of parameters is to substantially enhance the noninteracting charge stiffness.
Non-trivial θ-vacuum effects in the 2-d O(3) model
NASA Astrophysics Data System (ADS)
Bögli, M.; Niedermayer, F.; Pepe, M.; Wiese, U.-J.
2012-04-01
We study θ-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at θ ne 0 , and there are different continuum theories for each value 0 ≤ θ ≤ π. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at θ = π.
Strategies to Support Students' Mathematical Modeling
ERIC Educational Resources Information Center
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
Mathematical Modeling in the High School Curriculum
ERIC Educational Resources Information Center
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
Problem Posing and Solving with Mathematical Modeling
ERIC Educational Resources Information Center
English, Lyn D.; Fox, Jillian L.; Watters, James J.
2005-01-01
Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
ERIC Educational Resources Information Center
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
The simulation of 3D mass models in 2D digital mammography and breast tomosynthesis
Shaheen, Eman De Keyzer, Frederik; Bosmans, Hilde; Ongeval, Chantal Van; Dance, David R.; Young, Kenneth C.
2014-08-15
Purpose: This work proposes a new method of building 3D breast mass models with different morphological shapes and describes the validation of the realism of their appearance after simulation into 2D digital mammograms and breast tomosynthesis images. Methods: Twenty-five contrast enhanced MRI breast lesions were collected and each mass was manually segmented in the three orthogonal views: sagittal, coronal, and transversal. The segmented models were combined, resampled to have isotropic voxel sizes, triangularly meshed, and scaled to different sizes. These masses were referred to as nonspiculated masses and were then used as nuclei onto which spicules were grown with an iterative branching algorithm forming a total of 30 spiculated masses. These 55 mass models were projected into 2D projection images to obtain mammograms after image processing and into tomographic sequences of projection images, which were then reconstructed to form 3D tomosynthesis datasets. The realism of the appearance of these mass models was assessed by five radiologists via receiver operating characteristic (ROC) analysis when compared to 54 real masses. All lesions were also given a breast imaging reporting and data system (BIRADS) score. The data sets of 2D mammography and tomosynthesis were read separately. The Kendall's coefficient of concordance was used for the interrater observer agreement assessment for the BIRADS scores per modality. Further paired analysis, using the Wilcoxon signed rank test, of the BIRADS assessment between 2D and tomosynthesis was separately performed for the real masses and for the simulated masses. Results: The area under the ROC curves, averaged over all observers, was 0.54 (95% confidence interval [0.50, 0.66]) for the 2D study, and 0.67 (95% confidence interval [0.55, 0.79]) for the tomosynthesis study. According to the BIRADS scores, the nonspiculated and the spiculated masses varied in their degrees of malignancy from normal (BIRADS 1) to highly
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.
Mathematical modeling of drug delivery.
Siepmann, J; Siepmann, F
2008-12-08
Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design
Summer Camp of Mathematical Modeling in China
ERIC Educational Resources Information Center
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Mathematical Modelling of Folate Metabolism
Panetta, John C.; Paugh, Steven W.
2013-01-01
Folate metabolism is a complex biological process that is influenced by many variables including transporters, co-factors and enzymes. Mathematical models provide a useful tool to evaluate this complex system and to elucidate hypotheses that would be otherwise untenable to test in vitro or in vivo. Forty years of model development and refinement along with enhancements in technology have led to systematic improvement in our biological understanding from these models. However, increased complexity does not always lead to increased understanding, and a balanced approach to modelling the system is often advantageous. This approach should address questions about sensitivity of the model to variation and incorporate genomic data. The folate model is a useful platform for investigating the effects of antifolates on the folate pathway. The utility of the model is demonstrated through interrogation of drug resistance, drug-drug interactions, drug selectivity, and drug doses and schedules. Mathematics can be used to create models with the ability to design and improve rationale therapeutic interventions. PMID:23703958
2D-Raman-THz spectroscopy: A sensitive test of polarizable water models
NASA Astrophysics Data System (ADS)
Hamm, Peter
2014-11-01
In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model.
ERIC Educational Resources Information Center
Park, Elisa L.
2009-01-01
The purpose of this study is to understand the dynamics of Korean students' international mobility to study abroad by using the 2-D Model. The first D, "the driving force factor," explains how and what components of the dissatisfaction with domestic higher education perceived by Korean students drives students' outward mobility to seek…
2D-Raman-THz spectroscopy: A sensitive test of polarizable water models
Hamm, Peter
2014-11-14
In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model.
New technologies of 2-D and 3-D modeling for analysis and management of natural resources
NASA Astrophysics Data System (ADS)
Cheremisina, E. N.; Lyubimova, A. V.; Kirpicheva, E. Yu.
2016-09-01
For ensuring technological support of research and administrative activity in the sphere of environmental management a specialized modular program complex was developed. The special attention in developing a program complex is focused to creation of convenient and effective tools for creation and visualization 2d and 3D models providing the solution of tasks of the analysis and management of natural resources.
Breach modelling by overflow with TELEMAC 2D: Comparison with large-scale experiments
Technology Transfer Automated Retrieval System (TEKTRAN)
An erosion law has been implemented in TELEMAC 2D to represent the surface erosion process to model the breach formation of a levee. We focus on homogeneous and earth fill levee to simplify this first implementation. The first part of this study reveals the ability of this method to represent simu...
Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...
Multiple Ising models coupled to 2-d gravity: a CSD analysis
NASA Astrophysics Data System (ADS)
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-04-01
We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.
A novel explicit 2D+t cyclic shape model applied to echocardiography.
Casero, Ramón; Noble, J Alison
2008-01-01
In this paper, we propose a novel explicit 2D+t cyclic shape model that extends the Point Distribution Model (PDM) to shapes like myocardial contours with cyclic dynamics. We also propose an extension to Procrustes alignment that removes pose and subject size variability while maintaining dynamic effects. Our model draws on ideas from Principal Component Analysis (PCA), Multidimensional Scaling (MDS) and Kernel PCA (KPCA) and solves 3 shortcomings of previous implicit models: (1) cardiac cycles in the data set do not each need to have the same number of frames, (2) the required number of subjects for statistically significant results is substantially reduced and (3) the displacement of contour points incorporates time as an explicit variable. We illustrate our method by computing models of the myocardium in the 4 principal planes of 2D+t echocardiography data.
Molecular Dynamics implementation of BN2D or 'Mercedes Benz' water model
NASA Astrophysics Data System (ADS)
Scukins, Arturs; Bardik, Vitaliy; Pavlov, Evgen; Nerukh, Dmitry
2015-05-01
Two-dimensional 'Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.
MODELING THE TRANSVERSE THERMAL CONDUCTIVITY OF 2-D SICF/SIC COMPOSITES MADE WITH WOVEN FABRIC
Youngblood, Gerald E; Senor, David J; Jones, Russell H
2004-06-01
The hierarchical two-layer (H2L) model describes the effective transverse thermal conductivity (Keff) of a 2D-SiCf/SiC composite plate made from stacked and infiltrated woven fabric layers in terms of constituent properties and microstructural and architectural variables. The H2L model includes the effects of fiber-matrix interfacial conductance, high fiber packing fractions within individual tows and the non-uniform nature of 2D fabric/matrix layers that usually include a significant amount of interlayer porosity. Previously, H2L model Keff-predictions were compared to measured values for two versions of 2D Hi-Nicalon/PyC/ICVI-SiC composite, one with a “thin” (0.11m) and the other with a “thick” (1.04m) pyrocarbon (PyC) fiber coating, and for a 2D Tyranno SA/”thin” PyC/FCVI-SIC composite. In this study, H2L model Keff-predictions were compared to measured values for a 2D-SiCf/SiC composite made using the ICVI-process with Hi-Nicalon type S fabric and a “thin” PyC fiber coating. The values of Keff determined for the latter composite were significantly greater than the Keff-values determined for the composites made with either the Hi-Nicalon or the Tyranno SA fabrics. Differences in Keff-values were expected for the different fiber types, but major differences also were due to observed microstructural and architectural variations between the composite systems, and as predicted by the H2L model.
A Deformed Shape Monitoring Model for Building Structures Based on a 2D Laser Scanner
Choi, Se Woon; Kim, Bub Ryur; Lee, Hong Min; Kim, Yousok; Park, Hyo Seon
2013-01-01
High-rise buildings subjected to lateral loads such as wind and earthquake loads must be checked not to exceed the limits on the maximum lateral displacement or the maximum inter-story drift ratios. In this paper, a sensing model for deformed shapes of a building structure in motion is presented. The deformed shape sensing model based on a 2D scanner consists of five modules: (1) module for acquiring coordinate information of a point in a building; (2) module for coordinate transformation and data arrangement for generation of time history of the point; (3) module for smoothing by adjacent averaging technique; (4) module for generation of the displacement history for each story and deformed shape of a building, and (5) module for evaluation of the serviceability of a building. The feasibility of the sensing model based on a 2D laser scanner is tested through free vibration tests of a three-story steel frame structure with a relatively high slenderness ratio of 5.0. Free vibration responses measured from both laser displacement sensors and a 2D laser scanner are compared. In the experimentation, the deformed shapes were obtained from three different methods: the model based on the 2D laser scanner, the direct measurement based on laser displacement sensors, and the numerical method using acceleration data and the displacements from GPS. As a result, it is confirmed that the deformed shape measurement model based on a 2D laser scanner can be a promising alternative for high-rise buildings where installation of laser displacement sensors is impossible. PMID:23698269
Numerical Simulation of Slinger Combustor Using 2-D Axisymmetric Computational Model
NASA Astrophysics Data System (ADS)
Lee, Semin; Park, Soo Hyung; Lee, Donghun
2010-06-01
Small-size turbojet engines have difficulties in maintaining the chemical reaction due to the limitation of chamber size. The combustion chamber is generally designed to improve the reaction efficiency by the generation of vortices in the chamber and to enhance air-fuel mixing characteristics. In the initial stage of designing the combustor, analysis of the 3-D full configuration is not practical due to the huge time consuming computation and grid generation followed by modifications of the geometry. In the present paper, an axisymmetric model maintaining geometric similarity and flow characteristic of 3-D configuration is developed. Based on numerical results from the full 3-D configuration, model reduction is achieved toward 2-D axisymmetric configuration. In the modeling process, the area and location of each hole in 3-D full configuration are considered reasonably and replaced to the 2-D axisymmetric model. By using the 2-D axisymmetric model, the factor that can affect the performance is investigated with the assumption that the flow is non-reacting and turbulent. Numerical results from the present model show a good agreement with numerical results from 3-D full configuration model such as existence of vortex pair in forward region and total pressure loss. By simplifying the complex 3-D model, computing time can be remarkably reduced and it makes easy to find effects of geometry modification.
ADMET: ADipocyte METabolism mathematical model.
Micheloni, Alessio; Orsi, Gianni; De Maria, Carmelo; Vozzi, Giovanni
2015-01-01
White fat cells have an important physiological role in maintaining triglyceride and free fatty acid levels due to their fundamental storage property, as well as determining insulin resistance. ADipocyte METabolism is a mathematical model that mimics the main metabolic pathways of human white fat cell, connecting inputs (composition of culture medium) to outputs (glycerol and free fatty acid release). It is based on a set of nonlinear differential equations, implemented in Simulink® and controlled by cellular energetic state. The validation of this model is based on a comparison between the simulation results and a set of experimental data collected from the literature.
Mathematical Modeling of Kidney Transport
Layton, Anita T.
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. PMID:23852667
Simplified 2D Bidomain Model of Whole Heart Electrical Activity and ECG Generation
NASA Astrophysics Data System (ADS)
Sovilj, Siniša; Magjarević, Ratko; Abed, Amr Al; Lovell, Nigel H.; Dokos, Socrates
2014-06-01
The aim of this study was the development of a geometrically simple and highly computationally-efficient two dimensional (2D) biophysical model of whole heart electrical activity, incorporating spontaneous activation of the sinoatrial node (SAN), the specialized conduction system, and realistic surface ECG morphology computed on the torso. The FitzHugh-Nagumo (FHN) equations were incorporated into a bidomain finite element model of cardiac electrical activity, which was comprised of a simplified geometry of the whole heart with the blood cavities, the lungs and the torso as an extracellular volume conductor. To model the ECG, we placed four electrodes on the surface of the torso to simulate three Einthoven leads VI, VII and VIII from the standard 12-lead system. The 2D model was able to reconstruct ECG morphology on the torso from action potentials generated at various regions of the heart, including the sinoatrial node, atria, atrioventricular node, His bundle, bundle branches, Purkinje fibers, and ventricles. Our 2D cardiac model offers a good compromise between computational load and model complexity, and can be used as a first step towards three dimensional (3D) ECG models with more complex, precise and accurate geometry of anatomical structures, to investigate the effect of various cardiac electrophysiological parameters on ECG morphology.
Mathematical Model for Mapping Students' Cognitive Capability
ERIC Educational Resources Information Center
Tambunan, Hardi
2016-01-01
The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…
Coupled BOUSS-2D and CMS-Wave Modeling Approach for Harbor Projects
2012-08-01
channels, erosion problems at coastal inlets, and aid in design and Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for...Harbor Projects by Lihwa Lin and Zeki Demirbilek PURPOSE: This Coastal and Hydraulics Engineering Technical Note (CHETN) describes the coupled...application of two advanced coastal wave models, BOUSS-2D and CMS-Wave, for harbor applications. The two models have different computational features and
Mathematical models of bipolar disorder
NASA Astrophysics Data System (ADS)
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical models in medicine: Diseases and epidemics
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.
Mathematical Models Of Turbulence In Hypersonic Flow
NASA Technical Reports Server (NTRS)
Marvin, J. G.; Coakley, T. J.
1991-01-01
Report discusses mathematical models of turbulence used in numerical simulations of complicated viscous, hypersonic flows. Includes survey of essential features of models and their statuses in applications.
In vitro systems to study nephropharmacology: 2D versus 3D models.
Sánchez-Romero, Natalia; Schophuizen, Carolien M S; Giménez, Ignacio; Masereeuw, Rosalinde
2016-11-05
The conventional 2-dimensional (2D) cell culture is an invaluable tool in, amongst others, cell biology and experimental pharmacology. However, cells cultured in 2D, on the top of stiff plastic plates lose their phenotypical characteristics and fail in recreating the physiological environment found in vivo. This is a fundamental requirement when the goal of the study is to get a rigorous predictive response of human drug action and safety. Recent approaches in the field of renal cell biology are focused on the generation of 3D cell culture models due to the more bona fide features that they exhibit and the fact that they are more closely related to the observed physiological conditions, and better predict in vivo drug handling. In this review, we describe the currently available 3D in vitro models of the kidney, and some future directions for studying renal drug handling, disease modeling and kidney regeneration.
A depth-averaged 2-D model of flow and sediment transport in coastal waters
NASA Astrophysics Data System (ADS)
Sanchez, Alejandro; Wu, Weiming; Beck, Tanya M.
2016-11-01
A depth-averaged 2-D model has been developed to simulate unsteady flow and nonuniform sediment transport in coastal waters. The current motion is computed by solving the phase-averaged 2-D shallow water flow equations reformulated in terms of total-flux velocity, accounting for the effects of wave radiation stresses and general diffusion or mixing induced by current, waves, and wave breaking. The cross-shore boundary conditions are specified by assuming fully developed longshore current and wave setup that are determined using the reduced 1-D momentum equations. A 2-D wave spectral transformation model is used to calculate the wave height, period, direction, and radiation stresses, and a surface wave roller model is adopted to consider the effects of surface roller on the nearshore currents. The nonequilibrium transport of nonuniform total-load sediment is simulated, considering sediment entrainment by current and waves, the lag of sediment transport relative to the flow, and the hiding and exposure effect of nonuniform bed material. The flow and sediment transport equations are solved using an implicit finite volume method on a variety of meshes including nonuniform rectangular, telescoping (quadtree) rectangular, and hybrid triangular/quadrilateral meshes. The flow and wave models are integrated through a carefully designed steering process. The model has been tested in three field cases, showing generally good performance.
Mathematical modeling of glycerol biotransformation
NASA Astrophysics Data System (ADS)
Popova-Krumova, Petya; Yankova, Sofia; Ilieva, Biliana
2013-12-01
A method for mathematical modeling of glycerol biotransformation by Klebsiella oxytoca is presented. Glycerol is a renewable resource for it is formed as a by-product during biodiesel production. Because of its large volume production, it seems to be a good idea to develop a technology that converts this waste into products of high value (1, 3-Propanediol; 2, 3-Butanediol). The kinetic model of this process consists of many equations and parameters. The minimization of the least square function will be used for model parameters identification. In cases of parameters identification in multiparameter models the minimization of the least square function is very difficult because it is multiextremal. This is the main problem in the multiextremal function minimization which will be solved on the base a hierarchical approach, using a polynomial approximation of the experimental data.
Mathematical model for gyroscope effects
NASA Astrophysics Data System (ADS)
Usubamatov, Ryspek
2015-05-01
Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).
TRENT2D WG: a smart web infrastructure for debris-flow modelling and hazard assessment
NASA Astrophysics Data System (ADS)
Zorzi, Nadia; Rosatti, Giorgio; Zugliani, Daniel; Rizzi, Alessandro; Piffer, Stefano
2016-04-01
Mountain regions are naturally exposed to geomorphic flows, which involve large amounts of sediments and induce significant morphological modifications. The physical complexity of this class of phenomena represents a challenging issue for modelling, leading to elaborate theoretical frameworks and sophisticated numerical techniques. In general, geomorphic-flows models proved to be valid tools in hazard assessment and management. However, model complexity seems to represent one of the main obstacles to the diffusion of advanced modelling tools between practitioners and stakeholders, although the UE Flood Directive (2007/60/EC) requires risk management and assessment to be based on "best practices and best available technologies". Furthermore, several cutting-edge models are not particularly user-friendly and multiple stand-alone software are needed to pre- and post-process modelling data. For all these reasons, users often resort to quicker and rougher approaches, leading possibly to unreliable results. Therefore, some effort seems to be necessary to overcome these drawbacks, with the purpose of supporting and encouraging a widespread diffusion of the most reliable, although sophisticated, modelling tools. With this aim, this work presents TRENT2D WG, a new smart modelling solution for the state-of-the-art model TRENT2D (Armanini et al., 2009, Rosatti and Begnudelli, 2013), which simulates debris flows and hyperconcentrated flows adopting a two-phase description over a mobile bed. TRENT2D WG is a web infrastructure joining advantages offered by the software-delivering model SaaS (Software as a Service) and by WebGIS technology and hosting a complete and user-friendly working environment for modelling. In order to develop TRENT2D WG, the model TRENT2D was converted into a service and exposed on a cloud server, transferring computational burdens from the user hardware to a high-performing server and reducing computational time. Then, the system was equipped with an
NASA Technical Reports Server (NTRS)
Gao, Shou-Ting; Ping, Fan; Li, Xiao-Fan; Tao, Wei-Kuo
2004-01-01
Although dry/moist potential vorticity is a useful physical quantity for meteorological analysis, it cannot be applied to the analysis of 2D simulations. A convective vorticity vector (CVV) is introduced in this study to analyze 2D cloud-resolving simulation data associated with 2D tropical convection. The cloud model is forced by the vertical velocity, zonal wind, horizontal advection, and sea surface temperature obtained from the TOGA COARE, and is integrated for a selected 10-day period. The CVV has zonal and vertical components in the 2D x-z frame. Analysis of zonally-averaged and mass-integrated quantities shows that the correlation coefficient between the vertical component of the CVV and the sum of the cloud hydrometeor mixing ratios is 0.81, whereas the correlation coefficient between the zonal component and the sum of the mixing ratios is only 0.18. This indicates that the vertical component of the CVV is closely associated with tropical convection. The tendency equation for the vertical component of the CVV is derived and the zonally-averaged and mass-integrated tendency budgets are analyzed. The tendency of the vertical component of the CVV is determined by the interaction between the vorticity and the zonal gradient of cloud heating. The results demonstrate that the vertical component of the CVV is a cloud-linked parameter and can be used to study tropical convection.
Fekkes, Stein; Swillens, Abigail E S; Hansen, Hendrik H G; Saris, Anne E C M; Nillesen, Maartje M; Iannaccone, Francesco; Segers, Patrick; de Korte, Chris L
2016-08-25
Three-dimensional strain estimation might improve the detection and localization of high strain regions in the carotid artery for identification of vulnerable plaques. This study compares 2D vs. 3D displacement estimation in terms of radial and circumferential strain using simulated ultrasound images of a patient specific 3D atherosclerotic carotid artery model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on literature data. A Philips L11-3 linear array transducer was simulated which transmitted plane waves at 3 alternating angles at a pulse repetition rate of 10 kHz. Inter-frame radiofrequency ultrasound data were simulated in Field II for 191 equally spaced longitudinal positions of the internal carotid artery. Accumulated radial and circumferential displacements were estimated using tracking of the inter-frame displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2D and 3D method was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3D displacement estimation for the entire cardiac cycle. The 3D technique clearly outperformed the 2D technique in phases with high inter-frame longitudinal motion. In fact the large inter-frame longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2D technique.
Fekkes, Stein; Swillens, Abigail E S; Hansen, Hendrik H G; Saris, Anne E C M; Nillesen, Maartje M; Iannaccone, Francesco; Segers, Patrick; de Korte, Chris L
2016-10-01
Three-dimensional (3-D) strain estimation might improve the detection and localization of high strain regions in the carotid artery (CA) for identification of vulnerable plaques. This paper compares 2-D versus 3-D displacement estimation in terms of radial and circumferential strain using simulated ultrasound (US) images of a patient-specific 3-D atherosclerotic CA model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on the literature data. A Philips L11-3 linear array transducer was simulated, which transmitted plane waves at three alternating angles at a pulse repetition rate of 10 kHz. Interframe (IF) radio-frequency US data were simulated in Field II for 191 equally spaced longitudinal positions of the internal CA. Accumulated radial and circumferential displacements were estimated using tracking of the IF displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least-squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2-D and 3-D methods was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3-D displacement estimation for the entire cardiac cycle. The 3-D technique clearly outperformed the 2-D technique in phases with high IF longitudinal motion. In fact, the large IF longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2-D technique.
Mathematical modeling of cold cap
Pokorny, Richard; Hrma, Pavel R.
2012-10-13
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional (1D) mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
A preliminary 3D model for cytochrome P450 2D6 constructed by homology model building.
Koymans, L M; Vermeulen, N P; Baarslag, A; Donné-Op den Kelder, G M
1993-06-01
A homology model building study of cytochrome P450 2D6 has been carried out based on the crystal structure of cytochrome P450 101. The primary sequences of P450 101 and P450 2D6 were aligned by making use of an automated alignment procedure. This alignment was adjusted manually by matching alpha-helices (C, D, G, I, J, K and L) and beta-sheets (beta 3/beta 4) of P450 101 that are proposed to be conserved in membrane-bound P450s (Ouzounis and Melvin [Eur. J. Biochem., 198 (1991) 307]) to the corresponding regions in the primary amino acid sequence of P450 2D6. Furthermore, alpha-helices B, B' and F were found to be conserved in P450 2D6. No significant homology between the remaining regions of P450 101 and P450 2D6 could be found and these regions were therefore deleted. A 3D model of P450 2D6 was constructed by copying the coordinates of the residues from the crystal structure of P450 101 to the corresponding residues in P450 2D6. The regions without a significant homology with P450 101 were not incorporated into the model. After energy-minimization of the resulting 3D model of P450 2D6, possible active site residues were identified by fitting the substrates debrisoquine and dextrometorphan into the proposed active site. Both substrates could be positioned into a planar pocket near the heme region formed by residues Val370, Pro371, Leu372, Trp316, and part of the oxygen binding site of P450 2D6. Furthermore, the carboxylate group of either Asp100 or Asp301 was identified as a possible candidate for the proposed interaction with basic nitrogen atom(s) of the substrates.(ABSTRACT TRUNCATED AT 250 WORDS)
Hard Copy to Digital Transfer: 3D Models that Match 2D Maps
ERIC Educational Resources Information Center
Kellie, Andrew C.
2011-01-01
This research describes technical drawing techniques applied in a project involving digitizing of existing hard copy subsurface mapping for the preparation of three dimensional graphic and mathematical models. The intent of this research was to identify work flows that would support the project, ensure the accuracy of the digital data obtained,…
A Neural-FEM tool for the 2-D magnetic hysteresis modeling
NASA Astrophysics Data System (ADS)
Cardelli, E.; Faba, A.; Laudani, A.; Lozito, G. M.; Riganti Fulginei, F.; Salvini, A.
2016-04-01
The aim of this work is to present a new tool for the analysis of magnetic field problems considering 2-D magnetic hysteresis. In particular, this tool makes use of the Finite Element Method to solve the magnetic field problem in real device, and fruitfully exploits a neural network (NN) for the modeling of 2-D magnetic hysteresis of materials. The NS has as input the magnetic inductions components B at the k-th simulation step and returns as output the corresponding values of the magnetic field H corresponding to the input pattern. It is trained by vector measurements performed on the magnetic material to be modeled. This input/output scheme is directly implemented in a FEM code employing the magnetic potential vector A formulation. Validations through measurements on a real device have been performed.
Laser irradiated fluorescent perfluorocarbon microparticles in 2-D and 3-D breast cancer cell models
NASA Astrophysics Data System (ADS)
Niu, Chengcheng; Wang, Long; Wang, Zhigang; Xu, Yan; Hu, Yihe; Peng, Qinghai
2017-03-01
Perfluorocarbon (PFC) droplets were studied as new generation ultrasound contrast agents via acoustic or optical droplet vaporization (ADV or ODV). Little is known about the ODV irradiated vaporization mechanisms of PFC-microparticle complexs and the stability of the new bubbles produced. In this study, fluorescent perfluorohexane (PFH) poly(lactic-co-glycolic acid) (PLGA) particles were used as a model to study the process of particle vaporization and bubble stability following excitation in two-dimensional (2-D) and three-dimensional (3-D) cell models. We observed localization of the fluorescent agent on the microparticle coating material initially and after vaporization under fluorescence microscopy. Furthermore, the stability and growth dynamics of the newly created bubbles were observed for 11 min following vaporization. The particles were co-cultured with 2-D cells to form 3-D spheroids and could be vaporized even when encapsulated within the spheroids via laser irradiation, which provides an effective basis for further work.
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
NASA Astrophysics Data System (ADS)
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-02-01
We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
Mathematical model for classification of EEG signals
NASA Astrophysics Data System (ADS)
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
A simple 2-D inundation model for incorporating flood damage in urban drainage planning
NASA Astrophysics Data System (ADS)
Pathirana, A.; Tsegaye, S.; Gersonius, B.; Vairavamoorthy, K.
2008-11-01
In this paper a new inundation model code is developed and coupled with Storm Water Management Model, SWMM, to relate spatial information associated with urban drainage systems as criteria for planning of storm water drainage networks. The prime objective is to achive a model code that is simple and fast enough to be consistently be used in planning stages of urban drainage projects. The formulation for the two-dimensional (2-D) surface flow model algorithms is based on the Navier Stokes equation in two dimensions. An Alternating Direction Implicit (ADI) finite difference numerical scheme is applied to solve the governing equations. This numerical scheme is used to express the partial differential equations with time steps split into two halves. The model algorithm is written using C++ computer programming language. This 2-D surface flow model is then coupled with SWMM for simulation of both pipe flow component and surcharge induced inundation in urban areas. In addition, a damage calculation block is integrated within the inundation model code. The coupled model is shown to be capable of dealing with various flow conditions, as well as being able to simulate wetting and drying processes that will occur as the flood flows over an urban area. It has been applied under idealized and semi-hypothetical cases to determine detailed inundation zones, depths and velocities due to surcharged water on overland surface.
Model-based 3D/2D deformable registration of MR images.
Marami, Bahram; Sirouspour, Shahin; Capson, David W
2011-01-01
A method is proposed for automatic registration of 3D preoperative magnetic resonance images of deformable tissue to a sequence of its 2D intraoperative images. The algorithm employs a dynamic continuum mechanics model of the deformation and similarity (distance) measures such as correlation ratio, mutual information or sum of squared differences for registration. The registration is solely based on information present in the 3D preoperative and 2D intraoperative images and does not require fiducial markers, feature extraction or image segmentation. Results of experiments with a biopsy training breast phantom show that the proposed method can perform well in the presence of large deformations. This is particularly useful for clinical applications such as MR-based breast biopsy where large tissue deformations occur.
Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin
2014-07-01
Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.
Nested 1D-2D approach for urban surface flood modeling
NASA Astrophysics Data System (ADS)
Murla, Damian; Willems, Patrick
2015-04-01
Floods in urban areas as a consequence of sewer capacity exceedance receive increased attention because of trends in urbanization (increased population density and impermeability of the surface) and climate change. Despite the strong recent developments in numerical modeling of water systems, urban surface flood modeling is still a major challenge. Whereas very advanced and accurate flood modeling systems are in place and operation by many river authorities in support of flood management along rivers, this is not yet the case in urban water management. Reasons include the small scale of the urban inundation processes, the need to have very high resolution topographical information available, and the huge computational demands. Urban drainage related inundation modeling requires a 1D full hydrodynamic model of the sewer network to be coupled with a 2D surface flood model. To reduce the computational times, 0D (flood cones), 1D/quasi-2D surface flood modeling approaches have been developed and applied in some case studies. In this research, a nested 1D/2D hydraulic model has been developed for an urban catchment at the city of Gent (Belgium), linking the underground sewer (minor system) with the overland surface (major system). For the overland surface flood modelling, comparison was made of 0D, 1D/quasi-2D and full 2D approaches. The approaches are advanced by considering nested 1D-2D approaches, including infiltration in the green city areas, and allowing the effects of surface storm water storage to be simulated. An optimal nested combination of three different mesh resolutions was identified; based on a compromise between precision and simulation time for further real-time flood forecasting, warning and control applications. Main streets as mesh zones together with buildings as void regions constitute one of these mesh resolution (3.75m2 - 15m2); they have been included since they channel most of the flood water from the manholes and they improve the accuracy of
ICF target 2D modeling using Monte Carlo SNB electron thermal transport in DRACO
NASA Astrophysics Data System (ADS)
Chenhall, Jeffrey; Cao, Duc; Moses, Gregory
2016-10-01
The iSNB (implicit Schurtz Nicolai Busquet multigroup diffusion electron thermal transport method is adapted into a Monte Carlo (MC) transport method to better model angular and long mean free path non-local effects. The MC model was first implemented in the 1D LILAC code to verify consistency with the iSNB model. Implementation of the MC SNB model in the 2D DRACO code enables higher fidelity non-local thermal transport modeling in 2D implosions such as polar drive experiments on NIF. The final step is to optimize the MC model by hybridizing it with a MC version of the iSNB diffusion method. The hybrid method will combine the efficiency of a diffusion method in intermediate mean free path regions with the accuracy of a transport method in long mean free path regions allowing for improved computational efficiency while maintaining accuracy. Work to date on the method will be presented. This work was supported by Sandia National Laboratories and the Univ. of Rochester Laboratory for Laser Energetics.
3D/2D Model-to-Image Registration for Quantitative Dietary Assessment.
Chen, Hsin-Chen; Jia, Wenyan; Li, Zhaoxin; Sun, Yung-Nien; Sun, Mingui
2012-12-31
Image-based dietary assessment is important for health monitoring and management because it can provide quantitative and objective information, such as food volume, nutrition type, and calorie intake. In this paper, a new framework, 3D/2D model-to-image registration, is presented for estimating food volume from a single-view 2D image containing a reference object (i.e., a circular dining plate). First, the food is segmented from the background image based on Otsu's thresholding and morphological operations. Next, the food volume is obtained from a user-selected, 3D shape model. The position, orientation and scale of the model are optimized by a model-to-image registration process. Then, the circular plate in the image is fitted and its spatial information is used as constraints for solving the registration problem. Our method takes the global contour information of the shape model into account to obtain a reliable food volume estimate. Experimental results using regularly shaped test objects and realistically shaped food models with known volumes both demonstrate the effectiveness of our method.
Uncertainties in modelling Mt. Pinatubo eruption with 2-D AER model and CCM SOCOL
NASA Astrophysics Data System (ADS)
Kenzelmann, P.; Weisenstein, D.; Peter, T.; Luo, B. P.; Rozanov, E.; Fueglistaler, S.; Thomason, L. W.
2009-04-01
Large volcanic eruptions may introduce a strong forcing on climate. They challenge the skills of climate models. In addition to the short time attenuation of solar light by ashes the formation of stratospheric sulphate aerosols, due to volcanic sulphur dioxide injection into the lower stratosphere, may lead to a significant enhancement of the global albedo. The sulphate aerosols have a residence time of about 2 years. As a consequence of the enhanced sulphate aerosol concentration both the stratospheric chemistry and dynamics are strongly affected. Due to absorption of longwave and near infrared radiation the temperature in the lower stratosphere increases. So far chemistry climate models overestimate this warming [Eyring et al. 2006]. We present an extensive validation of extinction measurements and model runs of the eruption of Mt. Pinatubo in 1991. Even if Mt. Pinatubo eruption has been the best quantified volcanic eruption of this magnitude, the measurements show considerable uncertainties. For instance the total amount of sulphur emitted to the stratosphere ranges from 5-12 Mt sulphur [e.g. Guo et al. 2004, McCormick, 1992]. The largest uncertainties are in the specification of the main aerosol cloud. SAGE II, for instance, could not measure the peak of the aerosol extinction for about 1.5 years, because optical termination was reached. The gap-filling of the SAGE II [Thomason and Peter, 2006] using lidar measurements underestimates the total extinctions in the tropics for the first half year after the eruption by 30% compared to AVHRR [Rusell et. al 1992]. The same applies to the optical dataset described by Stenchikov et al. [1998]. We compare these extinction data derived from measurements with extinctions derived from AER 2D aerosol model calculations [Weisenstein et al., 2007]. Full microphysical calculations with injections of 14, 17, 20 and 26 Mt SO2 in the lower stratosphere were performed. The optical aerosol properties derived from SAGE II
The Activity System of School-Teaching Mathematics and Mathematical Modelling.
ERIC Educational Resources Information Center
Julie, Cyril
2002-01-01
Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…
A New Approach to Calculate Indirect GWPs using the UIUC 2-D CRT and RTM Model
NASA Astrophysics Data System (ADS)
Li, Y.; Youn, D.; Patten, K.; Wuebbles, D.
2006-12-01
Global warming potentials (GWPs) are defined to be the total impact over time of adding a unit mass of a greenhouse gas to the atmosphere. Indirect GWPs are due to ozone depletion effects in the stratosphere for a certain compound and therefore stand for the long-term global cooling effects. Previously, indirect GWPs were calculated using a box model, which was not able to consider the complex processes in the atmosphere. As a step towards obtaining indirect GWPs through a more robust approach, the UIUC 2-D CRT model was used as the computational tool to derive ozone changes. The 2-D model has more realistic chemical, physical, and dynamical processes in the atmosphere and a relatively complete transport system, which makes it useful for a more accurate analysis. Furthermore, the University of Illinois at Urbana-Champaign (UIUC) radiative transfer model (RTM) is employed to derive the corresponding time-dependent radiative forcings from the 2-D CRT outputs. Two Halon compounds, Halon-1211 and Halon-1301, were selected to be studied for their indirect GWPs. The results showed that instantaneous and stratospheric adjusted indirect GWPs for a 100-year horizon are -10004.8 and -10237.1 for Halon-1211, while for Halon-1301 they are -19218.0 and -19627.6. The indirect GWPs for Halon-1211 and -1301 presented here are two to three times smaller compared to the results in WMO (2006) draft. Further analysis on indirect GWPs will be carried out using our 3-D MOZART-3 model.
RVE Model with Porosity for 2D Woven CVI SiCf/SiC Composites
NASA Astrophysics Data System (ADS)
Shen, Xiuli; Gong, Longdong
2016-12-01
A representative volume element (RVE) model with porosity for 2D woven chemical vapor infiltration (CVI) SiCf/SiC composites is presented, and its mechanical properties are analyzed. Samples are divided after a tensile test, and their cross sections are scanned with a scanning electron microscope. The size of the feature structure of the RVE model is determined based on the measurement statistics of the feature structure parameters. In accordance with CVI technology, the deposition rates of the matrix in each direction along the surface of fiber bundles are assumed to be similar. The porosity structure is formed naturally when the RVE model is established. The RVE model conforms to the real structure and accurately shows the location and geometric shape of internal porosity. The relative error of the tensile modulus value estimated from the RVE model through the asymptotic expansion homogenization method and experimental data is 3.26%. Therefore, the RVE model is accurate and efficient.
Yue, Xiaoshan; Lukowski, Jessica K; Weaver, Eric M; Skube, Susan B; Hummon, Amanda B
2016-12-02
Cell cultures are widely used model systems. Some immortalized cell lines can be grown in either two-dimensional (2D) adherent monolayers or in three-dimensional (3D) multicellular aggregates, or spheroids. Here, the quantitative proteome and phosphoproteome of colon carcinoma HT29 cells cultures in 2D monolayers and 3D spheroids were compared with a stable isotope labeling of amino acids (SILAC) labeling strategy. Two biological replicates from each sample were examined, and notable differences in both the proteome and the phosphoproteome were determined by nanoliquid chromatography tandem mass spectrometry (LC-MS/MS) to assess how growth configuration affects molecular expression. A total of 5867 protein groups, including 2523 phosphoprotein groups and 8733 phosphopeptides were identified in the samples. The Gene Ontology analysis revealed enriched GO terms in the 3D samples for RNA binding, nucleic acid binding, enzyme binding, cytoskeletal protein binding, and histone binding for their molecular functions (MF) and in the process of cell cycle, cytoskeleton organization, and DNA metabolic process for the biological process (BP). The KEGG pathway analysis indicated that 3D cultures are enriched for oxidative phosphorylation pathways, metabolic pathways, peroxisome pathways, and biosynthesis of amino acids. In contrast, analysis of the phosphoproteomes indicated that 3D cultures have decreased phosphorylation correlating with slower growth rates and lower cell-to-extracellular matrix interactions. In sum, these results provide quantitative assessments of the effects on the proteome and phosphoproteome of culturing cells in 2D versus 3D cell culture configurations.
INTERACTIONS BETWEEN TOPOGRAPHY AND ROUGHNESS IN A 2D RASTER-BASED HYDRAULIC MODEL
NASA Astrophysics Data System (ADS)
Casas, M.; Yu, D.; Lane, S. N.; Benito-Ferrandez, G.
2009-12-01
Analysis of river flow using hydraulic modelling and its implications in derived environmental applications are inextricably connected with the way in which the river boundary shape is represented. This relationship is scale-dependent upon the modelling resolution which in turn determines the importance of a subscale performance of the model and the way subscale (surface and flow) processes are parameterised. This work aims to explore scaling effects associated with the parameterisation of topography and roughness (i.e. surface at different scales) and possible interactions between its components (mesh resolution, topographic content of the DEM and roughness parameterisation) within a 2D raster-based diffusion-wave model. A distributed roughness variable which is scale dependent on the mesh resolution and the surface roughness of the DEM is incorporated to the hydraulic model. The roughness parameterisation is carried out on the basis of a LiDAR-derived vegetation height model and applied in a raster based 2D diffusion wave model. Topographic models with different topographic contents and a constant mesh resolution are generated using LiDAR data and different vertical thresholds. Five DEMs are generated with different topographic contents (±Δz), (DEM±5cm, DEM±10cm, DEM±25cm, DEM±50cm) and four mesh resolutions (1, 2, 4 and 8m) are assessed. A sensitivity analysis on the model results to mesh resolution due to interpolation and resampling procedures of topographic data is performed. Interactions between topographic and roughness parameterisation are related to model results and finally, geostatistical methods are used to document scaling effects in hydraulic modelling results and model performance. This method explicitly recognises the three-way interaction between the discretised mesh resolution and the topographic content in the DEM with the roughness parameterisation. The work shows how the subscale behaviour of the 2D hydraulic model is not well
García-Usach, F; Ribes, J; Ferrer, J; Seco, A
2010-10-01
This paper presents the results of an experimental study for the modelling and calibration of denitrifying activity of polyphosphate accumulating organisms (PAOs) in full-scale WWTPs that incorporate simultaneous nitrogen and phosphorus removal. The convenience of using different yields under aerobic and anoxic conditions for modelling biological phosphorus removal processes with the ASM2d has been demonstrated. Thus, parameter η(PAO) in the model is given a physical meaning and represents the fraction of PAOs that are able to follow the DPAO metabolism. Using stoichiometric relationships, which are based on assumed biochemical pathways, the anoxic yields considered in the extended ASM2d can be obtained as a function of their respective aerobic yields. Thus, this modification does not mean an extra calibration effort to obtain the new parameters. In this work, an off-line calibration methodology has been applied to validate the model, where general relationships among stoichiometric parameters are proposed to avoid increasing the number of parameters to calibrate. The results have been validated through a UCT scheme pilot plant that is fed with municipal wastewater. The good concordance obtained between experimental and simulated values validates the use of anoxic yields as well as the calibration methodology. Deterministic modelling approaches, together with off-line calibration methodologies, are proposed to assist in decision-making about further process optimization in biological phosphate removal, since parameter values obtained by off-line calibration give valuable information about the activated sludge process such as the amount of DPAOs in the system.
Modeling the Elastic Modulus of 2D Woven CVI SiC Composites
NASA Technical Reports Server (NTRS)
Morscher, Gregory N.
2006-01-01
The use of fiber, interphase, CVI SiC minicomposites as structural elements for 2D-woven SiC fiber reinforced chemically vapor infiltrated (CVI) SiC matrix composites is demonstrated to be a viable approach to model the elastic modulus of these composite systems when tensile loaded in an orthogonal direction. The 0deg (loading direction) and 90deg (perpendicular to loading direction) oriented minicomposites as well as the open porosity and excess SiC associated with CVI SiC composites were all modeled as parallel elements using simple Rule of Mixtures techniques. Excellent agreement for a variety of 2D woven Hi-Nicalon(TradeMark) fiber-reinforced and Sylramic-iBN reinforced CVI SiC matrix composites that differed in numbers of plies, constituent content, thickness, density, and number of woven tows in either direction (i.e, balanced weaves versus unbalanced weaves) was achieved. It was found that elastic modulus was not only dependent on constituent content, but also the degree to which 90deg minicomposites carried load. This depended on the degree of interaction between 90deg and 0deg minicomposites which was quantified to some extent by composite density. The relationships developed here for elastic modulus only necessitated the knowledge of the fractional contents of fiber, interphase and CVI SiC as well as the tow size and shape. It was concluded that such relationships are fairly robust for orthogonally loaded 2D woven CVI SiC composite system and can be implemented by ceramic matrix composite component modelers and designers for modeling the local stiffness in simple or complex parts fabricated with variable constituent contents.
Using 2D and 3D Modeling to Infer the Depth of the Okavango Dyke Swarm
NASA Astrophysics Data System (ADS)
Dailey, M. K.; Mortimer, D.; Atekwana, E. A.
2009-12-01
The 179 Ma N110°-striking Okavango Dyke swarm (ODS) extends from southern Zimbabwe for approximately 1500 km northwest into Namibia. The emplacement of dyke swarms is typically associated with the initiation of continental breakup and has been suggested that ODS was emplaced during the breakup of Gondwana along an existing zone of weakness. However, the understanding of how these giant dyke swarms are emplaced over large distances for hundreds of kilometers is limited- do these giant dike swarms propagate from a single source for hundreds of kilometers or do they propagate from sub-crustal magma chambers along a zone of weakness? To address these questions we investigated the ODS in northern Botswana. The dyke swarm is exposed at the surface in the east close to its origin but is buried in the northwest within the Okavango Rift Zone. Using airborne magnetic and ground gravity survey data along with rock property data from the exposed sections, 2D and 3D models were created in order to determine the depth of the dyke swarm. Initially several 2D models were used to test hypothesis of varying depths and rock parameters. The 2D models were then used to ‘seed’ the 3D models with similar density, susceptibility, and depth parameters. The dykes appear to have relatively shallow and finite depths, in the range of 2 to 5 km deep. These results are consistent with a lateral emplacement stemming from the failed triple junction and thus ruling out an infinite depth extent which would have been the case if the dykes were propagated vertically from sub-crustal magma chambers.
An Implicit 2-D Depth-Averaged Finite-Volume Model of Flow and Sediment Transport in Coastal Waters
2010-01-01
Two-dimensional depth-averaged circulation model CMS- M2D : Version 3.0, Report 2: Sediment transport and morphology change, Technical Report ERDC/CHL TR...dimensional depth-averaged circulation model M2D : Version 2.0, Report 1, Technical documentation and user’s guide. ERDC/CHL TR-04-2, Coastal and Hydraulics
A solidification constitutive model for NIKE2D and NIKE3D
Raboin, P.J.
1994-03-17
This memo updates the current status of a solidification material model development which has been underway for more than a year. Significant modeling goals such as predicting cut-off stresses, thermo-elasto-plasticity, strain rate dependent plasticity and dynamic recovery have been completed. The model is called SOLMAT for solidification material model, and while developed for NIKE2D, it has already been implemented in NIKE3D and NIT03D by B. Maker. This memo details the future development strategy of SOLMAT including liquid and solid constitutive improvements, coupling of deviatoric and dilatational deformation and a plan to switch between constitutive theories. It explains some of the difficulties associated solidification modeling and proposes two experiments to measure properties for using SOLMAT. Due to the sensitive nature of these plans in relation to programmatic and CRADA concerns, this memo should be treated as confidential document.
An Integrative Model of Excitation Driven Fluid Flow in a 2D Uterine Channel
NASA Astrophysics Data System (ADS)
Maggio, Charles; Fauci, Lisa; Chrispell, John
2009-11-01
We present a model of intra-uterine fluid flow in a sagittal cross-section of the uterus by inducing peristalsis in a 2D channel. This is an integrative multiscale computational model that takes as input fluid viscosity, passive tissue properties of the uterine channel and a prescribed wave of membrane depolarization. This voltage pulse is coupled to a model of calcium dynamics inside a uterine smooth muscle cell, which in turn drives a kinetic model of myosin phosphorylation governing contractile muscle forces. Using the immersed boundary method, these muscle forces are communicated to a fluid domain to simulate the contractions which occur in a human uterus. An analysis of the effects of model parameters on the flow properties and emergent geometry of the peristaltic channel will be presented.
2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration
NASA Astrophysics Data System (ADS)
Hakobyan, Davit; Heuer, Andreas
2017-02-01
Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.
NASA Astrophysics Data System (ADS)
Mendoza-Torres, F.; Diaz-Viera, M. A.
2015-12-01
In many natural fractured porous media, such as aquifers, soils, oil and geothermal reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependency relationships that may exist between the geometric properties of fractures (direction, length, aperture, etc), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in a case study for a fractured rock sample from a carbonate reservoir outcrop.
Momentum Transport: 2D and 3D Cloud Resolving Model Simulations
NASA Technical Reports Server (NTRS)
Tao, Wei-Kuo
2001-01-01
The major objective of this study is to investigate the momentum budgets associated with several convective systems that developed during the TOGA COARE IOP (west Pacific warm pool region) and GATE (east Atlantic region). The tool for this study is the improved Goddard Cumulas Ensemble (GCE) model which includes a 3-class ice-phase microphysical scheme, explicit cloud radiative interactive processes and air-sea interactive surface processes. The model domain contains 256 x 256 grid points (with 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km) in the vertical. The 2D domain has 1024 grid points. The simulations were performed over a 7-day time period (December 19-26, 1992, for TOGA COARE and September 1-7, 1994 for GATE). Cyclic literal boundary conditions are required for this type of long-term integration. Two well organized squall systems (TOGA, COARE February 22, 1993, and GATE September 12, 1994) were also simulated using the 3D GCE model. Only 9 h simulations were required to cover the life time of the squall systems. the lateral boundary conditions were open for these two squall systems simulations. the following will be examined: (1) the momentum budgets in the convective and stratiform regions, (2) the relationship between momentum transport and cloud organization (i.e., well organized squall lines versus less organized convective), (3) the differences and similarities in momentum transport between 2D and 3D simulated convective systems, and (4) the differences and similarities in momentum budgets between cloud systems simulated with open and cyclic lateral boundary conditions. Preliminary results indicate that there are only small differences between 2D and 3D simulated momentum budgets. Major differences occur, however, between momentum budgets associated with squall systems simulated using different lateral boundary conditions.
An interactive 2-D power-line modeling and simulation tool
NASA Astrophysics Data System (ADS)
Hull, David; Adelman, Ross
2012-06-01
The U.S. Army Research Laboratory's Power-Line unmanned aerial vehicle (UAV) Modeling and Simulation (ARL-PLUMS) is a tool for estimating and analyzing quasi-static electric and magnetic fields due to power lines. This tool consists of an interactive 2-D graphical user interface (GUI) and a compute engine that can be used to calculate and visualize the E-Field and H-Field due to as many as seven conductors (two 3-phase circuits and a ground wire). ARL-PLUMS allows the user to set the geometry of the lines and the load conditions on those lines, and then calculate Ey, Ez, Hy, or Hz along a linear path or cutting plane, or in the form of a movie. The path can be along the ground or in the air to simulate the fields that might be observed, for example, by a robotic vehicle or a UAV. ARL-PLUMS makes several simplifying assumptions in order to allow simulations to be completed on a laptop PC interactively. In most cases, the results are excellent, providing a "90% solution" in just a few minutes of total modeling and simulation time. This paper describes the physics used by ARL-PLUMS, including the simplifying assumptions and the 2-D Method of Moments solver. Examples of electric and magnetic fields for different wire configurations, including typical 3-phase distribution and transmissions lines, are provided. Comparisons to similar results using a full 3-D model are also shown, and a discussion of errors that may be expected from the 2-D simulations is provided.
JetCurry: Modeling 3D geometry of AGN jets from 2D images
NASA Astrophysics Data System (ADS)
Kosak, Katie; Li, KunYang; Avachat, Sayali S.; Perlman, Eric S.
2017-02-01
Written in Python, JetCurry models the 3D geometry of jets from 2-D images. JetCurry requires NumPy and SciPy and incorporates emcee (ascl:1303.002) and AstroPy (ascl:1304.002), and optionally uses VPython. From a defined initial part of the jet that serves as a reference point, JetCurry finds the position of highest flux within a bin of data in the image matrix and fits along the x axis for the general location of the bends in the jet. A spline fitting is used to smooth out the resulted jet stream.
JetCurry: Modeling 3D geometry of AGN jets from 2D images
NASA Astrophysics Data System (ADS)
Li, Kunyang; Kosak, Katie; Avachat, Sayali S.; Perlman, Eric S.
2017-02-01
Written in Python, JetCurry models the 3D geometry of AGN jets from 2-D images. JetCurry requires NumPy and SciPy and incorporates emcee (ascl:1303.002) and AstroPy (ascl:1304.002), and optionally uses VPython. From a defined initial part of the jet that serves as a reference point, JetCurry finds the position of highest flux within a bin of data in the image matrix and fits along the x axis for the general location of the bends in the jet. A spline fitting is used to smooth out the resulted jet stream.
A 2D Axisymmetric Mixture Multiphase Model for Bottom Stirring in a BOF Converter
NASA Astrophysics Data System (ADS)
Kruskopf, Ari
2017-02-01
A process model for basic oxygen furnace (BOF) steel converter is in development. The model will take into account all the essential physical and chemical phenomena, while achieving real-time calculation of the process. The complete model will include a 2D axisymmetric turbulent multiphase flow model for iron melt and argon gas mixture, a steel scrap melting model, and a chemical reaction model. A novel liquid mass conserving mixture multiphase model for bubbling gas jet is introduced in this paper. In-house implementation of the model is tested and validated in this article independently from the other parts of the full process model. Validation data comprise three different water models with different volume flow rates of air blown through a regular nozzle and a porous plug. The water models cover a wide range of dimensionless number R_{{p}} , which include values that are similar for industrial-scale steel converter. The k- ɛ turbulence model is used with wall functions so that a coarse grid can be utilized. The model calculates a steady-state flow field for gas/liquid mixture using control volume method with staggered SIMPLE algorithm.
Self-Organization in 2D Traffic Flow Model with Jam-Avoiding Drive
NASA Astrophysics Data System (ADS)
Nagatani, Takashi
1995-04-01
A stochastic cellular automaton (CA) model is presented to investigate the traffic jam by self-organization in the two-dimensional (2D) traffic flow. The CA model is the extended version of the 2D asymmetric exclusion model to take into account jam-avoiding drive. Each site contains either a car moving to the up, a car moving to the right, or is empty. A up car can shift right with probability p ja if it is blocked ahead by other cars. It is shown that the three phases (the low-density phase, the intermediate-density phase and the high-density phase) appear in the traffic flow. The intermediate-density phase is characterized by the right moving of up cars. The jamming transition to the high-density jamming phase occurs with higher density of cars than that without jam-avoiding drive. The jamming transition point p 2c increases with the shifting probability p ja. In the deterministic limit of p ja=1, it is found that a new jamming transition occurs from the low-density synchronized-shifting phase to the high-density moving phase with increasing density of cars. In the synchronized-shifting phase, all up cars do not move to the up but shift to the right by synchronizing with the move of right cars. We show that the jam-avoiding drive has an important effect on the dynamical jamming transition.
Constructing a Model of Mathematical Literacy.
ERIC Educational Resources Information Center
Pugalee, David K.
1999-01-01
Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…
Mathematical Modelling as a Professional Task
ERIC Educational Resources Information Center
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mathematical Modelling of Data: Software for Pedagogy.
ERIC Educational Resources Information Center
Bellomonte, L.; Sperandeo-Mineo, R. M.
1993-01-01
Discussion of mathematical modeling, particularly for high school physics curricula, focuses on software that is connected with laboratory work and the inference of mathematical models based on measurements of physical quantities. Fitting procedures are described, and user interface is explained. (Contains nine references.) (LRW)
Modelling and Optimizing Mathematics Learning in Children
ERIC Educational Resources Information Center
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Scaffolding Mathematical Modelling with a Solution Plan
ERIC Educational Resources Information Center
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
A comparative 2D modeling of debris-flow propagation and outcomes for end-users
NASA Astrophysics Data System (ADS)
Bettella, F.; Bertoldi, G.; Pozza, E.; McArdell, B. W.; D'Agostino, V.
2012-04-01
In Alpine regions gravity-driven natural hazards, in particular debris flows, endanger settlements and human life. Mitigation strategies based on hazard maps are necessary tools for land planning. These maps can be made more precise by using numerical models to forecasting the inundated areas after a careful setting of those 'key parameters' (K-P) which directly affect the flow motion and its interaction with the ground surface. Several physically based 2D models are available for practitioners and governmental agencies, but the selection criteria of model type and of the related K-P remain flexible and partly subjective. This remark has driven us to investigate how different models simulate different types of debris flows (from granular to muddy debris flows, going through intermediate types), in particular when the flow is influenced by the presence of deposition basins. Two commercial 2D physical models (RAMMS and FLO-2D) have been tested for five well-documented debris flows events from five Italian catchments were different geology and flow dynamics are observed: 1) a viscous debris flow occurred in 2009 in a catchment with a metamorphic geology (Gadria torrent, Bolzano Province); 2) the 2009 granular debris flow in an granitic geological setting (Rio Dosson, Trento Province); 3-4) two events occurred in the 'rio Val del Lago' and 'rio Molinara' (Trento Province) in 2010 where porphyritic lithology prevails (intermediate granular debris flow); 5) the Rotolon torrent (Vicenza Province) 2009 debris flow containing sedimentary rocks enclosed in an abundant clay-rich matrix (intermediate viscous case). Event volumes range from 5.000 to 50.000 cubic meters. The Gadria, Rotolon and Val del Lago events are also influenced by artificial retention basins. Case study simulations allowed delineation of some practical end-user suggestions and good practices in order to guide the model choice and the K-P setting, particularly related to different flow dynamics. The
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
Kinetic parameter estimation in N. europaea biofilms using a 2-D reactive transport model.
Lauchnor, Ellen G; Semprini, Lewis; Wood, Brian D
2015-06-01
Biofilms of the ammonia oxidizing bacterium Nitrosomonas europaea were cultivated to study microbial processes associated with ammonia oxidation in pure culture. We explored the hypothesis that the kinetic parameters of ammonia oxidation in N. europaea biofilms were in the range of those determined with batch suspended cells. Oxygen and pH microelectrodes were used to measure dissolved oxygen (DO) concentrations and pH above and inside biofilms and reactive transport modeling was performed to simulate the measured DO and pH profiles. A two dimensional (2-D) model was used to simulate advection parallel to the biofilm surface and diffusion through the overlying fluid while reaction and diffusion were simulated in the biofilm. Three experimental studies of microsensor measurements were performed with biofilms: i) NH3 concentrations near the Ksn value of 40 μM determined in suspended cell tests ii) Limited buffering capacity which resulted in a pH gradient within the biofilms and iii) NH3 concentrations well below the Ksn value. Very good fits to the DO concentration profiles both in the fluid above and in the biofilms were achieved using the 2-D model. The modeling study revealed that the half-saturation coefficient for NH3 in N. europaea biofilms was close to the value measured in suspended cells. However, the third study of biofilms with low availability of NH3 deviated from the model prediction. The model also predicted shifts in the DO profiles and the gradient in pH that resulted for the case of limited buffering capacity. The results illustrate the importance of incorporating both key transport and chemical processes in a biofilm reactive transport model.
NASA Astrophysics Data System (ADS)
Richwalski, S. M.; Parolai, S.; Wang, R.; Roth, F.
The effect of sedimentary basins on the seismic wavefield is mainly twofold: The shaking at resonance frequencies is amplified and the shaking duration is increased. We study these effects for the area of Cologne (Germany), which is situated in the Lower Rhine Embayment. This is an active tectonic region with a horst/graben struc- ture where moderate sized earthquakes occur along the fault systems. The Erft fault system for example, with the closest surface exposure only 15 km West of the city of Cologne and its high concentration of industrial facilities, is the most important po- tential fault (Ahorner, 2001, DGG Mittlg., 2, p 3). This research is part of the German Research Network for Natural Disasters (DFNK) which aims at an integrated approach for assessing the seismic hazard in this region. Seismic modelling may aid the mitigation of earthquake risk by providing shaking sce- narios for possible source locations and parameters. For modelling, we use a hybrid technique, which combines an improved Thomson-Haskell algorithm (Wang, 1999, BSSA, p 733) with a 2D finite-difference algorithm (Zahradník and Moczo, 1996, PAGEOPH, p 21). This allows for including realistic sources, a regional background model, and a detailed near surface model for the basin. The increase in the shaking duration is already visible in the seismograms but bet- ter visualised by sonograms that show the distribution of the spectral energy in time. Resonance frequencies can be identified using the classical spectral ratio method. The necessary reference site can be created by repeating the modelling using only the re- gional background model but not the basin structure. We also compare the results of 1D and 2D modelling.
Assessing soil fluxes using meteoric 10Be: development and application of the Be2D model
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Govers, Gerard; Vanacker, Veerle; Baken, Stijn; Smolders, Erik; Vanderborght, Jan
2015-04-01
Meteoric 10Be is a promising and increasingly popular tool to better understand soil fluxes at different timescales. Unlike other, more classical, methods such as the study of sedimentary archives it enables a direct coupling between eroding and deposition sites. However, meteoric 10Be can be mobilized within the soil. Therefore, spatial variations in meteoric 10Be inventories cannot directly be translated into spatial variations in erosion and sedimentation rates: a correct interpretation of measured 10Be inventories requires that both lateral and vertical movement of meteoric 10Be are accounted for. Here, we present a spatially explicit 2D model that allows to simulate the behaviour of meteoric 10Be in the soil system over timescales of up to 1 million year and use the model to investigate the impact of accelerated erosion on meteoric 10Be inventories. The model consists of two parts. A first component deals with advective and diffusive mobility within the soil profile, whereas a second component describes lateral soil (and meteoric 10Be) fluxes over the hillslope. Soil depth is calculated dynamically, accounting for soil production through weathering and lateral soil fluxes. Different types of erosion such as creep, water and tillage erosion are supported. Model runs show that natural soil fluxes can be well reconstructed based on meteoric 10Be inventories, and this for a wide range of geomorphological and pedological conditions. However, extracting signals of human impact and distinguishing them from natural soil fluxes is only feasible when the soil has a rather high retention capacity so that meteoric 10Be is retained in the top soil layer. Application of the Be2D model to an existing data set in the Appalachian Mountains [West et al.,2013] using realistic parameter values for the soil retention capacity as well as for vertical advection resulted in a good agreement between simulated and observed 10Be inventories. This confirms the robustness of the model. We
The concept models and implementations of multiport neural net associative memory for 2D patterns
NASA Astrophysics Data System (ADS)
Krasilenko, Vladimir G.; Nikolskyy, Aleksandr I.; Yatskovskaya, Rimma A.; Yatskovsky, Victor I.
2011-04-01
The paper considers neural net models and training and recognizing algorithms with base neurobiologic operations: p-step autoequivalence and non-equivalenc The Modified equivalently models (MEMs) of multiport neural net associative memory (MNNAM) are offered with double adaptive - equivalently weighing (DAEW) for recognition of 2D-patterns (images). It is shown, the computing process in MNNAM under using the proposed MEMs, is reduced to two-step and multi-step algorithms and step-by-step matrix-matrix (tensor-tensor) procedures. The given results of computer simulations confirmed the perspective of such models. Besides the result was received when MNNAM capacity on base of MEMs exceeded the amount of neurons.
Longtime Well-posedness for the 2D Groma-Balogh Model
NASA Astrophysics Data System (ADS)
Wan, Renhui; Chen, Jiecheng
2016-12-01
In this paper, we consider the cauchy problem for the 2D Groma-Balogh model (Acta Mater 47:3647-3654, 1999). From the works Cannone et al. (Arch Ration Mech Anal 196:71-96, 2010) and El Hajj (Ann Inst Henri Poincaré Anal Nonlinéaire 27:21-35, 2010), one can see global well-posedness for this model is an open question. However, we can prove longtime well-posedness. In particular, we show that this model admits a unique solution with the lifespan T^star satisfying T^star log ^2(1+T^star )≳ ɛ ^{-2} if the initial data is of size ɛ . To achieve this, we first establish some new decay estimates concerning the operator e^{-{R}_{12}^2t}. Then, we prove the longtime well-posedness by utilizing the weak dissipation to deal with the nonlinear terms.
Partitioning of crustal shortening during continental collision: 2-D thermomechanical modeling
NASA Astrophysics Data System (ADS)
Liao, Jie; Gerya, Taras
2017-01-01
Partitioning of crustal shortening between the colliding continental plates is highly variable in nature. Physical controls of such variability remain largely enigmatic and require quantitative understanding. In this study, we employ 2-D thermomechanical numerical modeling to investigate the influence of the rheological properties of the continental crust on the dynamics and distribution of crustal shortening during continental collision. Three major physical parameters, (i) the mechanical strength of the upper crust, (ii) the Moho temperature, and (iii) the convergence rate, are investigated, and their influences on crustal shortening partitioning between the lower and upper plates are systematically documented. Numerical modeling results suggest that a strong upper crust of the lower plate, high Moho temperature, and slow convergence rate favor migration of crustal shortening from the lower to the upper plate. Our numerical modeling results compare well with natural observations from the Alpine orogenic system where variable partitioning of crustal deformation between the plates is documented.
Rival approaches to mathematical modelling in immunology
NASA Astrophysics Data System (ADS)
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
Efficient finite element modeling of scattering for 2D and 3D problems
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2010-03-01
The scattering of waves by defects is central to ultrasonic NDE and SHM. In general, scattering problems must be modeled using direct numerical methods such as finite elements (FE), which is very computationally demanding. The most efficient way is to only model the scatterer itself and a minimal region of the surrounding host medium, and this was previously demonstrated for 2-dimensional (2D) bulk wave scattering problems in isotropic media. An encircling array of monopole and dipole sources is used to inject an arbitrary wavefront onto the scatterer and the scattered field is monitored by a second encircling array of monitoring points. From this data, the scattered field can be projected out to any point in space. If the incident wave is chosen to be a plane wave incident from a given angle and the scattered field is projected to distant points in the far-field of the scatterer, the far-field scattering or S-matrix may be obtained, which encodes all the available scattering information. In this paper, the technique is generalized to any elastic wave geometry in both 2D and 3D, where the latter can include guided wave scattering problems. A further refinement enables the technique to be employed with free FE meshes of triangular or tetrahedral elements.
Laser irradiated fluorescent perfluorocarbon microparticles in 2-D and 3-D breast cancer cell models
Niu, Chengcheng; Wang, Long; Wang, Zhigang; Xu, Yan; Hu, Yihe; Peng, Qinghai
2017-01-01
Perfluorocarbon (PFC) droplets were studied as new generation ultrasound contrast agents via acoustic or optical droplet vaporization (ADV or ODV). Little is known about the ODV irradiated vaporization mechanisms of PFC-microparticle complexs and the stability of the new bubbles produced. In this study, fluorescent perfluorohexane (PFH) poly(lactic-co-glycolic acid) (PLGA) particles were used as a model to study the process of particle vaporization and bubble stability following excitation in two-dimensional (2-D) and three-dimensional (3-D) cell models. We observed localization of the fluorescent agent on the microparticle coating material initially and after vaporization under fluorescence microscopy. Furthermore, the stability and growth dynamics of the newly created bubbles were observed for 11 min following vaporization. The particles were co-cultured with 2-D cells to form 3-D spheroids and could be vaporized even when encapsulated within the spheroids via laser irradiation, which provides an effective basis for further work. PMID:28262671
Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal
NASA Astrophysics Data System (ADS)
Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun
2013-05-01
Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart. PMID:26583141
Tropical Oceanic Precipitation Processes over Warm Pool: 2D and 3D Cloud Resolving Model Simulations
NASA Technical Reports Server (NTRS)
Tao, W.- K.; Johnson, D.
1998-01-01
Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere, The vertical distribution of convective latent-heat release modulates the large-scale circulations of the tropics, Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate models simulate cloud processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMS) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and cloud systems, The major objective of this paper is to investigate the latent heating, moisture and momenti,im budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (CCE) model which includes a 3-class ice-phase microphysical scheme, The model domain contains 256 x 256 grid points (using 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km depth) in the vertical, The 2D domain has 1024 grid points. The simulations are performed over a 7 day time period. We will examine (1) the precipitation processes (i.e., condensation/evaporation) and their interaction with warm pool; (2) the heating and moisture budgets in the convective and
5D Data Modelling: Full Integration of 2D/3D Space, Time and Scale Dimensions
NASA Astrophysics Data System (ADS)
van Oosterom, Peter; Stoter, Jantien
This paper proposes an approach for data modelling in five dimensions. Apart from three dimensions for geometrical representation and a fourth dimension for time, we identify scale as fifth dimensional characteristic. Considering scale as an extra dimension of geographic information, fully integrated with the other dimensions, is new. Through a formal definition of geographic data in a conceptual 5D continuum, the data can be handled by one integrated approach assuring consistency across scale and time dimensions. Because the approach is new and challenging, we choose to step-wise studying several combinations of the five dimensions, ultimately resulting in the optimal 5D model. We also propose to apply mathematical theories on multidimensional modelling to well established principles of multidimensional modelling in the geo-information domain. The result is a conceptual full partition of the 3Dspace+time+scale space (i.e. no overlaps, no gaps) realised in a 5D data model implemented in a Database Management System.
Mathematical modeling in soil science
NASA Astrophysics Data System (ADS)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Dynamical modeling of sub-grid scales in 2D turbulence
NASA Astrophysics Data System (ADS)
Laval, Jean-Philippe; Dubrulle, Bérengère; Nazarenko, Sergey
2000-08-01
We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123-138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor’s regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k-3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence.
Locally adaptive 2D-3D registration using vascular structure model for liver catheterization.
Kim, Jihye; Lee, Jeongjin; Chung, Jin Wook; Shin, Yeong-Gil
2016-03-01
Two-dimensional-three-dimensional (2D-3D) registration between intra-operative 2D digital subtraction angiography (DSA) and pre-operative 3D computed tomography angiography (CTA) can be used for roadmapping purposes. However, through the projection of 3D vessels, incorrect intersections and overlaps between vessels are produced because of the complex vascular structure, which makes it difficult to obtain the correct solution of 2D-3D registration. To overcome these problems, we propose a registration method that selects a suitable part of a 3D vascular structure for a given DSA image and finds the optimized solution to the partial 3D structure. The proposed algorithm can reduce the registration errors because it restricts the range of the 3D vascular structure for the registration by using only the relevant 3D vessels with the given DSA. To search for the appropriate 3D partial structure, we first construct a tree model of the 3D vascular structure and divide it into several subtrees in accordance with the connectivity. Then, the best matched subtree with the given DSA image is selected using the results from the coarse registration between each subtree and the vessels in the DSA image. Finally, a fine registration is conducted to minimize the difference between the selected subtree and the vessels of the DSA image. In experimental results obtained using 10 clinical datasets, the average distance errors in the case of the proposed method were 2.34±1.94mm. The proposed algorithm converges faster and produces more correct results than the conventional method in evaluations on patient datasets.
2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.
ERIC Educational Resources Information Center
Horton, Robert M.; Leonard, William H.
2005-01-01
In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-07
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Be2D: A model to understand the distribution of meteoric 10Be in soilscapes
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Vanacker, Veerle; Vanderborght, Jan; Govers, Gerard
2016-04-01
Cosmogenic nuclides have revolutionised our understanding of earth surface process rates. They have become one of the standard tools to quantify soil production by weathering, soil redistribution and erosion. Especially Beryllium-10 has gained much attention due to its long half-live and propensity to be relatively conservative in the landscape. The latter makes 10Be an excellent tool to assess denudation rates over the last 1000 to 100 × 103 years, bridging the anthropogenic and geological time scale. Nevertheless, the mobility of meteoric 10Be in soil systems makes translation of meteoric 10Be inventories into erosion and deposition rates difficult. Here we present a coupled soil hillslope model, Be2D, that is applied to synthetic and real topography to address the following three research questions. (i) What is the influence of vertical meteoric Be10 mobility, caused by chemical mobility, clay translocation and bioturbation, on its lateral redistribution over the soilscape, (ii) How does vertical mobility influence erosion rates and soil residence times inferred from meteoric 10Be inventories and (iii) To what extent can a tracer with a half-life of 1.36 Myr be used to distinguish between natural and human-disturbed soil redistribution rates? The model architecture of Be2D is designed to answer these research questions. Be2D is a dynamic model including physical processes such as soil formation, physical weathering, clay migration, bioturbation, creep, overland flow and tillage erosion. Pathways of meteoric 10Be mobility are simulated using a two step approach which is updated each timestep. First, advective and diffusive mobility of meteoric 10Be is simulated within the soil profile and second, lateral redistribution because of lateral soil fluxes is calculated. The performance and functionality of the model is demonstrated through a number of synthetic and real model runs using existing datasets of meteoric 10Be from case-studies in southeastern US. Brute
Estimating nitrogen losses in furrow irrigated soil amended by compost using HYDRUS-2D model
NASA Astrophysics Data System (ADS)
Iqbal, Shahid; Guber, Andrey; Zaman Khan, Haroon; ullah, Ehsan
2014-05-01
Furrow irrigation commonly results in high nitrogen (N) losses from soil profile via deep infiltration. Estimation of such losses and their reduction is not a trivial task because furrow irrigation creates highly nonuniform distribution of soil water that leads to preferential water and N fluxes in soil profile. Direct measurements of such fluxes are impractical. The objective of this study was to assess applicability of HYDRUS-2D model for estimating nitrogen balance in manure amended soil under furrow irrigation. Field experiments were conducted in a sandy loam soil amended by poultry manure compost (PMC) and pressmud compost (PrMC) fertilizers. The PMC and PrMC contained 2.5% and 0.9% N and were applied at 5 rates: 2, 4, 6, 8 and 10 ton/ha. Plots were irrigated starting from 26th day from planting using furrows with 1x1 ridge to furrow aspect ratio. Irrigation depths were 7.5 cm and time interval between irrigations varied from 8 to 15 days. Results of the field experiments showed that approximately the same corn yield was obtained with considerably higher N application rates using PMC than using PrMC as a fertilizer. HYDRUS-2D model was implemented to evaluate N fluxes in soil amended by PMC and PrMC fertilizers. Nitrogen exchange between two pools of organic N (compost and soil) and two pools of mineral N (soil NH4-N and soil NO3-N) was modeled using mineralization and nitrification reactions. Sources of mineral N losses from soil profile included denitrification, root N uptake and leaching with deep infiltration of water. HYDRUS-2D simulations showed that the observed increases in N root water uptake and corn yields associated with compost application could not be explained by the amount of N added to soil profile with the compost. Predicted N uptake by roots significantly underestimated the field data. Good agreement between simulated and field-estimated values of N root uptake was achieved when the rate of organic N mineralization was increased
Destabilization of survival factor MEF2D mRNA by neurotoxin in models of Parkinson's disease.
Wang, Bao; Cai, Zhibiao; Lu, Fangfang; Li, Chen; Zhu, Xiaofei; Su, Linna; Gao, Guodong; Yang, Qian
2014-09-01
Progressive loss of dopaminergic (DA) neurons in the substantial nigra pars compacta (SNc) is an important pathological feature in Parkinson's disease (PD). Loss of transcription factor myocyte enhancer factor 2D (MEF2D), a key neuronal survival factor, has been shown to underlie the loss of DA neurons in SNc and the pathogenic process of PD. It is known that PD-associated neurotoxins reduce the level of MEF2D protein to trigger neuronal death. Although neurotoxins clearly destabilize MEF2D by post-translational mechanisms, it is not known whether regulation of MEF2D mRNA contributes to neurotoxin-induced decrease in MEF2D protein. In this work, we showed that MPP(+), the toxic metabolite of MPTP, caused a significant decrease in the half-life and total level of MEF2D mRNA in a DA neuronal cell line, SN4741 cells. Quantitative PCR analysis of the SNc DA neurons captured by immune-laser capture microdissection showed that exposure to MPTP led to a marked reduction in the level of MEF2D mRNA in SNc DA neurons compared to controls. Down-regulation of MEF2D mRNA alone reduced the viability of SN4741 cells and sensitized the cells to MPP(+)-induced toxicity. These results suggest that destabilization and reduction in MEF2D mRNA is in part responsible for neurotoxin-induced decrease in MEF2D protein and neuronal viability. Myocyte enhancer factor 2D (MEF2D) plays an important role in neuronal survival. How MEF2D mRNA is deregulated under toxic stress is unclear. We found that PD-associated neurotoxins destabilize MEF2D mRNA and reduce its level in vitro and in vivo. Reduction in MEF2D mRNA is sufficient to sensitize model cells to neurotoxin-induced toxicity, suggesting that destabilization of MEF2D mRNA is part of the mechanism by which neurotoxins trigger deregulation of neuronal survival.
A Seminar in Mathematical Model-Building.
ERIC Educational Resources Information Center
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
A computationally efficient 2D hydraulic approach for global flood hazard modeling
NASA Astrophysics Data System (ADS)
Begnudelli, L.; Kaheil, Y.; Sanders, B. F.
2014-12-01
We present a physically-based flood hazard model that incorporates two main components: a hydrologic model and a hydraulic model. For hydrology we use TOPNET, a more comprehensive version of the original TOPMODEL. To simulate flood propagation, we use a 2D Godunov-type finite volume shallow water model. Physically-based global flood hazard simulation poses enormous computational challenges stemming from the increasingly fine resolution of available topographic data which represents the key input. Parallel computing helps to distribute the computational cost, but the computationally-intensive hydraulic model must be made far faster and agile for global-scale feasibility. Here we present a novel technique for hydraulic modeling whereby the computational grid is much coarser (e.g., 5-50 times) than the available topographic data, but the coarse grid retains the storage and conveyance (cross-sectional area) of the fine resolution data. This allows the 2D hydraulic model to be run on extremely large domains (e.g. thousands km2) with a single computational processor, and opens the door to global coverage with parallel computing. The model also downscales the coarse grid results onto the high-resolution topographic data to produce fine-scale predictions of flood depths and velocities. The model achieves computational speeds typical of very coarse grids while achieving an accuracy expected of a much finer resolution. In addition, the model has potential for assimilation of remotely sensed water elevations, to define boundary conditions based on water levels or river discharges and to improve model results. The model is applied to two river basins: the Susquehanna River in Pennsylvania, and the Ogeechee River in Florida. The two rivers represent different scales and span a wide range of topographic characteristics. Comparing spatial resolutions ranging between 30 m to 500 m in both river basins, the new technique was able to reduce simulation runtime by at least 25 fold
Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition
NASA Astrophysics Data System (ADS)
Avrutin, Viktor; Dibak, Christoph; Dal Forno, Arianna; Merlone, Ugo
In this work, we investigate the dynamics of a piecewise linear 2D discontinuous map modeling a simple network showing the Braess paradox. This paradox represents an example in which adding a new route to a specific congested transportation network makes all the travelers worse off in terms of their individual travel time. In the particular case in which the modeled network corresponds to a binary choice situation, the map is defined on two partitions and its dynamics has already been described. In the general case corresponding to a ternary choice, a third partition appears leading to significantly more complex bifurcation structures formed by border collision bifurcations of stable cycles with points located in all three partitions. Considering a map taking a constant value on one of the partitions, we provide a first systematic description of possible dynamics for this case.
An investigation of DTNS2D for use as an incompressible turbulence modelling test-bed
NASA Technical Reports Server (NTRS)
Steffen, Christopher J., Jr.
1992-01-01
This paper documents an investigation of a two dimensional, incompressible Navier-Stokes solver for use as a test-bed for turbulence modelling. DTNS2D is the code under consideration for use at the Center for Modelling of Turbulence and Transition (CMOTT). This code was created by Gorski at the David Taylor Research Center and incorporates the pseudo compressibility method. Two laminar benchmark flows are used to measure the performance and implementation of the method. The classical solution of the Blasius boundary layer is used for validating the flat plate flow, while experimental data is incorporated in the validation of backward facing step flow. Velocity profiles, convergence histories, and reattachment lengths are used to quantify these calculations. The organization and adaptability of the code are also examined in light of the role as a numerical test-bed.
NASA Astrophysics Data System (ADS)
Bezzeccheri, E.; Colasanti, S.; Falco, A.; Liguori, R.; Rubino, A.; Lugli, P.
2016-05-01
Vertical Organic Transistors and Phototransistors have been proven to be promising technologies due to the advantages of reduced channel length and larger sensitive area with respect to planar devices. Nevertheless, a real improvement of their performance is subordinate to the quantitative description of their operation mechanisms. In this work, we present a comparative study on the modeling of vertical and planar Organic Phototransistor (OPT) structures. Computer-based simulations of the devices have been carried out with Synopsys Sentaurus TCAD in a 2D Drift-Diffusion framework. The photoactive semiconductor material has been modeled using the virtual semiconductor approach as the archetypal P3HT:PC61BM bulk heterojunction. It has been found that both simulated devices have comparable electrical and optical characteristics, accordingly to recent experimental reports on the subject.
Brief Communication: 2-D numerical modeling of the transformation mechanism of a braided channel
NASA Astrophysics Data System (ADS)
Xiao, Y.; Yang, S. F.; Shao, X.; Chen, W. X.; Xu, X. M.
2014-05-01
This paper investigates the controls on the transformation mechanism among different channel patterns. A 2-D depth-averaged numerical model is applied to produce the evolution of channel patterns with complex interactions among water flow, sediment transport, and bank erosion. Changes of the variables as discharge, sediment supply, and vegetation are considered in the numerical experiments, leading to the transformation from a braided pattern into a meandering one. What controls the transformation is discussed with the numerical results: vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition; a decrease in discharge and sediment supply could lead a braided pattern to a meandering one. The conclusion is in agreement with various previous field work, confirming the two dimensional model's potential in predicting the transition between different rivers and improving understanding of patterning processes.
Saraceno, Marilena; Massarelli, Ilaria; Imbriani, Marcello; James, Thomas L; Bianucci, Anna M
2011-08-01
The cytochrome P450 isozyme CYP2D6 binds a large variety of drugs, oxidizing many of them, and plays a crucial role in establishing in vivo drug levels, especially in multidrug regimens. The current study aimed to develop reliable predictive models for estimating the CYP2D6 inhibition properties of drug candidates. Quantitative structure-activity relationship (QSAR) studies utilizing 51 known CYP2D6 inhibitors were carried out. Performance achieved using models based on two-dimensional (2D) molecular descriptors was compared with performance using models entailing additional molecular descriptors that depend upon the three-dimensional (3D) structure of ligands. To properly compute the descriptors, all the 3D inhibitor structures were optimized such that induced-fit binding of the ligand to the active site was accommodated. CODESSA software was used to obtain equations for correlating the structural features of the ligands to their pharmacological effects on CYP2D6 (inhibition). The predictive power of all the QSAR models obtained was estimated by applying rigorous statistical criteria. To assess the robustness and predictability of the models, predictions were carried out on an additional set of known molecules (prediction set). The results showed that only models incorporating 3D descriptors in addition to 2D molecular descriptors possessed the requisite high predictive power for CYP2D6 inhibition.
Preliminary results for model identification in characterizing 2-D topographic road profiles
NASA Astrophysics Data System (ADS)
Kern, Joshua V.; Ferris, John B.
2006-05-01
Load data representing severe customer usage is needed throughout a chassis development program; the majority of these chassis loads originate with the excitation from the road. These chassis loads are increasingly derived from vehicle simulations. Simulating a vehicle traversing long roads is simply impractical, however, and a greatly reduced set of characteristic roads must be found. In order to characterize a road, certain modeling assumptions must be made. Several models have been proposed making various assumptions about the properties that road profiles possess. The literature in this field is reviewed before focusing on two modeling assumptions of particular interest: the stationarity of the signal (homogeneity of the road) and the corresponding interval over which previous data points are correlated to the current data point. In this work, 2-D topographic road profiles are considered to be signals that are realizations of a stochastic process. The objective of this work is to investigate the stationarity assumption and the interval of influence for several carefully controlled sections of highway pavement in the United States. Two statistical techniques are used in analyzing these data: the autocorrelation and the partial autocorrelation. It is shown that the road profile signals in their original form are not stationary and have an extremely long interval of influence on the order of 25m. By differencing the data, however, it is often possible to generate stationary residuals and a very short interval of influence on the order of 250mm. By examining the autocorrelation and the partial autocorrelation, various versions of ARIMA models appear to be appropriate for further modeling. Implications to modeling the signals as Markov Chains are also discussed. In this way, roads can be characterized by the model architecture and the particular parameterization of the model. Any synthetic road realized from a particular model represents all profiles in this set
NASA Astrophysics Data System (ADS)
Mo, Yike; Greenhalgh, Stewart A.; Robertsson, Johan O. A.; Karaman, Hakki
2015-05-01
Lateral velocity variations and low velocity near-surface layers can produce strong scattered and guided waves which interfere with reflections and lead to severe imaging problems in seismic exploration. In order to investigate these specific problems by laboratory seismic modelling, a simple 2D ultrasonic model facility has been recently assembled within the Wave Propagation Lab at ETH Zurich. The simulated geological structures are constructed from 2 mm thick metal and plastic sheets, cut and bonded together. The experiments entail the use of a piezoelectric source driven by a pulse amplifier at ultrasonic frequencies to generate Lamb waves in the plate, which are detected by piezoelectric receivers and recorded digitally on a National Instruments recording system, under LabVIEW software control. The 2D models employed were constructed in-house in full recognition of the similitude relations. The first heterogeneous model features a flat uniform low velocity near-surface layer and deeper dipping and flat interfaces separating different materials. The second model is comparable but also incorporates two rectangular shaped inserts, one of low velocity, the other of high velocity. The third model is identical to the second other than it has an irregular low velocity surface layer of variable thickness. Reflection as well as transmission experiments (crosshole & vertical seismic profiling) were performed on each model. The two dominant Lamb waves recorded are the fundamental symmetric mode (non-dispersive) and the fundamental antisymmetric (flexural) dispersive mode, the latter normally being absent when the source transducer is located on a model edge but dominant when it is on the flat planar surface of the plate. Experimental group and phase velocity dispersion curves were determined and plotted for both modes in a uniform aluminium plate. For the reflection seismic data, various processing techniques were applied, as far as pre-stack Kirchhoff migration. The
Turbulence modeling for subsonic separated flows over 2-D airfoils and 3-D wings
NASA Astrophysics Data System (ADS)
Rosen, Aaron M.
Accurate predictions of turbulent boundary layers and flow separation through computational fluid dynamics (CFD) are becoming more and more essential for the prediction of loads in the design of aerodynamic flight components. Standard eddy viscosity models used in many commercial codes today do not capture the nonequilibrium effects seen in a separated flow and thus do not generally make accurate separation predictions. Part of the reason for this is that under nonequilibrium conditions such as a strong adverse pressure gradient, the history effects of the flow play an important role in the growth and decay of turbulence. More recent turbulence models such as Olsen and Coakley's Lag model and Lillard's lagRST model seek to simulate these effects by lagging the turbulent variables when nonequilibrium effects become important. The purpose of the current research is to assess how these nonequilibrium turbulence models capture the separated regions on various 2-D airfoils and 3-D wings. Nonequilibrium models including the Lag model and the lagRST model are evaluated in comparison with three baseline models (Spalart-Allmaras, Wilcox's k-omega, and Menter's SST) using a modified version of the OVERFLOW code. Tuning the model coefficients of the Lag and lagRST models is also explored. Results show that the various lagRST formulations display an improvement in velocity profile predictions over the standard RANS models, but have trouble capturing the edge of the boundary layer. Experimental separation location measurements were not available, but several trends are noted which may be useful to tuning the model coefficients in the future.
Mathematical Modelling in the Early School Years
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…
2D-photochemical modeling of Saturn’s stratosphere: hydrocarbon and water distributions
NASA Astrophysics Data System (ADS)
Hue, Vincent; Cavalié, Thibault; Hersant, Franck; Dobrijevic, Michel; Greathouse, Thomas; Lellouch, Emmanuel; Hartogh, Paul; Cassidy, Timothy; Spiga, Aymeric; Guerlet, Sandrine; Sylvestre, Melody
2014-11-01
Saturn’s axial tilt of 27° produces seasons in a similar way as on Earth. The seasonal forcing over Saturn’s 30 years period influences the production/loss of the major atmospheric absorbers and coolants through photochemistry, and influences therefore Saturn’s stratospheric temperatures. We have developed a 2D time-dependent photochemical model of Saturn’s atmosphere [Hue et al., in prep.], coupled to a radiative-climate model [Greathouse et al., 2008] to study seasonal effects on its atmospheric composition. Cassini spacecraft has revealed that the distribution of hydrocarbons in Saturn’s stratosphere [Guerlet et al., 2009] differs from pure photochemical predictions, i.e. without meridional transport [Moses et al., 2005]. Differences between the observed distribution of hydrocarbons and 2D-photochemical predictions are likely to be an indicator of dynamical forcing.Disentangling the origin of water in the stratosphere of this planet has been a long-term issue. Due to Saturn’s cold tropopause trap, which acts as a transport barrier, the water vapor observed by the Infrared Space Observatory (ISO) [Feuchtgruber et al., 1997] has an external origin. Three external sources have been identified: (i) permanent flux from interplanetary dust particles, (ii) local sources form planetary environments (rings, satellites), (iii) large cometary impacts, similar to Shoemaker-Levy 9 on Jupiter. Previous observations of Saturn with Herschel’s Hsso program [Hartogh et al., 2009] led to the detection of a water torus around Saturn [Hartogh et al., 2011], fed by Enceladus’ geysers. A substantial fraction of this torus is predicted to be a local source of water for Saturn’s and its satellites, as it will spread in this system [Cassidy et al., 2010]. Using the new 2D-photochemical model, we test here the validity of Enceladus’ torus as the source of Saturn’s stratospheric water.References : Hue et al., in prep. Greathouse et al., 2008. AGU Fall Meeting
The combined effect of attraction and orientation zones in 2D flocking models
NASA Astrophysics Data System (ADS)
Iliass, Tarras; Cambui, Dorilson
2016-01-01
In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed.
Coronary arteries motion modeling on 2D x-ray images
NASA Astrophysics Data System (ADS)
Gao, Yang; Sundar, Hari
2012-02-01
During interventional procedures, 3D imaging modalities like CT and MRI are not commonly used due to interference with the surgery and radiation exposure concerns. Therefore, real-time information is usually limited and building models of cardiac motion are difficult. In such case, vessel motion modeling based on 2-D angiography images become indispensable. Due to issues with existing vessel segmentation algorithms and the lack of contrast in occluded vessels, manual segmentation of certain branches is usually necessary. In addition, such occluded branches are the most important vessels during coronary interventions and obtaining motion models for these can greatly help in reducing the procedure time and radiation exposure. Segmenting different cardiac phases independently does not guarantee temporal consistency and is not efficient for occluded branches required manual segmentation. In this paper, we propose a coronary motion modeling system which extracts the coronary tree for every cardiac phase, maintaining the segmentation by tracking the coronary tree during the cardiac cycle. It is able to map every frame to the specific cardiac phase, thereby inferring the shape information of the coronary arteries using the model corresponding to its phase. Our experiments show that our motion modeling system can achieve promising results with real-time performance.
Study of Photovoltaic Cells Engineering Mathematical Model
NASA Astrophysics Data System (ADS)
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
NASA Astrophysics Data System (ADS)
Zhao, Hongbo; Engelbrecht, Jan R.
2000-03-01
At the Mean Field level (G. Murthy and R. Shankar, J. Phys. Condens. Matter, 7) (1995), the frustration due to an external field first makes the uniform BCS ground state unstable to an incommensurate (qne0) superconducting state and then to a spin-polarized Fermi Liquid state. Our interest is how fluctuations modify this picture, as well as the normal state of this system which has a quantum critical point. We use the Fluctuation-Exchange Approximation for the 2D Attractive Hubbard Model, to study this system beyond the Mean-Field level. Earlier work in zero field has shown that this numerical method successfully captures the critical scaling of the KT superconducting transition upon cooling in the normal state. Here we investigate how the pair-breaking external field modifies this picture, and the development of incommensurate pairing.
Calibration Of 2D Hydraulic Inundation Models In The Floodplain Region Of The Lower Tagus River
NASA Astrophysics Data System (ADS)
Pestanana, R.; Matias, M.; Canelas, R.; Araujo, A.; Roque, D.; Van Zeller, E.; Trigo-Teixeira, A.; Ferreira, R.; Oliveira, R.; Heleno, S.
2013-12-01
In terms of inundated area, the largest floods in Portugal occur in the Lower Tagus River. On average, the river overflows every 2.5 years, at times blocking roads and causing important agricultural damages. This paper focus on the calibration of 2D-horizontal flood simulation models for the floods of 2001 and 2006 on a 70-km stretch of the Lower Tagus River. Flood extent maps, derived from ERS SAR and ENVISAT ASAR imagery were compared with the flood extent maps obtained for each simulation, to calibrate roughness coefficients. The combination of the calibration results from the 2001 and 2006 floods provided a preliminary Manning coefficient map of the study area.
NASA Astrophysics Data System (ADS)
Albella, P.; Moreno, F.; Saiz, J. M.; González, F.
2007-07-01
An interaction model developed in previous research [de la Peña JL, González F, Saiz JM, Moreno F, Valle PJ. Sizing particles on substrates. A general method for oblique incidence. J Appl Phys 1999; 85:432] is extended to the study of two-scaled systems consisting of particles located on larger structures. Far-field scattering patterns produced by these systems can be obtained by coherent addition of different electromagnetic contributions, each one obtained from an independent isolated particle calculation. Results are performed on a 2D scheme, where they can be easily compared with those given by an exact method. This analysis shows some features of the scattering patterns that can be obtained with high reliability. Research on this kind of systems can be applied to 3D situations like particle substrate contamination and particle particle contamination.
Robust autonomous model learning from 2D and 3D data sets.
Langs, Georg; Donner, René; Peloschek, Philipp; Bischof, Horst
2007-01-01
In this paper we propose a weakly supervised learning algorithm for appearance models based on the minimum description length (MDL) principle. From a set of training images or volumes depicting examples of an anatomical structure, correspondences for a set of landmarks are established by group-wise registration. The approach does not require any annotation. In contrast to existing methods no assumptions about the topology of the data are made, and the topology can change throughout the data set. Instead of a continuous representation of the volumes or images, only sparse finite sets of interest points are used to represent the examples during optimization. This enables the algorithm to efficiently use distinctive points, and to handle texture variations robustly. In contrast to standard elasticity based deformation constraints the MDL criterion accounts for systematic deformations typical for training sets stemming from medical image data. Experimental results are reported for five different 2D and 3D data sets.
An application of the distributed hydrologic model CASC2D to a tropical montane watershed
NASA Astrophysics Data System (ADS)
Marsik, Matt; Waylen, Peter
2006-11-01
SummaryIncreased stormflow in the Quebrada Estero watershed (2.5 km 2), in the northwestern Central Valley tectonic depression of Costa Rica, reportedly has caused flooding of the city of San Ramón in recent decades. Although scientifically untested, urban expansion was deemed the cause and remedial measures were recommended by the Programa de Investigación en Desarrollo Humano Sostenible (ProDUS). CASC2D, a physically-based, spatially explicit hydrologic model, was constructed and calibrated to a June 10th 2002 storm that delivered 110.5 mm of precipitation in 4.5 h visibly exceeded the bankfull stage (0.9 m) of the Quebrada flooding portions of San Ramón. The calibrated hydrograph showed a peak discharge 16.68% (2.5 m 3 s -1) higher, an above flood stage duration 20% shorter, and time to peak discharge 11 min later than the same observed discharge hydrograph characteristics. Simulations of changing land cover conditions from 1979 to 1999 showed an increase also in the peak discharge, above flood stage duration, and time to peak discharge. Analysis using a modified location quotient identified increased urbanization in lower portions of the watershed over the time period studied. These results suggest that increased urbanization in the Quebrada Estero watershed have increased flooding peaks, and durations above threshold, confirming the ProDUS report. These results and the CASC2D model offer an easy-to-use, pragmatic planning tool for policymakers in San Ramón to assess future development scenarios and their potential flooding impacts to San Ramón.
Field Evaluation of a Novel 2D Preferential Flow Snowpack Hydrology Model
NASA Astrophysics Data System (ADS)
Leroux, N.; Pomeroy, J. W.; Kinar, N. J.
2015-12-01
Accurate estimation of snowmelt flux is of primary importance for runoff hydrograph prediction, which is used for water management and flood forecasting. Lateral flows and preferential flow pathways in porous media flow have proven critical for improving soil and groundwater flow models, but though many physically-based layered snowmelt models have been developed, only 1D matrix flow is accounted for in these models. Therefore, there is a need for snowmelt models that include these processes so as to examine the potential to improve snowmelt hydrological modelling. A 2D model is proposed that enables an improved understanding of energy and water flows within deep heterogeneous snowpacks, including those on slopes. A dual pathway theory is presented that simulates the formation of preferential flow paths, vertical and lateral water flows through the snow matrix and flow fingers, internal energy fluxes, melt, wet snow metamorphism, and internal refreezing. The dual pathway model utilizes an explicit finite volume method to solve for the energy and water flux equations over a non-orthogonal grid. It was run and evaluated using in-situ data collected from snowpit - accessed gravimetric, thermometric, photographic, and dielectric observations and novel non-invasive acoustic observations of layering, temperature, flowpath geometry, density and wetness at the Fortress Mountain Snow Laboratory, Alberta, Canada. The melt of a natural snowpack was artificially generated after detailed observation of snowpack initial conditions such as snow layer properties, temperature, and liquid water content. Snowpack ablation and liquid water content distribution over time were then measured and used for model parameterization and validation. Energy available at the snow surface and soil slope angle were set as mondel inputs. Model verification was based on snowpack property evolution. The heterogeneous flow model can be an important tool to help understand snowmelt flow processes, how
Thermochemical Nonequilibrium 2D Modeling of Nitrogen Inductively Coupled Plasma Flow
NASA Astrophysics Data System (ADS)
Yu, Minghao; Yusuke, Takahashi; Hisashi, Kihara; Ken-ichi, Abe; Kazuhiko, Yamada; Takashi, Abe; Satoshi, Miyatani
2015-09-01
Two-dimensional (2D) numerical simulations of thermochemical nonequilibrium inductively coupled plasma (ICP) flows inside a 10-kW inductively coupled plasma wind tunnel (ICPWT) were carried out with nitrogen as the working gas. Compressible axisymmetric Navier-Stokes (N-S) equations coupled with magnetic vector potential equations were solved. A four-temperature model including an improved electron-vibration relaxation time was used to model the internal energy exchange between electron and heavy particles. The third-order accuracy electron transport properties (3rd AETP) were applied to the simulations. A hybrid chemical kinetic model was adopted to model the chemical nonequilibrium process. The flow characteristics such as thermal nonequilibrium, inductive discharge, effects of Lorentz force were made clear through the present study. It was clarified that the thermal nonequilibrium model played an important role in properly predicting the temperature field. The prediction accuracy can be improved by applying the 3rd AETP to the simulation for this ICPWT. supported by Grant-in-Aid for Scientific Research (No. 23560954), sponsored by the Japan Society for the Promotion of Science
Spin Circuit Model for 2D Channels with Spin-Orbit Coupling.
Hong, Seokmin; Sayed, Shehrin; Datta, Supriyo
2016-03-02
In this paper we present a general theory for an arbitrary 2D channel with "spin momentum locking" due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, -). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U-, and D-. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green's function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.
Establishing an Explanatory Model for Mathematics Identity.
Cribbs, Jennifer D; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M
2015-04-01
This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence in mathematics directly impact their identity as a "math person," findings indicate that students' self-perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students' interest and external recognition in mathematics. Thus, the model indicates that students' competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition.
NASA Astrophysics Data System (ADS)
Wörz, Stefan; Heinzer, Stephan; Weiss, Matthias; Rohr, Karl
2008-03-01
We introduce a model-based approach for segmenting and quantifying GFP-tagged subcellular structures of the Golgi apparatus in 2D and 3D microscopy images. The approach is based on 2D and 3D intensity models, which are directly fitted to an image within 2D circular or 3D spherical regions-of-interest (ROIs). We also propose automatic approaches for the detection of candidates, for the initialization of the model parameters, and for adapting the size of the ROI used for model fitting. Based on the fitting results, we determine statistical information about the spatial distribution and the total amount of intensity (fluorescence) of the subcellular structures. We demonstrate the applicability of our new approach based on 2D and 3D microscopy images.
A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds
Li, Tingwen; Zhang, Yongmin
2013-10-11
Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve the 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.
Mathematical Modeling and Simulation of Seated Stability
Tanaka, Martin L.; Ross, Shane D.; Nussbaum, Maury A.
2009-01-01
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications. PMID:20018288
Mathematical Modeling of Chemical Stoichiometry
ERIC Educational Resources Information Center
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
ERIC Educational Resources Information Center
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Mathematical Model Development and Simulation Support
NASA Technical Reports Server (NTRS)
Francis, Ronald C.; Tobbe, Patrick A.
2000-01-01
This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.
Cooking Potatoes: Experimentation and Mathematical Modeling.
ERIC Educational Resources Information Center
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
ERIC Educational Resources Information Center
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Transectional heat transfer in thermoregulating bigeye tuna (Thunnus obesus) - a 2D heat flux model.
Boye, Jess; Musyl, Michael; Brill, Richard; Malte, Hans
2009-11-01
We developed a 2D heat flux model to elucidate routes and rates of heat transfer within bigeye tuna Thunnus obesus Lowe 1839 in both steady-state and time-dependent settings. In modeling the former situation, we adjusted the efficiencies of heat conservation in the red and the white muscle so as to make the output of the model agree as closely as possible with observed cross-sectional isotherms. In modeling the latter situation, we applied the heat exchanger efficiencies from the steady-state model to predict the distribution of temperature and heat fluxes in bigeye tuna during their extensive daily vertical excursions. The simulations yielded a close match to the data recorded in free-swimming fish and strongly point to the importance of the heat-producing and heat-conserving properties of the white muscle. The best correspondence between model output and observed data was obtained when the countercurrent heat exchangers in the blood flow pathways to the red and white muscle retained 99% and 96% (respectively) of the heat produced in these tissues. Our model confirms that the ability of bigeye tuna to maintain elevated muscle temperatures during their extensive daily vertical movements depends on their ability to rapidly modulate heating and cooling rates. This study shows that the differential cooling and heating rates could be fully accounted for by a mechanism where blood flow to the swimming muscles is either exclusively through the heat exchangers or completely shunted around them, depending on the ambient temperature relative to the body temperature. Our results therefore strongly suggest that such a mechanism is involved in the extensive physiological thermoregulatory abilities of endothermic bigeye tuna.
Wuebbles, D.J.; Connell, P.S.; Grant, K.E.; Tarp, R.; Taylor, K.E.
1987-09-01
Significant progress has been made at LLNL in the development of a zonally averaged (two-dimensional) chemical-radiative-transport model of the troposphere and stratosphere. Although further model development and refinement is being planned the LLNL 2-D model is currently ready to be applied to appropriately designed research studies of stratospheric chemical processes and interactions. Several such studies are now underway. This paper provides a description of the existing 2-D model and discusses some of the pertinent results for evaluating the capabilities of the model. Special attempts at improving the timing of the model are also discussed. 6 figs.
Simulation of abrasive flow machining process for 2D and 3D mixture models
NASA Astrophysics Data System (ADS)
Dash, Rupalika; Maity, Kalipada
2015-12-01
Improvement of surface finish and material removal has been quite a challenge in a finishing operation such as abrasive flow machining (AFM). Factors that affect the surface finish and material removal are media viscosity, extrusion pressure, piston velocity, and particle size in abrasive flow machining process. Performing experiments for all the parameters and accurately obtaining an optimized parameter in a short time are difficult to accomplish because the operation requires a precise finish. Computational fluid dynamics (CFD) simulation was employed to accurately determine optimum parameters. In the current work, a 2D model was designed, and the flow analysis, force calculation, and material removal prediction were performed and compared with the available experimental data. Another 3D model for a swaging die finishing using AFM was simulated at different viscosities of the media to study the effects on the controlling parameters. A CFD simulation was performed by using commercially available ANSYS FLUENT. Two phases were considered for the flow analysis, and multiphase mixture model was taken into account. The fluid was considered to be a
Model-guided respiratory organ motion prediction of the liver from 2D ultrasound.
Preiswerk, Frank; De Luca, Valeria; Arnold, Patrik; Celicanin, Zarko; Petrusca, Lorena; Tanner, Christine; Bieri, Oliver; Salomir, Rares; Cattin, Philippe C
2014-07-01
With the availability of new and more accurate tumour treatment modalities such as high-intensity focused ultrasound or proton therapy, accurate target location prediction has become a key issue. Various approaches for diverse application scenarios have been proposed over the last decade. Whereas external surrogate markers such as a breathing belt work to some extent, knowledge about the internal motion of the organs inherently provides more accurate results. In this paper, we combine a population-based statistical motion model and information from 2d ultrasound sequences in order to predict the respiratory motion of the right liver lobe. For this, the motion model is fitted to a 3d exhalation breath-hold scan of the liver acquired before prediction. Anatomical landmarks tracked in the ultrasound images together with the model are then used to reconstruct the complete organ position over time. The prediction is both spatial and temporal, can be computed in real-time and is evaluated on ground truth over long time scales (5.5 min). The method is quantitatively validated on eight volunteers where the ultrasound images are synchronously acquired with 4D-MRI, which provides ground-truth motion. With an average spatial prediction accuracy of 2.4 mm, we can predict tumour locations within clinically acceptable margins.
Field-induced magnetization jumps and quantum criticality in the 2D J-Q model
NASA Astrophysics Data System (ADS)
Iaizzi, Adam; Sandvik, Anders
The J-Q model is a `designer hamiltonian' formed by adding a four spin `Q' term to the standard antiferromagnetic S = 1 / 2 Heisenberg model. The Q term drives a quantum phase transition to a valence-bond solid (VBS) state: a non-magnetic state with a pattern of local singlets which breaks lattice symmetries. The elementary excitations of the VBS are triplons, i.e. gapped S=1 quasiparticles. There is considerable interest in the quantum phase transition between the Néel and VBS states as an example of deconfined quantum criticality. Near the phase boundary, triplons deconfine into pairs of bosonic spin-1/2 excitations known as spinons. Using exact diagonalization and the stochastic series expansion quantum monte carlo method, we study the 2D J-Q model in the presence of an external magnetic field. We use the field to force a nonzero density of magnetic excitations at T=0 and look for signatures of Bose-Einstein condensation of spinons. At higher magnetic fields, there is a jump in the induced magnetization caused by the onset of an effective attractive interaction between magnons on a ferromagnetic background. We characterize the first order quantum phase transition and determine the minimum value of the coupling ratio q ≡ Q / J required to produce this jump. Funded by NSF DMR-1410126.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Automatic mathematical modeling for space application
NASA Technical Reports Server (NTRS)
Wang, Caroline K.
1987-01-01
A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.
2D dynamical magma propagation modeling: application to the 2001 Mount Etna eruption
NASA Astrophysics Data System (ADS)
Pinel, Virginie; Carrara, Alexandre; Maccaferri, Francesco; Rivalta, Eleonora; Corbi, Fabio
2016-04-01
Numerical and analog studies of dike propagation in a stress field induced by volcanic edifice construction have shown that surface loading tends both to attract the magma and to reduce its velocity. Available numerical models can either calculate the trajectory or the velocity of the ascending dikes, but not both of them simultaneously. We developed a hybrid model of dyke propagation in two dimensions solving both for the magma trajectory and velocity as a function of the source overpressure, the magma physical properties (density and viscosity) as well as the crustal density and stress field. We first calculate a dyke trajectory in 2D and secondly run a 1D dynamical model of dyke propagation along this trajectory taken into account the influence of the stress field seen by the magma along this path. This model is used to characterize the influence of surface load on magma migration towards the surface and compared to previous results obtained by analog modeling.We find that the amplitude of dyke deflection and magma velocity variation depend on the ratio between the dyke driving pressure (source overpressure as well buoyancy) and the stress field perturbation. Our model is then applied to the July 2001 eruption of Etna, where the final dyke deflection had been previously interpreted as due to the topographic load by Bonaccorso et al. [2010]. We show that the velocity decrease observed during the last stage of the propagation can also be attributed to the local stress field. We use the dyke propagation duration to estimate the magma overpressure at the dyke bottom to be less than 4 MPa.
Govind Rajan, Ananth; Warner, Jamie H; Blankschtein, Daniel; Strano, Michael S
2016-04-26
Transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS2) and tungsten disulfide (WS2) are layered materials capable of growth to one monolayer thickness via chemical vapor deposition (CVD). Such CVD methods, while powerful, are notoriously difficult to extend across different reactor types and conditions, with subtle variations often confounding reproducibility, particularly for 2D TMD growth. In this work, we formulate the first generalized TMD synthetic theory by constructing a thermodynamic and kinetic growth mechanism linked to CVD reactor parameters that is predictive of specific geometric shape, size, and aspect ratio from triangular to hexagonal growth, depending on specific CVD reactor conditions. We validate our model using experimental data from Wang et al. (Chem. Mater. 2014, 26, 6371-6379) that demonstrate the systemic evolution of MoS2 morphology down the length of a flow CVD reactor where variations in gas phase concentrations can be accurately estimated using a transport model (CSulfur = 9-965 μmol/m(3); CMoO3 = 15-16 mmol/m(3)) under otherwise isothermal conditions (700 °C). A stochastic model which utilizes a site-dependent activation energy barrier based on the intrinsic TMD bond energies and a series of Evans-Polanyi relations leads to remarkable, quantitative agreement with both shape and size evolution along the reactor. The model is shown to extend to the growth of WS2 at 800 °C and MoS2 under varied process conditions. Finally, a simplified theory is developed to translate the model into a "kinetic phase diagram" of the growth process. The predictive capability of this model and its extension to other TMD systems promise to significantly increase the controlled synthesis of such materials.
2D application of a friction-limited model for debris flow propagation
NASA Astrophysics Data System (ADS)
Jaboyedoff, M.; Demierre, J.; Rudaz, B.
2012-04-01
Debris flows are each year responsible of severe infrastructure damages and human losses. Accurate simulation of this phenomenon allows for prevention of risks related to such events and can help for a sustainable territorial planning. A simple and intuitive 2-D debris flow model is developed using MatLab. It is based on the coupling of a mass point motion along the slope and the flattening of a volume linked to this mass point. Three main parameters have to be tuned in order to obtain a realistic prediction: the basal friction angle, the flattening coefficient and the debris flow maximum velocity. The model enables to simulate the location of the debris as a function of time and thus predict an important parameter of debris flow events, the runout distance. This tool allows for rapid calculations and has the advantage to use parameters that are easily assessable, such as the thickness of the debris flow deposit. The model is applied and compared to a debris flow event that occurred in Switzerland (Fully, VS) in October 2000. Following heavy rainfall and a hydroelectric pipe failure, a morainic deposit failed and propagated as a debris flow, reaching human-occupied areas (vineyards and roads). The event is well documented, with the initiation point, the flow velocity and runout distance known. A good agreement is found between the model prediction and the data from the debris flow event described above. This shows that the developed simple model can be an efficient tool to predict important debris flow characteristics, such as the runout distance. A further development would be to implement a 3-D model based on this approach
Modelling Mathematical Reasoning in Physics Education
NASA Astrophysics Data System (ADS)
Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-04-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
Mathematical Modeling of Circadian and Homeostatic Interaction
2011-11-16
REM ) sleep , and non- REM ( NREM ) sleep states. Using this mathematical modeling framework, the Pis conducted modeling studies on several...The model network exhibits realistic polyphasic sleep -wake behavior consisting of wake, rapid eye movement ( REM ) sleep , and non- REM ( NREM ) sleep ...states. In addition, the model captures stereotypical sleep patterning including cycling between NREM and REM sleep . Using this
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
NASA Astrophysics Data System (ADS)
Aricò, C.; Sinagra, M.; Begnudelli, L.; Tucciarelli, T.
2011-11-01
A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains the Delaunay condition for all the triangle sides without changing the original nodes location and also maintains the internal boundaries. The original governing system is solved applying a fractional time step procedure, that solves consecutively a convective prediction system and a diffusive correction system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system of the order of the number of computational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discretized formulation of the governing equations allows to handle also wetting and drying processes without any additional specific treatment. Local energy dissipations, mainly the effect of vertical walls and hydraulic jumps, can be easily included in the model. Several numerical experiments have been carried out in order to test (1) the stability of the proposed model with regard to the size of the Courant number and to the mesh irregularity, (2) its computational performance, (3) the convergence order by means of mesh refinement. The model results are also compared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented.
2D spectral element modeling of GPR wave propagation in inhomogeneous media
NASA Astrophysics Data System (ADS)
Zarei, Sajad; Oskooi, Behrooz; Amini, Navid; Dalkhani, Amin Rahimi
2016-10-01
We present a spectral element method, for simulation of ground-penetrating radar (GPR) in two dimensions. The technique is based upon a weak formulation of the equations of Maxwell and combines the flexibility of the elemental-based methods with the accuracy of the spectral based methods. The wave field on the elements is discretized using high-degree Lagrange interpolation and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. As a result, the mass matrix and the damping matrix are always diagonal, which drastically reduces the computational cost. We first develop the formulation of 2D spectral element method (SEM) in the time-domain based on Maxwell's equations. The presented formulation is with matrix notation that simplifies the implementation of the relations in computer programs, especially in MATLAB application. We discuss the differences between spectral element method and finite-element method in the time-domain. Also, we show that the SEM numerical dispersion is much lower than FEM. To absorb waves at the edges of the modeling domain, we implement first order Clayton and Engquist absorbing boundary conditions (CE-ABC) introduced in numerical finite-difference modeling of seismic wave propagation. We used the SEM to simulate a complex model to show its abilities and limitations. As well as, one distinct advantage of SEM is that we can easily define our model features in nodal points, because the integration points and the interpolation points are similar that makes it very flexible in simulation of complex models.
A friction to flow constitutive law and its application to a 2-D modeling of earthquakes
NASA Astrophysics Data System (ADS)
Shimamoto, Toshihiko; Noda, Hiroyuki
2014-11-01
Establishment of a constitutive law from friction to high-temperature plastic flow has long been a challenging task for solving problems such as modeling earthquakes and plate interactions. Here we propose an empirical constitutive law that describes this transitional behavior using only friction and flow parameters, with good agreements with experimental data on halite shear zones. The law predicts steady state and transient behaviors, including the dependence of the shear resistance of fault on slip rate, effective normal stress, and temperature. It also predicts a change in velocity weakening to velocity strengthening with increasing temperature, similar to the changes recognized for quartz and granite gouge under hydrothermal conditions. A slight deviation from the steady state friction law due to the involvement of plastic deformation can cause a large change in the velocity dependence. We solved seismic cycles of a fault across the lithosphere with the law using a 2-D spectral boundary integral equation method, revealing dynamic rupture extending into the aseismic zone and rich evolution of interseismic creep including slow slip prior to earthquakes. Seismic slip followed by creep is consistent with natural pseudotachylytes overprinted with mylonitic deformation. Overall fault behaviors during earthquake cycles are insensitive to transient flow parameters. The friction-to-flow law merges "Christmas tree" strength profiles of the lithosphere and rate dependency fault models used for earthquake modeling on a unified basis. Strength profiles were drawn assuming a strain rate for the flow regime, but we emphasize that stress distribution evolves reflecting the fault behavior. A fault zone model was updated based on the earthquake modeling.
2D positive streamer modelling in NTP air under extreme pulse fronts. What about runaway electrons?
NASA Astrophysics Data System (ADS)
Marode, E.; Dessante, Ph; Tardiveau, P.
2016-12-01
Using a 2D model, an attempt is made to understand the properties and aspects of a diffuse discharge, appearing in a positive point-to-plane gap submitted to very high voltage pulses. After presenting the model, comparisons between the computed low and high pulse heights of 10 kV and 50 kV, respectively, will be shown and analysed. A streamer ionising wave is still formed, but its role in ionising a region of low field is replaced by the role of providing a plasma within which the electrons will benefit from the presence of a high electrical field meant to induce strong electron collision activities. A comparison between the aspect of the computed and experimental discharge carried out in the same conditions at 50 kV will be presented, which seems to be in agreement with the diffuse aspect. Although the difference in order of magnitude of the speed of development and the height of the current must be underlined, similarities between the structures of both situations will, however, be recognised. A high probability of obtaining highly energetic electrons and runaways (RAEs) will also be derived following a simple approach.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
NASA Astrophysics Data System (ADS)
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-08-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
Beyond Flood Hazard Maps: Detailed Flood Characterization with Remote Sensing, GIS and 2d Modelling
NASA Astrophysics Data System (ADS)
Santillan, J. R.; Marqueso, J. T.; Makinano-Santillan, M.; Serviano, J. L.
2016-09-01
Flooding is considered to be one of the most destructive among many natural disasters such that understanding floods and assessing the risks associated to it are becoming more important nowadays. In the Philippines, Remote Sensing (RS) and Geographic Information System (GIS) are two main technologies used in the nationwide modelling and mapping of flood hazards. Although the currently available high resolution flood hazard maps have become very valuable, their use for flood preparedness and mitigation can be maximized by enhancing the layers of information these maps portrays. In this paper, we present an approach based on RS, GIS and two-dimensional (2D) flood modelling to generate new flood layers (in addition to the usual flood depths and hazard layers) that are also very useful in flood disaster management such as flood arrival times, flood velocities, flood duration, flood recession times, and the percentage within a given flood event period a particular location is inundated. The availability of these new layers of flood information are crucial for better decision making before, during, and after occurrence of a flood disaster. The generation of these new flood characteristic layers is illustrated using the Cabadbaran River Basin in Mindanao, Philippines as case study area. It is envisioned that these detailed maps can be considered as additional inputs in flood disaster risk reduction and management in the Philippines.
A 2D mechanical-magneto-thermal model for direction-dependent magnetoelectric effect in laminates
NASA Astrophysics Data System (ADS)
Zhang, Shunzu; Yao, Hong; Gao, Yuanwen
2017-04-01
A two dimensional (2D) mechanical-magneto-thermal model of direction-dependent magnetoelectric (ME) effect in Terfenol-D/PZT/Terfenol-D laminated composites is established. The expressions of ME coefficient at low and resonance frequencies are derived by the average field method, respectively. The prediction of theoretical model presents a good agreement with the experimental data. The combined effect of orientation-dependent stress and magnetic fields, as well as operating temperature on ME coefficient is discussed. It is shown that ME effect presents a significantly nonlinear change with the increasing pre-stress under different loading angles. There exists an optimal angle and value of pre-stress corresponding to the best ME effect, improving the angle of pre-stress can get more prominent ME coupling than in x axis state. Note that an optimal angle of magnetic field gradually increases with the rise of pre-stress, which can further lead to the enhancement of ME coefficient. Meanwhile, reducing the operating temperature can enhance ME coefficient. Furthermore, resonance frequency, affected by pre-stress, magnetic field and temperature via ; ΔE effect;, can enhance ME coefficient about 100 times than that at low frequency.
2D stochastic-integral models for characterizing random grain noise in titanium alloys
Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Cherry, Matthew; Pilchak, Adam; Knopp, Jeremy S.; Blodgett, Mark P.
2014-02-18
We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the 'clumping' of crystallites into long chains that appear during the processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loève (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conductivity tensor of the metal. We study two possible covariances, Gaussian and double-exponential, which are the kernel of the K-L integral equation, and find that the double-exponential appears to satisfy measurements more closely of the two. Results based on data from a Ti-7Al sample will be given, and further applications of HDMR and ANOVA will be discussed.
The success of Fermi gas model for overall scaling of 2D metal-to-insulator transition data
NASA Astrophysics Data System (ADS)
Cheremisin, M. V.
2017-03-01
The melting condition for two-dimensional Wigner solid (Platzman and Fukuyama, 1974) [14] is shown to contain an error of a factor of π. The analysis of experimental data for apparent 2D metal-to-insulator transition shows that the Wigner solidification (Tanatar and Ceperley, 1989) [16] has been never achieved. Within routine Fermi gas model both the metallic and insulating behavior of different 2D system for actual range of carrier densities and temperatures is explained.
Robust initialization for 2D/3D registration of knee implant models to single-plane fluoroscopy
NASA Astrophysics Data System (ADS)
Hermans, J.; Claes, P.; Bellemans, J.; Vandermeulen, D.; Suetens, P.
2007-03-01
A fully automated initialization method is proposed for the 2D/3D registration of 3D CAD models of knee implant components to a single-plane calibrated fluoroscopy. The algorithm matches edge segments, detected in the fluoroscopy image, with pre-computed libraries of expected 2D silhouettes of the implant components. Each library entry represents a different combination of out-of-plane registration transformation parameters. Library matching is performed by computing point-based 2D/2D registrations in between each library entry and each detected edge segment in the fluoroscopy image, resulting in an estimate of the in-plane registration transformation parameters. Point correspondences for registration are established by template matching of the bending patterns on the contours. A matching score for each individual 2D/2D registration is computed by evaluating the transformed library entry in an edge-encoded (characteristic) image, which is derived from the original fluoroscopy image. A matching scores accumulator is introduced to select and suggest one or more initial pose estimates. The proposed method is robust against occlusions and partial segmentations. Validation results are shown on simulated fluoroscopy images. In all cases a library match is found for each implant component which is very similar to the shape information in the fluoroscopy. The feasibility of the proposed method is demonstrated by initializing an intensity-based 2D/3D registration method with the automatically obtained estimation of the registration transformation parameters.
ERIC Educational Resources Information Center
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
ERIC Educational Resources Information Center
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
ERIC Educational Resources Information Center
Zbiek, Rose Mary; Conner, Annamarie
2006-01-01
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
Hydraulic Modeling of Alluvial Fans along the Truckee Canal using the 2-Dimensional Model SRH2D
NASA Astrophysics Data System (ADS)
Wright, J.; Kallio, R.; Sankovich, V.
2013-12-01
Alluvial fans are gently sloping, fan-shaped landforms created by sediment deposition at the ends of mountain valleys. Their gentle slopes and scenic vistas are attractive to developers. Unfortunately, alluvial fans are highly flood-prone, and the flow paths of flood events are highly variable, thereby placing human developments at risk. Many studies have been performed on alluvial fans in the arid west because of the uncertainty of their flow paths and flood extents. Most of these studies have been focused on flood elevations and mitigation. This study is not focused on the flood elevations. Rather, it is focused on the attenuation effects of alluvial fans on floods entering and potentially failing a Reclamation canal. The Truckee Canal diverts water from the Truckee River to Lahontan Reservoir. The drainage areas along the canal are alluvial fans with complex distributary channel networks . Ideally, in nature, the sediment grain-size distribution along the alluvial fan flow paths would provide enough infiltration and subsurface storage to attenuate floods entering the canal and reduce risk to low levels. Human development, however, can prevent the natural losses from occurring due to concentrated flows within the alluvial fan. While the concentrated flows might mitigate flood risk inside the fan, they do not lower the flood risk of the canal. A 2-dimensional hydraulic model, SRH-2D, was coupled to a 1-dimensional rainfall-runoff model to estimate the flood attenuation effects of the alluvial fan network surrounding an 11 mile stretch of the Truckee Canal near Fernley, Nevada. Floods having annual exceedance probabilities ranging from 1/10 to 1/100 were computed and analyzed. SRH-2D uses a zonal approach for modeling river systems, allowing areas to be divided into separate zones based on physical parameters such as surface roughness and infiltration. One of the major features of SRH-2D is the adoption of an unstructured hybrid mixed element mesh, which is based
Mathematical biodynamic feedthrough model applied to rotorcraft.
Venrooij, Joost; Mulder, Mark; Abbink, David A; van Paassen, Marinus M; Mulder, Max; van der Helm, Frans C T; Bulthoff, Heinrich H
2014-07-01
Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model.
Lithospheric architecture of the Levant Basin (Eastern Mediterranean region): A 2D modeling approach
NASA Astrophysics Data System (ADS)
Inati, Lama; Zeyen, Hermann; Nader, Fadi Henri; Adelinet, Mathilde; Sursock, Alexandre; Rahhal, Muhsin Elie; Roure, François
2016-12-01
This paper discusses the deep structure of the lithosphere underlying the easternmost Mediterranean region, in particular the Levant Basin and its margins, where the nature of the crust, continental versus oceanic, remains debated. Crustal thickness and the depth of the lithosphere-asthenosphere boundary (LAB) as well as the crustal density distribution were calculated by integrating surface heat flow data, free-air gravity anomaly, geoid and topography. Accordingly, two-dimensional, lithospheric models of the study area are discussed, demonstrating the presence of a progressively attenuated crystalline crust from E to W (average thickness from 35 to 8 km). The crystalline crust is best interpreted as a strongly thinned continental crust under the Levant Basin, represented by two distinct components, an upper and a lower crust. Further to the west, the Herodotus Basin is believed to be underlain by an oceanic crust, with a thickness between 6 and 10 km. The Moho under the Arabian Plate is 35-40 km deep and becomes shallower towards the Mediterranean coast. It appears to be situated at depths ranging between 20 and 23 km below the Levant Basin and 26 km beneath the Herodotus Basin, based on our proposed models. At the Levantine margin, the thinning of the crust in the transitional domain between the onshore and the offshore is gradual, indicating successive extensional regimes that did not reach the beak up stage. In addition, the depth to LAB is around 120 km under the Arabian and the Eurasian Plates, 150 km under the Levant Basin, and it plunges to 180 km under the Herodotus Basin. This study shows that detailed 2D lithosphere modeling using integrated geophysical data can help understand the mechanisms responsible for the modelled lithospheric architecture when constrained with geological findings.
Adaptation of a 2-D Photochemical Model to Improve Our Understanding of Saturn's Atmosphere
NASA Astrophysics Data System (ADS)
Edgington, Scott G.; Simon-Miller, A. A.; Achterberg, R.; Bjoraker, G.; Romani, P.; Flasar, F. M.; Colwell, J.
2006-09-01
We report progress in adapting a two dimensional photochemical model to Saturn. Previously, this model was applied to Jupiter (Edgington, et al., 2001) to track tracers such as ammonia in the Jovian troposphere. The chemistry portion of this model has the ability to model ammonia, phosphine, and hydrocarbon photochemical families (Edgington, et al., 1999). The transport portion is based on the transport model used to model the evolution of materials deposited by Comet Shoemaker-Levy 9 (Friedson, et al., 1999). The model is used to look at the variation of several molecules in Saturn's atmosphere accounting for the filtering of ultraviolet photons by Saturn's rings as measured by Cassini/UVIS and the thermal structure observed by Cassini/CIRS. We compare results from this model to the abundances of several molecules, e.g. propane (Simon-Miller, et al., 2005) and phosphine, derived from Cassini/CIRS, HST/FOS, and ISO data sets. Composition differences between the northern ring-shadowed atmophere and the nominal sunlit atmosphere will be examined. More research into Saturn's zonal averaged meridional circulation is needed. Edgington, S.G., et al., 1999. Ammonia and eddy mixing variations in the southern hemisphere of Jupiter from HST Faint Object Spectrograph Observations. Icarus, 142, 342-357. Edgington, S.G., West, R.A., Friedson, A.J., and Atreya, S.K., 2001. A 2-D photochemical model with meridional circulation and microphysics. Jupiter: Planet, Satellites, and Magnetosphere - Boulder, CO, June 25-30. Friedson, A.J.; West, R.A.; Hronek, A.K.; Larsen, N.A.; and Dalal, N., 1999. Transport and Mixing in Jupiter's Stratosphere Inferred from Comet S-L9 Dust Migration. Icarus, 138, 141-156. Simon-Miller, A.A., et al., 2005. Cassini CIRS Measurements of Benzene, Propane and Carbon Dioxide on Saturn. B.A.A.S. 37, 682. The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the
2D Biotope Mapping Using Combined LIDAR, Topographic Survey And Segmented 1D Flow Modelling
NASA Astrophysics Data System (ADS)
Entwistle, N. S.; Heritage, G. L.; Milan, D. J.
2009-12-01
Reach averaged habitat availability models such as PHABSIM are limited due principally to their failure to adequately map hydraulic habitat distribution at a representative scale. A lack of morphologic data, represented in the form of sparse geometric cross-sections fails to generate the necessary detail. Advances in data collection, improved spatial modelling algorithms and the advent of cross-section based segmentation routines in 1D hydraulic models provides the opportunity to revisit the issue of hydraulic habitat mapping and modelling. This paper presents a combined technique for habitat characterisation at the sub-bar scale is presented for the River Rede, Northumberland, UK. Terrestrial LIDAR data of floodplain, banks and exposed bar surfaces at an average 0.05 m spacing are combined with sparser total station survey data of submerged morphologic features. These data are interpolated to create a uniform DEM grid at 0.2 m spacing (adequate to detect the smallest variation in hydraulic habitat in this system). The data grid were then imported into the HECRAS 1D hydraulic model to generate a 2 m spaced series of cross-sections along a 220 m sinuous single thread reach exhibiting pool - riffle point-bar morphology. The hydraulic segmentation routine then generated estimates of depth averaged flow velocity, flow depth and sub unit discharge for 40 sub-divisions of the flow width for a series of flows from 0.5 m3s-1 up to bankfull flow of approximately 9 m3s-1. The resultant hydraulic data were exported in the project coordinate system and plotted to reveal the 2D pattern of hydraulic biotopes present across the range of flows modelled. The results reveal broadly realistic patterns consistent with previous empirical studies and compare well with LIDAR based biotope maps. Analysis of the temporal pattern of biotope change indicates that biotope diversity and complexity is at a maximum at lower flows and across shallower area (riffles) and that these dominate the
NASA Astrophysics Data System (ADS)
Fan, Cui-Ying; Zhao, Ming-Hao; Zhou, You-He
2009-09-01
The polarization saturation (PS) model [Gao, H., Barnett, D.M., 1996. An invariance property of local energy release rates in a strip saturation model of piezoelectric fracture. Int. J. Fract. 79, R25-R29; Gao, H., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491-510], and the dielectric breakdown (DB) model [Zhang, T.Y., Zhao, M.H., Cao, C.F., 2005. The strip dielectric breakdown model. Int. J. Fract. 132, 311-327] explain very well some experimental observations of fracture of piezoelectric ceramics. In this paper, the nonlinear hybrid extended displacement discontinuity-fundamental solution method (NLHEDD-FSM) is presented for numerical analysis of both the PS and DB models of two-dimensional (2D) finite piezoelectric media under impermeable and semi-permeable electric boundary conditions. In this NLHEDD-FSM, the solution is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack and the electric yielding zone. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy certain conditions on the boundary of the domain, on the crack face and the electric yielding zone. The zero electric displacement intensity factor in the PS model or the zero electric field strength intensity factor in the DB model at the outer tips of the electric yielding zone is used as a supplementary condition to determine the size of the electric yielding zone. Iteration approaches are adopted in the NLHEDD-FSM. The electric yielding zone is determined, and the extended intensity factors and the local J-integral are calculated for
Electrical resistivity tomography applied to a complex lava dome: 2D and 3D models comparison
NASA Astrophysics Data System (ADS)
Portal, Angélie; Fargier, Yannick; Lénat, Jean-François; Labazuy, Philippe
2015-04-01
The study of volcanic domes growth (e.g. St. Helens, Unzen, Montserrat) shows that it is often characterized by a succession of extrusion phases, dome explosions and collapse events. Lava dome eruptive activity may last from days to decades. Therefore, their internal structure, at the end of the eruption, is complex and includes massive extrusions and lava lobes, talus and pyroclastic deposits as well as hydrothermal alteration. The electrical resistivity tomography (ERT) method, initially developed for environmental and engineering exploration, is now commonly used for volcano structure imaging. Because a large range of resistivity values is often observed in volcanic environments, the method is well suited to study the internal structure of volcanic edifices. We performed an ERT survey on an 11ka years old trachytic lava dome, the Puy de Dôme volcano (French Massif Central). The analysis of a recent high resolution DEM (LiDAR 0.5 m), as well as other geophysical data, strongly suggest that the Puy de Dôme is a composite dome. 11 ERT profiles have been carried out, both at the scale of the entire dome (base diameter of ~2 km and height of 400 m) on the one hand, and at a smaller scale on the summit part on the other hand. Each profile is composed of 64 electrodes. Three different electrode spacing have been used depending on the study area (35 m for the entire dome, 10 m and 5 m for its summit part). Some profiles were performed with half-length roll-along acquisitions, in order to keep a good trade-off between depth of investigation and resolution. Both Wenner-alpha and Wenner-Schlumberger protocols were used. 2-D models of the electrical resistivity distribution were computed using RES2DINV software. In order to constrain inversion models interpretation, the depth of investigation (DOI) method was applied to those results. It aims to compute a sensitivity index on inversion results, illustrating how the data influence the model and constraining models
Mathematical Modelling with 9-Year-Olds
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…
Modelling 2001 lahars at Popocatépetl volcano using FLO2D numerical code
NASA Astrophysics Data System (ADS)
Caballero, L.; Capra, L.
2013-12-01
Popocatépetl volcano is located on the central part of the Transmexican Volcanic Belt. It is one of the most active volcanoes in Mexico and endanger more than 25 million people that lives in its surroundings. In the last months, the renewal of its volcanic activity put into alert scientific community. One of the possible scenarios is the 2001 explosive activity, which was characterized by a 8 km eruptive column and the subsequent formation of pumice flows up to 4 km from the crater. Lahars were generated few hours after, remobilizing the new deposits towards NE flank of the volcano, along Huiloac Gorge, almost reaching Santiago Xalitzintla town (Capra et al., 2004). The occurrence of a similar scenario makes very important to reproduce this event to delimitate accurately lahar hazard zones. In this work, 2001 lahar deposit is modeled using FLO2D numerical code. Geophone data is used to reconstruct initial hydrograph and sediment concentration. Sensitivity study of most important parameters used by this code like Manning, and α and β coefficients was conducted in order to achieve a good simulation. Results obtained were compared with field data and demonstrated a good agreement in thickness and flow distribution. A comparison with previously published data with laharZ program (Muñoz-Salinas, 2009) is also made. Additionally, lahars with fluctuating sediment concentrations but with similar volume are simulated to observe the influence of the rheological behavior on lahar distribution.
Krali, Emiljana; Curry, Richard J
2011-04-26
To improve the efficiency of organic photovoltaic devices the inclusion of semiconducting nanoparticles such as PbS has been used to enhance near-infrared absorption. Additionally the use of interdigitated heterojunctions has been explored as a means of improving charge extraction. In this paper we provide a two-dimensional model taking into account these approaches with the aim of predicting an optimized device geometry to maximize the efficiency. The steady-state exciton population has been calculated in each of the active regions taking into account the full optical response based on using a finite difference approach to obtain approximate numerical solutions to the 2D exciton diffusion equation. On the basis of this we calculate the contribution of each active material to the device short circuit current and power conversion efficiency. We show that optimized structures can lead to power conversions efficiencies of ∼50% compared to a maximum of ∼17% for planar heterojunction devices. To achieve this the interdigitated region thickness should be ∼800 nm with PbS and C(60) widths of ∼60 and 20 nm, respectively. Even modest nanopatterning using much thinner active regions provides improvements in efficiency and may be approached using a variety of methods including nanoimprinting lithography, nanotemplating, or the incorporation of presynthesized nanorod structures.
Spot size variation FCS in simulations of the 2D Ising model.
Burns, Margaret C; Nouri, Mariam; Veatch, Sarah L
2016-06-02
Spot variation fluorescence correlation spectroscopy (svFCS) was developed to study the movement and organization of single molecules in plasma membranes. This experimental technique varies the size of an illumination area while measuring correlations in time using standard fluorescence correlation methods. Frequently, this data is interpreted using the assumption that correlation measurements reflect the dynamics of single molecule motions, and not motions of the average composition. Here, we explore how svFCS measurements report on the dynamics of components diffusing within simulations of a 2D Ising model with a conserved order parameter. Simulated correlation functions report on both the fast dynamics of single component mobility and the slower dynamics of the average composition. Over a range of simulation conditions, a conventional svFCS analysis suggests the presence of anomalous diffusion even though single molecule motions are nearly Brownian in these simulations. This misinterpretation is most significant when the surface density of the fluorescent label is elevated, therefore we suggest future measurements be made over a range of tracer densities. Some simulation conditions reproduce qualitative features of published svFCS experimental data. Overall, this work emphasizes the need to probe membranes using multiple complimentary experimental methodologies in order to draw conclusions regarding the nature of spatial and dynamical heterogeneity in these systems.
Stability of superfluid phases in the 2D spin-polarized attractive Hubbard model
NASA Astrophysics Data System (ADS)
Kujawa-Cichy, A.; Micnas, R.
2011-08-01
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LPs) with increasing attraction, in the presence of the Zeeman magnetic field (h) for d=2, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation as well as the strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin-independent hopping integrals (t↑=t↓), we find no stable homogeneous polarized superfluid (SCM) state in the ground state for the strong attraction and obtain that for a two-component Fermi system on a 2D lattice with population imbalance, phase separation (PS) is favoured for a fixed particle concentration, even on the LP (BEC) side. We also examine the influence of spin-dependent hopping integrals (mass imbalance) on the stability of the SCM phase. We find a topological quantum phase transition (Lifshitz type) from the unpolarized superfluid phase (SC0) to SCM and tricritical points in the h-|U| and t↑/t↓-|U| ground-state phase diagrams. We also construct the finite temperature phase diagrams for both t↑=t↓ and t↑≠t↓ and analyze the possibility of occurrence of a spin-polarized KT superfluid.
Modeling of two-storey precast school building using Ruaumoko 2D program
Hamid, N. H.; Tarmizi, L. H.; Ghani, K. D.
2015-05-15
The long-distant earthquake loading from Sumatra and Java Island had caused some slight damages to precast and reinforced concrete buildings in West Malaysia such as cracks on wall panels, columns and beams. Subsequently, the safety of existing precast concrete building is needed to be analyzed because these buildings were designed using BS 8110 which did not include the seismic loading in the design. Thus, this paper emphasizes on the seismic performance and dynamic behavior of precast school building constructed in Malaysia under three selected past earthquakes excitations ; El Centro 1940 North-South, El Centro East-West components and San Fernando 1971 using RUAUMOKO 2D program. This program is fully utilized by using prototype precast school model and dynamic non-linear time history analysis. From the results, it can be concluded that two-storey precast school building has experienced severe damage and partial collapse especially at beam-column joint under San Fernando and El Centro North-South Earthquake as its exceeds the allowable inter-storey drift and displacement as specified in Eurocode 8. The San Fernando earthquake has produced a massive destruction to the precast building under viscous damping, ξ = 5% and this building has generated maximum building displacement of 435mm, maximum building drift of 0.68% and maximum bending moment at 8458kNm.
Modeling of two-storey precast school building using Ruaumoko 2D program
NASA Astrophysics Data System (ADS)
Hamid, N. H.; Tarmizi, L. H.; Ghani, K. D.
2015-05-01
The long-distant earthquake loading from Sumatra and Java Island had caused some slight damages to precast and reinforced concrete buildings in West Malaysia such as cracks on wall panels, columns and beams. Subsequently, the safety of existing precast concrete building is needed to be analyzed because these buildings were designed using BS 8110 which did not include the seismic loading in the design. Thus, this paper emphasizes on the seismic performance and dynamic behavior of precast school building constructed in Malaysia under three selected past earthquakes excitations ; El Centro 1940 North-South, El Centro East-West components and San Fernando 1971 using RUAUMOKO 2D program. This program is fully utilized by using prototype precast school model and dynamic non-linear time history analysis. From the results, it can be concluded that two-storey precast school building has experienced severe damage and partial collapse especially at beam-column joint under San Fernando and El Centro North-South Earthquake as its exceeds the allowable inter-storey drift and displacement as specified in Eurocode 8. The San Fernando earthquake has produced a massive destruction to the precast building under viscous damping, ξ = 5% and this building has generated maximum building displacement of 435mm, maximum building drift of 0.68% and maximum bending moment at 8458kNm.
The specific edge effects of 2D core/shell model for spin-crossover nanoparticles
NASA Astrophysics Data System (ADS)
Muraoka, Azusa; Boukheddaden, Kamel; Linarès, Jorge; Varret, Francois
2012-02-01
We analyzed the size effect of spin-crossover nanoparticles at the edges of the 2D square lattices core/shell model, where the edge atoms are constrained to the high spin (HS) state. We performed MC simulations using the Ising-like Hamiltonian, [ H=-J∑(i,j)∑l i'=±1; j'=±1 S( i,j )S( i+i',j+j' ) +( δ2-kBT2g )∑(i,j)S( i,j ) ] The molar entropy change is δS 50J/K/mol, lng=δS/R 6 (R is the perfect gas constant), energy gap is δ=1300K. The HS fixed edges were based on the observation of an increasing residual HS fraction at low temperature upon particle size reduction. This specific boundary condition acts as a negative pressure which shifts downwards the equilibrium temperature. The interplay between the equilibrium temperature (=δ/kBlng) variation and the expected variation of the effective interactions in the system leads to a non-monotonous dependence of the hysteresis loop width upon the particle size. We described how the occurrence condition of the first-order transition has to be adapted to the nanoscale.
1D and 2D urban dam-break flood modelling in Istanbul, Turkey
NASA Astrophysics Data System (ADS)
Ozdemir, Hasan; Neal, Jeffrey; Bates, Paul; Döker, Fatih
2014-05-01
Urban flood events are increasing in frequency and severity as a consequence of several factors such as reduced infiltration capacities due to continued watershed development, increased construction in flood prone areas due to population growth, the possible amplification of rainfall intensity due to climate change, sea level rise which threatens coastal development, and poorly engineered flood control infrastructure (Gallegos et al., 2009). These factors will contribute to increased urban flood risk in the future, and as a result improved modelling of urban flooding according to different causative factor has been identified as a research priority (Gallegos et al., 2009; Ozdemir et al. 2013). The flooding disaster caused by dam failures is always a threat against lives and properties especially in urban environments. Therefore, the prediction of dynamics of dam-break flows plays a vital role in the forecast and evaluation of flooding disasters, and is of long-standing interest for researchers. Flooding occurred on the Ayamama River (Istanbul-Turkey) due to high intensity rainfall and dam-breaching of Ata Pond in 9th September 2009. The settlements, industrial areas and transportation system on the floodplain of the Ayamama River were inundated. Therefore, 32 people were dead and millions of Euros economic loses were occurred. The aim of this study is 1 and 2-Dimensional flood modelling of the Ata Pond breaching using HEC-RAS and LISFLOOD-Roe models and comparison of the model results using the real flood extent. The HEC-RAS model solves the full 1-D Saint Venant equations for unsteady open channel flow whereas LISFLOOD-Roe is the 2-D shallow water model which calculates the flow according to the complete Saint Venant formulation (Villanueva and Wright, 2006; Neal et al., 2011). The model consists a shock capturing Godunov-type scheme based on the Roe Riemann solver (Roe, 1981). 3 m high resolution Digital Surface Model (DSM), natural characteristics of the pond
Advancing Nucleosynthesis in Core-Collapse Supernovae Models Using 2D CHIMERA Simulations
NASA Astrophysics Data System (ADS)
Harris, J. A.; Hix, W. R.; Chertkow, M. A.; Bruenn, S. W.; Lentz, E. J.; Messer, O. B.; Mezzacappa, A.; Blondin, J. M.; Marronetti, P.; Yakunin, K.
2014-01-01
The deaths of massive stars as core-collapse supernovae (CCSN) serve as a crucial link in understanding galactic chemical evolution since the birth of the universe via the Big Bang. We investigate CCSN in polar axisymmetric simulations using the multidimensional radiation hydrodynamics code CHIMERA. Computational costs have traditionally constrained the evolution of the nuclear composition in CCSN models to, at best, a 14-species α-network. However, the limited capacity of the α-network to accurately evolve detailed composition, the neutronization and the nuclear energy generation rate has fettered the ability of prior CCSN simulations to accurately reproduce the chemical abundances and energy distributions as known from observations. These deficits can be partially ameliorated by "post-processing" with a more realistic network. Lagrangian tracer particles placed throughout the star record the temporal evolution of the initial simulation and enable the extension of the nuclear network evolution by incorporating larger systems in post-processing nucleosynthesis calculations. We present post-processing results of the four ab initio axisymmetric CCSN 2D models of Bruenn et al. (2013) evolved with the smaller α-network, and initiated from stellar metallicity, non-rotating progenitors of mass 12, 15, 20, and 25 M⊙ from Woosley & Heger (2007). As a test of the limitations of post-processing, we provide preliminary results from an ongoing simulation of the 15 M⊙ model evolved with a realistic 150 species nuclear reaction network in situ. With more accurate energy generation rates and an improved determination of the thermodynamic trajectories of the tracer particles, we can better unravel the complicated multidimensional "mass-cut" in CCSN simulations and probe for less energetically significant nuclear processes like the νp-process and the r-process, which require still larger networks.
Approaches to Modeling Coupled Flow and Reaction in a 2-D Cementation Experiment
Steefel, Carl; Cochepin, B.; Trotignon, L.; Bildstein, O.; Steefel, C.; Lagneau, V.; van der Lee, J.
2008-04-01
Porosity evolution at reactive interfaces is a key process that governs the evolution and performances of many engineered systems that have important applications in earth and environmental sciences. This is the case, for example, at the interface between cement structures and clays in deep geological nuclear waste disposals. Although in a different transport regime, similar questions arise for permeable reactive barriers used for biogeochemical remediation in surface environments. The COMEDIE project aims at investigating the coupling between transport, hydrodynamics and chemistry when significant variations of porosity occur. The present work focuses on a numerical benchmark used as a design exercise for the future COMEDIE-2D experiment. The use of reactive transport simulation tools like Hytec and Crunch provides predictions of the physico-chemical evolutions that are expected during the future experiments in laboratory. Focus is given in this paper on the evolution during the simulated experiment of precipitate, permeability and porosity fields. A first case is considered in which the porosity is constant. Results obtained with Crunch and Hytec are in relatively good agreement. Differences are attributable to the models of reactive surface area taken into account for dissolution/precipitation processes. Crunch and Hytec simulations taking into account porosity variations are then presented and compared. Results given by the two codes are in qualitative agreement, with differences attributable in part to the models of reactive surface area for dissolution/precipitation processes. As a consequence, the localization of secondary precipitates predicted by Crunch leads to lower local porosities than for predictions obtained by Hytec and thus to a stronger coupling between flow and chemistry. This benchmark highlights the importance of the surface area model employed to describe systems in which strong porosity variations occur as a result of dissolution
D Recording for 2d Delivering - the Employment of 3d Models for Studies and Analyses -
NASA Astrophysics Data System (ADS)
Rizzi, A.; Baratti, G.; Jiménez, B.; Girardi, S.; Remondino, F.
2011-09-01
In the last years, thanks to the advances of surveying sensors and techniques, many heritage sites could be accurately replicated in digital form with very detailed and impressive results. The actual limits are mainly related to hardware capabilities, computation time and low performance of personal computer. Often, the produced models are not visible on a normal computer and the only solution to easily visualized them is offline using rendered videos. This kind of 3D representations is useful for digital conservation, divulgation purposes or virtual tourism where people can visit places otherwise closed for preservation or security reasons. But many more potentialities and possible applications are available using a 3D model. The problem is the ability to handle 3D data as without adequate knowledge this information is reduced to standard 2D data. This article presents some surveying and 3D modeling experiences within the APSAT project ("Ambiente e Paesaggi dei Siti d'Altura Trentini", i.e. Environment and Landscapes of Upland Sites in Trentino). APSAT is a multidisciplinary project funded by the Autonomous Province of Trento (Italy) with the aim documenting, surveying, studying, analysing and preserving mountainous and hill-top heritage sites located in the region. The project focuses on theoretical, methodological and technological aspects of the archaeological investigation of mountain landscape, considered as the product of sequences of settlements, parcelling-outs, communication networks, resources, and symbolic places. The mountain environment preserves better than others the traces of hunting and gathering, breeding, agricultural, metallurgical, symbolic activities characterised by different lengths and environmental impacts, from Prehistory to the Modern Period. Therefore the correct surveying and documentation of this heritage sites and material is very important. Within the project, the 3DOM unit of FBK is delivering all the surveying and 3D material to
NASA Astrophysics Data System (ADS)
Jung, J.; Arakawa, A.
2015-12-01
Through explicitly resolved cloud-scale processes by embedded 2-D cloud-resolving models (CRMs), the Multiscale Modeling Framework (MMF) known as the superparameterization has been reasonably successful to simulate various atmospheric events over a wide range of time scales. One thing to be justified is, however, if the influence of complex 3-D topography can be adequately represented by the embedded 2-D CRMs. In this study, simulations are performed in the presence of a variety of topography with embedded 3-D and 2-D CRMs in a single-column inactive GCM. Through the comparison between these simulations, it is demonstrated that the 2-D representation of topography is able to simulate the statistics of precipitation due to 3-D topography reasonably well as long as the topographic characteristics, such as the mean and standard deviation, are closely recognized. It is also shown that the use of two perpendicular sets of 2-D representations tends to reduce the error due to a 2-D representation.
Weinger, Jason G; Plaisted, Warren C; Maciejewski, Sonia M; Lanier, Lewis L; Walsh, Craig M; Lane, Thomas E
2014-10-01
Transplantation of major histocompatibility complex-mismatched mouse neural precursor cells (NPCs) into mice persistently infected with the neurotropic JHM strain of mouse hepatitis virus (JHMV) results in rapid rejection that is mediated, in part, by T cells. However, the contribution of the innate immune response to allograft rejection in a model of viral-induced neurological disease has not been well defined. Herein, we demonstrate that the natural killer (NK) cell-expressing-activating receptor NKG2D participates in transplanted allogeneic NPC rejection in mice persistently infected with JHMV. Cultured NPCs derived from C57BL/6 (H-2(b) ) mice express the NKG2D ligand retinoic acid early precursor transcript (RAE)-1 but expression was dramatically reduced upon differentiation into either glia or neurons. RAE-1(+) NPCs were susceptible to NK cell-mediated killing whereas RAE-1(-) cells were resistant to lysis. Transplantation of C57BL/6-derived NPCs into JHMV-infected BALB/c (H-2(d) ) mice resulted in infiltration of NKG2D(+) CD49b(+) NK cells and treatment with blocking antibody specific for NKG2D increased survival of allogeneic NPCs. Furthermore, transplantation of differentiated RAE-1(-) allogeneic NPCs into JHMV-infected BALB/c mice resulted in enhanced survival, highlighting a role for the NKG2D/RAE-1 signaling axis in allograft rejection. We also demonstrate that transplantation of allogeneic NPCs into JHMV-infected mice resulted in infection of the transplanted cells suggesting that these cells may be targets for infection. Viral infection of cultured cells increased RAE-1 expression, resulting in enhanced NK cell-mediated killing through NKG2D recognition. Collectively, these results show that in a viral-induced demyelination model, NK cells contribute to rejection of allogeneic NPCs through an NKG2D signaling pathway.
Pool Formation in Boulder-Bed Streams: Implications From 1-D and 2-D Numerical Modeling
NASA Astrophysics Data System (ADS)
Harrison, L. R.; Keller, E. A.
2003-12-01
In mountain rivers of Southern California, boulder-large roughness elements strongly influence flow hydraulics and pool formation and maintenance. In these systems, boulders appear to control the stream morphology by converging flow and producing deep pools during channel forming discharges. Our research goal is to develop quantitative relationships between boulder roughness elements, temporal patterns of scour and fill, and geomorphic processes that are important in producing pool habitat. The longitudinal distribution of shear stress, unit stream power and velocity were estimated along a 48 m reach on Rattlesnake Creek, using the HEC-RAS v 3.0 and River 2-D numerical models. The reach has an average slope of 0.02 and consists of a pool-riffle sequence with a large boulder constriction directly above the pool. Model runs were performed for a range of stream discharges to test if scour and fill thresholds for pool and riffle environments could be identified. Results from the HEC-RAS simulations identified that thresholds in shear stress, unit stream power and mean velocity occur above a discharge of 5.0 cms. Results from the one-dimensional analysis suggest that the reversal in competency is likely due to changes in cross-sectional width at varying flows. River 2-D predictions indicated that strong transverse velocity gradients were present through the pool at higher modeled discharges. At a flow of 0.5 cms (roughly 1/10th bankfull discharge), velocities are estimated at 0.6 m/s and 1.3 m/s for the pool and riffle, respectively. During discharges of 5.15 cms (approximate bankfull discharge), the maximum velocity in the pool center increased to nearly 3.0 m/s, while the maximum velocity over the riffle is estimated at approximately 2.5 cms. These results are consistent with those predicted by HEC-RAS, though the reversal appears to be limited to a narrow jet that occurs through the pool head and pool center. Model predictions suggest that the velocity reversal is
On craton thinning/destruction: Insight from 2D thermal-mechanical numerical modeling
NASA Astrophysics Data System (ADS)
Liao, J.
2014-12-01
Although most cratons maintain stable, some exceptions are present, such as the North China craton, North Atlantic craton, and Wyoming craton, which have experienced dramatic lithospheric deformation/thinning. Mechanisms triggering cratonic thinning remains enigmatic [Lee et al., 2011]. Using a 2D thermo-mechanical coupled numerical model [Gerya and Yuen, 2007], we investigate two possible mechanisms: (1) stratification of cratonic lithospheric mantle, and (2) rheological weakening due to hydration.Lithospheric mantle stratification is a common feature in cratonic areas which has been demonstrated by geophysical and geochemical studies [Thybo and Perchuc, 1997; Griffin et al., 2004; Romanowicz, 2009; Rychert and Shearer, 2009; Yuan and Romanowicz, 2010]. The influence of lithospheric mantle stratification during craton evolution remains poorly understood. A rheologically weak layer representing hydrated and/or metasomatized composition is implemented in the lithospheric mantle. Our results show that the weak mantle layer changes the dynamics of lithospheric extension by enhancing the deformation of the overlying mantle and crust and inhibiting deformation of the underlying mantle [Liao et al., 2013; Liao and Gerya, 2014]. Modeling results are compared with North China and North Atlantic cratons. Our work indicates that although the presence of a weak layer may not be sufficient to initiate craton deformation, it enhances deformation by lowering the required extensional plate boundary force. Rheological weakening due to hydration is a possible mechanism triggering/enhancing craton deformation, especially for cratons jaxtaposing with a subduction, since water can release from a subducting slab. We investigate the influence of wet mantle flow laws [Hirth and Kohlstedt, 2003], in which a water parameter (i.e. constant water content) is involved. Our results show that wet dislocation alone does not accelerate cratonic deformation significantly. However, if wet diffusion
Dynamical Models of SAURON and CALIFA Galaxies: 1D and 2D Rotational Curves
NASA Astrophysics Data System (ADS)
Kalinova, Veselina; van de Ven, G.; Lyubenova, M.; Falcon-Barroso, J.; van den Bosch, R.
2013-01-01
The mass of a galaxy is the most important parameter to understand its structure and evolution. The total mass we can infer by constructing dynamical models that fit the motion of the stars and gas in the galaxy. The dark matter content then follows after subtracting the luminous matter inferred from colors and/or spectra. Here, we present the mass distribution of a sample of 18 late-type spiral (Sb-Sd) galaxies, using two-dimensional stellar kinematics obtained with the integral-field spectrograph SAURON. The observed second order velocity moments of these galaxies are fitted with solutions of the Axisymmetric Jeans equations and give us an accurate estimation of the mass-to-light ratio profiles and rotational curves. The rotation curves of the galaxies are obtained by the Asymmetric Drift Correction (ADC) and Multi-Gaussian Expansion (MGE) methods, corresponding to one- and two-dimensional mass distribution. Their comparison shows that the mass distribution based on the 2D stellar kinematics is much more reliable than 1D one. SAURON integral field of view looks at the inner parts of the galaxies in contrast with CALIFA survey. CALIFA survey provides PMAS/PPAK integral-field spectroscopic data of ~ 600 nearby galaxies as part of the Calar Alto Legacy Integral Field Area. We show the first CALIFA dynamical models of different morphological type of galaxies, giving the clue about the mass distribution of galaxies through the whole Hubble sequence and their evolution from the blue cloud to the red sequence.
Facial Sketch Synthesis Using 2D Direct Combined Model-Based Face-Specific Markov Network.
Tu, Ching-Ting; Chan, Yu-Hsien; Chen, Yi-Chung
2016-08-01
A facial sketch synthesis system is proposed, featuring a 2D direct combined model (2DDCM)-based face-specific Markov network. In contrast to the existing facial sketch synthesis systems, the proposed scheme aims to synthesize sketches, which reproduce the unique drawing style of a particular artist, where this drawing style is learned from a data set consisting of a large number of image/sketch pairwise training samples. The synthesis system comprises three modules, namely, a global module, a local module, and an enhancement module. The global module applies a 2DDCM approach to synthesize the global facial geometry and texture of the input image. The detailed texture is then added to the synthesized sketch in a local patch-based manner using a parametric 2DDCM model and a non-parametric Markov random field (MRF) network. Notably, the MRF approach gives the synthesized results an appearance more consistent with the drawing style of the training samples, while the 2DDCM approach enables the synthesis of outcomes with a more derivative style. As a result, the similarity between the synthesized sketches and the input images is greatly improved. Finally, a post-processing operation is performed to enhance the shadowed regions of the synthesized image by adding strong lines or curves to emphasize the lighting conditions. The experimental results confirm that the synthesized facial images are in good qualitative and quantitative agreement with the input images as well as the ground-truth sketches provided by the same artist. The representing power of the proposed framework is demonstrated by synthesizing facial sketches from input images with a wide variety of facial poses, lighting conditions, and races even when such images are not included in the training data set. Moreover, the practical applicability of the proposed framework is demonstrated by means of automatic facial recognition tests.
NASA Astrophysics Data System (ADS)
Gvozdik, L.; Polak, M.; Zaruba, J.; Vanecek, M.
2010-12-01
A geological environment labeled as a Granite massif represents in terms of groundwater flow and transport a distinct hydrogeological environment from that of sedimentary basins, the characterisation of which is generally more complex and uncertain. Massifs are composed of hard crystalline rocks with the very low effective porosity. Due to their rheological properties such rocks are predisposed to brittle deformation resulting from changes in stress conditions. Our specific research project (Research on the influence of intergrangular porosity on deep geological disposal: geological formations, methodology and the development of measurement apparatus) is focussed on the problem of permeable zones within apparently undisturbed granitic rock matrix. The project including the both laboratory and in-situ tracer tests study migration along and through mineral grains in fresh and altered granite. The objective of the project is to assess whether intergranular porosity is a general characteristic of the granitic rock matrix or subject to significant evolution resulting from geochemical and/or hydrogeochemical processes, geotechnical and/or mechanical processes. Moreover, the research is focussed on evaluating methods quantifying intergranular porosity by both physical testing and mathematical modelling using verified standard hydrological software tools. Groundwater flow in microfractures and intergranular pores in granite rock matrix were simulated in three standard hydrogeological modeling programs with completely different conceptual approaches: MODFLOW (Equivalent Continuum concept), FEFLOW (Discrete Fracture and Equivalent Continuum concepts) and NAPSAC (Discrete Fracture Network concept). Specialized random fracture generators were used for creation of several 2D and 3D models in each of the chosen program. Percolation characteristics of these models were tested and analyzed. Several scenarios of laboratory tests of the rock samples permeability made in triaxial
Nutter, C.
1981-04-01
MAG2D is an interactive computer program used for modeling 2-1/2-dimensional magnetic data. A forward algorithm is used to give the theoretical attraction of magnetic intensity at a station due to a perturbing body given by the initial model. The resultant model can then be adjusted for a better fit by a combination of manual adjustment, one-dimensional automatic search, and Marquardt inversion. MAG2D has an interactive data management system for data manipulation and display built around subroutines to do a forward problem, a one-dimensional direct search and an inversion. These subroutines were originally separate batch-mode programs.
Mathematical Models of Tuberculosis Reactivation and Relapse
Wallis, Robert S.
2016-01-01
The natural history of human infection with Mycobacterium tuberculosis (Mtb) is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic. PMID:27242697
ERIC Educational Resources Information Center
Ciltas, Alper; Isik, Ahmet
2013-01-01
The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…
NASA Astrophysics Data System (ADS)
Croissant, Thomas; Lague, Dimitri; Davy, Philippe; Steer, Philippe
2016-04-01
In active mountain ranges, large earthquakes (Mw > 5-6) trigger numerous landslides that impact river dynamics. These landslides bring local and sudden sediment piles that will be eroded and transported along the river network causing downstream changes in river geometry, transport capacity and erosion efficiency. The progressive removal of landslide materials has implications for downstream hazards management and also for understanding landscape dynamics at the timescale of the seismic cycle. The export time of landslide-derived sediments after large-magnitude earthquakes has been studied from suspended load measurements but a full understanding of the total process, including the coupling between sediment transfer and channel geometry change, still remains an issue. Note that the transport of small sediment pulses has been studied in the context of river restoration, but the magnitude of sediment pulses generated by landslides may make the problem different. Here, we study the export of large volumes (>106 m3) of sediments with the 2D hydro-morphodynamic model, Eros. This model uses a new hydrodynamic module that resolves a reduced form of the Saint-Venant equations with a particle method. It is coupled with a sediment transport and lateral and vertical erosion model. Eros accounts for the complex retroactions between sediment transport and fluvial geometry, with a stochastic description of the floods experienced by the river. Moreover, it is able to reproduce several features deemed necessary to study the evacuation of large sediment pulses, such as river regime modification (single-thread to multi-thread), river avulsion and aggradation, floods and bank erosion. Using a synthetic and simple topography we first present how granulometry, landslide volume and geometry, channel slope and flood frequency influence 1) the dominance of pulse advection vs. diffusion during its evacuation, 2) the pulse export time and 3) the remaining volume of sediment in the catchment
Building a 2.5D Digital Elevation Model from 2D Imagery
NASA Technical Reports Server (NTRS)
Padgett, Curtis W.; Ansar, Adnan I.; Brennan, Shane; Cheng, Yang; Clouse, Daniel S.; Almeida, Eduardo
2013-01-01
When projecting imagery into a georeferenced coordinate frame, one needs to have some model of the geographical region that is being projected to. This model can sometimes be a simple geometrical curve, such as an ellipse or even a plane. However, to obtain accurate projections, one needs to have a more sophisticated model that encodes the undulations in the terrain including things like mountains, valleys, and even manmade structures. The product that is often used for this purpose is a Digital Elevation Model (DEM). The technology presented here generates a high-quality DEM from a collection of 2D images taken from multiple viewpoints, plus pose data for each of the images and a camera model for the sensor. The technology assumes that the images are all of the same region of the environment. The pose data for each image is used as an initial estimate of the geometric relationship between the images, but the pose data is often noisy and not of sufficient quality to build a high-quality DEM. Therefore, the source imagery is passed through a feature-tracking algorithm and multi-plane-homography algorithm, which refine the geometric transforms between images. The images and their refined poses are then passed to a stereo algorithm, which generates dense 3D data for each image in the sequence. The 3D data from each image is then placed into a consistent coordinate frame and passed to a routine that divides the coordinate frame into a number of cells. The 3D points that fall into each cell are collected, and basic statistics are applied to determine the elevation of that cell. The result of this step is a DEM that is in an arbitrary coordinate frame. This DEM is then filtered and smoothed in order to remove small artifacts. The final step in the algorithm is to take the initial DEM and rotate and translate it to be in the world coordinate frame [such as UTM (Universal Transverse Mercator), MGRS (Military Grid Reference System), or geodetic] such that it can be saved in
A mathematical model of a cloud
NASA Astrophysics Data System (ADS)
Wang, A. P.
1980-07-01
The model under consideration is a pencil of radiation incident on a cloud, and the problem is to determine the reflection and transmitted radiation. Based on the method of 'principle of invariance', three mathematical models are constructed. The first is the basic model, which describes the radiation system completely. The second is the flux integral model, in which the integral average intensity is considered. The third is the diffusion model, which gives the most important information about the diffused radiation field.
Mathematical Modeling in Continuum Mechanics
NASA Astrophysics Data System (ADS)
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
About a mathematical model of market
NASA Astrophysics Data System (ADS)
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Comprehensive Mathematical Model Of Real Fluids
NASA Technical Reports Server (NTRS)
Anderson, Peter G.
1996-01-01
Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.
Mathematical model for predicting human vertebral fracture
NASA Technical Reports Server (NTRS)
Benedict, J. V.
1973-01-01
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.
Mathematical Model For Scattering From Mirrors
NASA Technical Reports Server (NTRS)
Wang, Yaujen
1988-01-01
Additional terms account for effects of particulate contamination. Semiempirical mathematical model of scattering of light from surface of mirror gives improved account of effects of particulate contamination. Models that treated only scattering by microscopic irregularities in surface gave bidirectional reflectance distribution functions differing from measured scattering intensities over some ranges of angles.
2D condensation model for the inner Solar Nebula: an enstatite-rich environment
NASA Astrophysics Data System (ADS)
Pignatale, F. C.; Liffman, Kurt; Maddison, Sarah T.; Brooks, Geoffrey
2016-04-01
Infrared observations provide the dust composition in the protoplanetary discs surface layers, but cannot probe the dust chemistry in the mid-plane, where planet formation occurs. Meteorites show that dynamics was important in determining the dust distribution in the Solar Nebula and needs to be considered if we are to understand the global chemistry in discs. 1D radial condensation sequences can only simulate one disc layer at a time and cannot describe the global chemistry or the complexity of meteorites. To address these limitations, we compute for the first time the 2D distribution of condensates in the inner Solar Nebula using a thermodynamic equilibrium model, and derive time-scales for vertical settling and radial migration of dust. We find two enstatite-rich zones within 1 AU from the young Sun: a band ˜0.1 AU thick in the upper optically-thin layer of the disc interior to 0.8 AU, and in the optically-thick disc mid-plane out to ˜0.4 AU. The two enstatite-rich zones support recent evidence that Mercury and enstatite chondrites (ECs) shared a bulk material with similar composition. Our results are also consistent with infrared observation of protoplanetary disc which show emission of enstatite-rich dust in the inner surface of discs. The resulting chemistry and dynamics suggests that the formation of the bulk material of ECs occurred in the inner surface layer of the disc, within 0.4 AU. We also propose a simple alternative scenario in which gas fractionation and vertical settling of the condensates lead to an enstatite-chondritic bulk material.
Mathematical modeling relevant to closed artificial ecosystems
DeAngelis, D.L.
2003-01-01
The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.
Mathematical modeling relevant to closed artificial ecosystems.
DeAngelis, Donald L
2003-01-01
The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space.
Mathematical Modeling of Flow Through Vegetated Regions
2013-08-01
including stem population density and flow Reynolds number. These results are compared to well-respected experimental results. We model real- life beds of...We model real- life beds of Spartina alterniflora grass with represen- tative beds of flexible beams and perform similar comparisons. x 13 Table of...and pressure contours ( right ) for instanta- neous snapshots of flows of various Reynolds numbers in 2D porous media domain with circle diameter 0.25 m
Finite-size effects for anisotropic 2D Ising model with various boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh
2012-12-01
We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
A MODIFIED LIGHT TRANSMISSION VISUALIZATION METHOD FOR DNAPL SATURATION MEASUREMENTS IN 2-D MODELS
In this research, a light transmission visualization (LTV) method was used to quantify dense non-aqueous phase liquids (DNAPL) saturation in two-dimensional (2-D), two fluid phase systems. The method is an expansion of earlier LTV methods and takes into account both absorption an...
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
ERIC Educational Resources Information Center
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
The 2005 Vazcun Valley Lahar: Evaluation of the TITAN2D Two-Phase Flow Model Using an Actual Event.
NASA Astrophysics Data System (ADS)
Williams, R.; Stinton, A. J.; Sheridan, M. F.
2005-12-01
TITAN2D is a depth-averaged, thin-layer computational fluid dynamics (CFD) code, suitable for simulating a variety of geophysical mass flows. TITAN2D output data include pile thickness and flow momentum at each time step for all cells traversed by the flow during the simulation. From this the flow limit, run-out path, pile velocity, deposit thickness, and travel time can be calculated. Results can be visualized in the open source GRASS GIS software or with the built-in TITAN2D viewer. A new two-phase TITAN2D version allows simulation of flows containing various mixtures of water and solids. The purpose of this study is to compare simulations by the two-phase flow version of TITAN2D with an actual event. The chosen natural flow is a small ash-rich lahar (volume approximately 60,000 m3) that occurred on 12 February 2005 in the Vazcún Valley, located on the north-east flank of Volcán Tungurahua, Ecuador. Lahars and pyroclastic flows along this valley could potentially threaten the 20,000 inhabitants living in and near the city of Baños. A variety of data sources exist for this lahar, including: pre- and post-event meter-scale topography, and photographic, video, seismic and acoustic flow monitoring (AFM) records from during the event. These data permit detailed comparisons between the dynamics of the actual lahar and those of the TITAN2D simulated flow. In particular, detailed comparisons are made between run-up heights, flow velocity, inundation area, and deposit area and thickness. Simulations utilize a variety of data derived from field observations such as lahar volume, solid to pore-fluid ratio and pre-event topography. TITAN2D is important in modeling lahars because it allows assessment of the impact of the flows on buildings and infrastructure lifelines located near drainages that descend from volcanoes.
The (Mathematical) Modeling Process in Biosciences.
Torres, Nestor V; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.
The (Mathematical) Modeling Process in Biosciences
Torres, Nestor V.; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063
Liu, Wu; Ma, Xiangyu; Yan, Huagang; Chen, Zhe; Nath, Ravinder; Li, Haiyun
2017-03-06
Many real-time imaging techniques have been developed to localize the target in 3D space or in 2D beam's eye view (BEV) plane for intrafraction motion tracking in radiation therapy. With tracking system latency, 3D-modeled method is expected to be more accurate even in terms of 2D BEV tracking error. No quantitative analysis, however, has been reported. In this study, we simulated co-planar arc deliveries using respiratory motion data acquired from 42 patients to quantitatively compare the accuracy between 2D BEV and 3D-modeled tracking in arc therapy and determine whether 3D information is needed for motion tracking. We used our previously developed low kV dose adaptive MV-kV imaging and motion compensation framework as a representative of 3D-modeled methods. It optimizes the balance between additional kV imaging dose and 3D tracking accuracy and solves the MLC blockage issue. With simulated Gaussian marker detection errors (zero mean and 0.39 mm standard deviation) and ~155/310/460 ms tracking system latencies, the mean percentage of time that the target moved >2 mm from the predicted 2D BEV position are 1.1%/4.0%/7.8% and 1.3%/5.8%/11.6% for 3D-modeled and 2D-only tracking, respectively. The corresponding average BEV RMS errors are 0.67/0.90/1.13 mm and 0.79/1.10/1.37 mm. Compared to the 2D method, the 3D method reduced the average RMS unresolved motion along the beam direction from ~3 mm to ~1 mm, resulting on average only <1% dosimetric advantage in the depth direction. Only for a small fraction of the patients, when tracking latency is long, the 3D-modeled method showed significant improvement of BEV tracking accuracy, indicating potential dosimetric advantage. However, if the tracking latency is short (~150 ms or less), those improvements are limited. Therefore, 2D BEV tracking has sufficient targeting accuracy for most clinical cases. The 3D technique is, however, still important in solving the MLC blockage problem during 2D BEV tracking.
Mathematical and Computational Modeling of Polymer Exchange Membrane Fuel Cells
NASA Astrophysics Data System (ADS)
Ulusoy, Sehribani
In this thesis a comprehensive review of fuel cell modeling has been given and based on the review, a general mathematical fuel cell model has been developed in order to understand the physical phenomena governing the fuel cell behavior and in order to contribute to the efforts investigating the optimum performance at different operating conditions as well as with different physical parameters. The steady state, isothermal model presented here accounts for the combined effects of mass and species transfer, momentum conservation, electrical current distribution through the gas channels, the electrodes and the membrane, and the electrochemical kinetics of the reactions in the anode and cathode catalyst layers. One of the important features of the model is that it proposes a simpler modified pseudo-homogeneous/agglomerate catalyst layer model which takes the advantage of the simplicity of pseudo-homogenous modeling while taking into account the effects of the agglomerates in the catalyst layer by using experimental geometric parameters published. The computation of the general mathematical model can be accomplished in 3D, 2D and 1D with the proper assumptions. Mainly, there are two computational domains considered in this thesis. The first modeling domain is a 2D Membrane Electrode Assembly (MEA) model including the modified agglomerate/pseudo-homogeneous catalyst layer modeling with consistent treatment of water transport in the MEA while the second domain presents a 3D model with different flow filed designs: straight, stepped and tapered. COMSOL Multiphysics along with Batteries and Fuel Cell Module have been used for 2D & 3D model computations while ANSYS FLUENT PEMFC Module has been used for only 3D two-phase computation. Both models have been validated with experimental data. With 2D MEA model, the effects of temperature and water content of the membrane as well as the equivalent weight of the membrane on the performance have been addressed. 3D COMSOL simulation
Two Mathematical Models of Nonlinear Vibrations
NASA Technical Reports Server (NTRS)
Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William
2007-01-01
Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.
To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling
ERIC Educational Resources Information Center
Lingefjard, Thomas; Holmquist, Mikael
2005-01-01
Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…
Mathematical Modeling of Wildfire Dynamics
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Drew, Donald
2012-11-01
Wildfires have been a long-standing problem in today's society. In this paper, we derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two dimensional flow around a rising plume above a concentrated heat source, modeling a fire line. This flow assumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. The flow outside the plume is described by a Biot-Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady evolution of the mass, momentum, energy, and vorticity inside the plume, with sources derived to model mixing in the style of Morton, et al. 1956]. The fire is then modeled using a conservation derivation, allowing the fire to propagate, coupling back to the plume model. The results show that this model is capable of capturing the complex interaction of the plume with the surrounding air and fuel layer. Funded by NSF GRFP.
Using a homology model of cytochrome P450 2D6 to predict substrate site of metabolism
NASA Astrophysics Data System (ADS)
Unwalla, Rayomand J.; Cross, Jason B.; Salaniwal, Sumeet; Shilling, Adam D.; Leung, Louis; Kao, John; Humblet, Christine
2010-03-01
CYP2D6 is an important enzyme that is involved in first pass metabolism and is responsible for metabolizing 25% of currently marketed drugs. A homology model of CYP2D6 was built using X-ray structures of ligand-bound CYP2C5 complexes as templates. This homology model was used in docking studies to rationalize and predict the site of metabolism of known CYP2D6 substrates. While the homology model was generally found to be in good agreement with the recently solved apo (ligand-free) X-ray structure of CYP2D6, significant differences between the structures were observed in the B' and F-G helical region. These structural differences are similar to those observed between ligand-free and ligand-bound structures of other CYPs and suggest that these conformational changes result from induced-fit adaptations upon ligand binding. By docking to the homology model using Glide, it was possible to identify the correct site of metabolism for a set of 16 CYP2D6 substrates 85% of the time when the 5 top scoring poses were examined. On the other hand, docking to the apo CYP2D6 X-ray structure led to a loss in accuracy in predicting the sites of metabolism for many of the CYP2D6 substrates considered in this study. These results demonstrate the importance of describing substrate-induced conformational changes that occur upon binding. The best results were obtained using Glide SP with van der Waals scaling set to 0.8 for both the receptor and ligand atoms. A discussion of putative binding modes that explain the distribution of metabolic sites for substrates, as well as a relationship between the number of metabolic sites and substrate size, are also presented. In addition, analysis of these binding modes enabled us to rationalize the typical hydroxylation and O-demethylation reactions catalyzed by CYP2D6 as well as the less common N-dealkylation.
Establishing an Explanatory Model for Mathematics Identity
ERIC Educational Resources Information Center
Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.
2015-01-01
This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…
Introduction to mathematical models and methods
Siddiqi, A. H.; Manchanda, P.
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
Identification of the noise using mathematical modelling
NASA Astrophysics Data System (ADS)
Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav
2016-03-01
In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
NASA Technical Reports Server (NTRS)
Dyominov, I. G.
1989-01-01
On the basis of the 2-D radiative-photochemical model of the ozone layer at heights 0 to 60 km in the Northern Hemisphere there are revealed and analyzed in detail the characteristic features of the season-altitude-latitude variations of ozone and temperature due to changes of the solar flux during the 11 year cycle, electron and proton precipitations.
NASA Astrophysics Data System (ADS)
Bandrowski, D.; Lai, Y.; Bradley, N.; Gaeuman, D. A.; Murauskas, J.; Som, N. A.; Martin, A.; Goodman, D.; Alvarez, J.
2014-12-01
In the field of river restoration sciences there is a growing need for analytical modeling tools and quantitative processes to help identify and prioritize project sites. 2D hydraulic models have become more common in recent years and with the availability of robust data sets and computing technology, it is now possible to evaluate large river systems at the reach scale. The Trinity River Restoration Program is now analyzing a 40 mile segment of the Trinity River to determine priority and implementation sequencing for its Phase II rehabilitation projects. A comprehensive approach and quantitative tool has recently been developed to analyze this complex river system referred to as: 2D-Hydrodynamic Based Logic Modeling (2D-HBLM). This tool utilizes various hydraulic output parameters combined with biological, ecological, and physical metrics at user-defined spatial scales. These metrics and their associated algorithms are the underpinnings of the 2D-HBLM habitat module used to evaluate geomorphic characteristics, riverine processes, and habitat complexity. The habitat metrics are further integrated into a comprehensive Logic Model framework to perform statistical analyses to assess project prioritization. The Logic Model will analyze various potential project sites by evaluating connectivity using principal component methods. The 2D-HBLM tool will help inform management and decision makers by using a quantitative process to optimize desired response variables with balancing important limiting factors in determining the highest priority locations within the river corridor to implement restoration projects. Effective river restoration prioritization starts with well-crafted goals that identify the biological objectives, address underlying causes of habitat change, and recognizes that social, economic, and land use limiting factors may constrain restoration options (Bechie et. al. 2008). Applying natural resources management actions, like restoration prioritization, is
Mathematical Modeling of Loop Heat Pipes
NASA Technical Reports Server (NTRS)
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
Matrone, G; Quaglia, F; Magenes, G
2010-01-01
Modern ultrasound imaging instrumentation for clinical applications allows real-time volumetric scanning of the patients' body. 4D imaging has been made possible thanks to the development of new echographic probes which consist in 2D phased arrays of piezoelectric transducers. In these new devices it is the system electronics which properly drives the matrix elements and focuses the beam in order to obtain a sequence of volumetric images. This paper introduces an ultrasound field simulator based on the Spatial Impulse Response method which is being properly developed to analyze the characteristics of the ultrasound field generated by a 2D phased array of transducers. Thanks to its high configurability by the user, it will represent a very useful tool for electronics designers in developing 4D ultrasound imaging systems components.
Driven microswimmers on a 2D substrate: A stochastic towed sled model
Marchegiani, Giampiero; Marchesoni, Fabio
2015-11-14
We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques.
2-D Reflectometer Modeling for Optimizing the ITER Low-field Side Reflectometer System
Kramer, G.J.; Nazikian, R.; Valeo, E.J.; Budny, R.V.; Kessel, C.; Johnson, D.
2005-09-02
The response of a low-field side reflectometer system for ITER is simulated with a 2?D reflectometer code using a realistic plasma equilibrium. It is found that the reflected beam will often miss its launch point by as much as 40 cm and that a vertical array of receiving antennas is essential in order to observe a reflection on the low-field side of ITER.
Reference measurements on a Francis model turbine with 2D Laser-Doppler-Anemometry
NASA Astrophysics Data System (ADS)
Frey, A.; Kirschner, O.; Riedelbauch, S.; Jester-Zuerker, R.; Jung, A.
2016-11-01
To validate the investigations of a high-resolution CFD simulation of a Francis turbine, measurements with 2D Laser-Doppler-Anemometry are carried out. The turbine is operated in part load, where a rotating vortex rope occurs. To validate both, mean velocities and velocity fluctuations, the measurements are classified relative to the vortex rope position. Several acrylic glass windows are installed in the turbine walls such as upstream of the spiral case inlet, in the vaneless space and in the draft tube. The current investigation is focused on a measurement plane below the runner. 2D velocity components are measured on this whole plane by measuring several narrow spaced radial lines. To avoid optical refraction of the laser beam a plan parallel window is inserted in the cone wall. The laser probe is positioned with a 2D traverse system consisting of a circumferential rail and a radial aligned linear traverse. The velocity data are synchronized with the rotational frequency of the rotating vortex rope. The results of one measurement line show the dependency of the axial and circumferential velocities on the vortex rope position.
Synaptic Deficits at Neuromuscular Junctions in Two Mouse Models of Charcot–Marie–Tooth Type 2d
Spaulding, Emily L.; Sleigh, James N.; Morelli, Kathryn H.; Pinter, Martin J.; Burgess, Robert W.
2016-01-01
Patients with Charcot–Marie–Tooth Type 2D (CMT2D), caused by dominant mutations in Glycl tRNA synthetase (GARS), present with progressive weakness, consistently in the hands, but often in the feet also. Electromyography shows denervation, and patients often report that early symptoms include cramps brought on by cold or exertion. Based on reported clinical observations, and studies of mouse models of CMT2D, we sought to determine whether weakened synaptic transmission at the neuromuscular junction (NMJ) is an aspect of CMT2D. Quantal analysis of NMJs in two different mouse models of CMT2D (GarsP278KY, GarsC201R), found synaptic deficits that correlated with disease severity and progressed with age. Results of voltage-clamp studies revealed presynaptic defects characterized by: (1) decreased frequency of spontaneous release without any change in quantal amplitude (miniature endplate current), (2) reduced amplitude of evoked release (endplate current) and quantal content, (3) age-dependent changes in the extent of depression in response to repetitive stimulation, and (4) release failures at some NMJs with high-frequency, long-duration stimulation. Drugs that modify synaptic efficacy were tested to see whether neuromuscular performance improved. The presynaptic action of 3,4 diaminopyridine was not beneficial, whereas postsynaptic-acting physostigmine did improve performance. Smaller mutant NMJs with correspondingly fewer vesicles and partial denervation that eliminates some release sites also contribute to the reduction of release at a proportion of mutant NMJs. Together, these voltage-clamp data suggest that a number of release processes, while essentially intact, likely operate suboptimally at most NMJs of CMT2D mice. SIGNIFICANCE STATEMENT We have uncovered a previously unrecognized aspect of axonal Charcot–Marie–Tooth disease in mouse models of CMT2D. Synaptic dysfunction contributes to impaired neuromuscular performance and disease progression. This
Numerical Simulations of High-Frequency Respiratory Flows in 2D and 3D Lung Bifurcation Models
NASA Astrophysics Data System (ADS)
Chen, Zixi; Parameswaran, Shamini; Hu, Yingying; He, Zhaoming; Raj, Rishi; Parameswaran, Siva
2014-07-01
To better understand the human pulmonary system and optimize the high-frequency oscillatory ventilation (HFOV) design, numerical simulations were conducted under normal breathing frequency and HFOV condition using a CFD code Ansys Fluent and its user-defined C programs. 2D and 3D double bifurcating lung models were created, and the geometry corresponds to fifth to seventh generations of airways with the dimensions based on the Weibel's pulmonary model. Computations were carried out for different Reynolds numbers (Re = 400 and 1000) and Womersley numbers (α = 4 and 16) to study the air flow fields, gas transportation, and wall shear stresses in the lung airways. Flow structure was compared with experimental results. Both 2D and 3D numerical models successfully reproduced many results observed in the experiment. The oxygen concentration distribution in the lung model was investigated to analyze the influence of flow oscillation on gas transport inside the lung model.
Mathematical models for principles of gyroscope theory
NASA Astrophysics Data System (ADS)
Usubamatov, Ryspek
2017-01-01
Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
ERIC Educational Resources Information Center
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
ERIC Educational Resources Information Center
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Modeling the Transverse Thermal Conductivity of 2-D SiCf/SiC Composites Made with Woven Fabric
Youngblood, Gerald E.; Senor, David J.; Jones, Russell H.
2004-06-30
The hierarchical two-layer (H2L) model was developed to describe the effective transverse thermal conductivity, Keff, of a 2D-SiCf/SiC composite made from stacked and infiltrated woven fabric layers in terms of constituent properties and microstructural and architectural variables. The H2L model includes the expected effects of fiber-matrix interfacial conductance as well as the effects of high fiber packing fractions within individual tows and the non-uniform nature of 2D-fabric layers that usually include a significant amount of interlayer porosity. Previously, H2L model predictions were compared to measured values of Keff for two versions of DuPont 2D-Hi NicalonÃ”/PyC/ICVI-SiC composite, one with a â€œthinâ€ (0.110 Î¼m) and the other with a â€œthickâ€ (1.040 Î¼m) pyrocarbon (PyC) fiber coating, and for a 2D-TyrannoÃ” SA/â€thinâ€ PyC/FCVI-SIC composite made by ORNL. In this study, H2L model predictions are compared to measured Keff-values for a 2D-SiCf/SiC composite made by GE Power Systems (formerly DuPont Lanxide) using the ICVI-process with Hi-NicalonÃ” type S fabric. The values of Keff determined for the composite made with the Hi-NicalonÃ” type S fabric were significantly greater than Keff-values determined for the composites made with either the Hi-NicalonÃ”or the TyrannoÃ” SA fabrics. Differences in Keff-values were expected for using different fiber types, but major differences also were due to observed microstructural variations between the systems, and as predicted by the H2L model.
NASA Astrophysics Data System (ADS)
Fang, F.; Zhang, T.; Pavlidis, D.; Pain, C. C.; Buchan, A. G.; Navon, I. M.
2014-10-01
A novel reduced order model (ROM) based on proper orthogonal decomposition (POD) has been developed for a finite-element (FE) adaptive mesh air pollution model. A quadratic expansion of the non-linear terms is employed to ensure the method remained efficient. This is the first time such an approach has been applied to air pollution LES turbulent simulation through three dimensional landscapes. The novelty of this work also includes POD's application within a FE-LES turbulence model that uses adaptive resolution. The accuracy of the reduced order model is assessed and validated for a range of 2D and 3D urban street canyon flow problems. By comparing the POD solutions against the fine detail solutions obtained from the full FE model it is shown that the accuracy is maintained, where fine details of the air flows are captured, whilst the computational requirements are reduced. In the examples presented below the size of the reduced order models is reduced by factors up to 2400 in comparison to the full FE model while the CPU time is reduced by up to 98% of that required by the full model.
Chen, J-S.; Drake, R.; Lin, Z.; Jewett, D. G.
2002-02-26
Five vadose zone models with different degrees of complexity (CHAIN, MULTIMED{_}DP, FECTUZ, HYDRUS, and CHAIN 2D) were selected for use in radionuclide soil screening level (SSL) calculations. A benchmarking analysis between the models was conducted for a radionuclide ({sup 99}Tc) release scenario at the Las Cruces Trench Site in New Mexico. Sensitivity of three model outputs to the input parameters were evaluated and compared among the models. The three outputs were peak contaminant concentrations, time to peak concentrations at the water table, and time to exceed the contaminants maximum critical level at a representative receptor well. Model parameters investigated include soil properties such as bulk density, water content, soil water retention parameters and hydraulic conductivity. Chemical properties examined include distribution coefficient, radionuclide half-life, dispersion coefficient, and molecular diffusion. Other soil characteristics, such as recharge rate, also were examined. Model sensitivity was quantified in the form of sensitivity and relative sensitivity coefficients. Relative sensitivities were used to compare the sensitivities of different parameters. The analysis indicates that soil water content, recharge rate, saturated soil water content, and soil retention parameter, {beta}, have a great influence on model outputs. In general, the results of sensitivities and relative sensitivities using five models are similar for a specific scenario. Slight differences were observed in predicted peak contaminant concentrations due to different mathematical treatment among models. The results of benchmarking and sensitivity analysis would facilitate the model selection and application of the model in SSL calculations.
2D MHD AND 1D HD MODELS OF A SOLAR FLARE—A COMPREHENSIVE COMPARISON OF THE RESULTS
Falewicz, R.; Rudawy, P.; Murawski, K.; Srivastava, A. K. E-mail: rudawy@astro.uni.wroc.pl E-mail: asrivastava.app@iitbhu.ac.in
2015-11-01
Without any doubt, solar flaring loops possess a multithread internal structure that is poorly resolved, and there are no means to observe heating episodes and thermodynamic evolution of the individual threads. These limitations cause fundamental problems in numerical modeling of flaring loops, such as selection of a structure and a number of threads, and an implementation of a proper model of the energy deposition process. A set of one-dimensional (1D) hydrodynamic and two-dimensional (2D) magnetohydrodynamic models of a flaring loop are developed to compare energy redistribution and plasma dynamics in the course of a prototypical solar flare. Basic parameters of the modeled loop are set according to the progenitor M1.8 flare recorded in AR 10126 on 2002 September 20 between 09:21 UT and 09:50 UT. The nonideal 1D models include thermal conduction and radiative losses of the optically thin plasma as energy-loss mechanisms, while the nonideal 2D models take into account viscosity and thermal conduction as energy-loss mechanisms only. The 2D models have a continuous distribution of the parameters of the plasma across the loop and are powered by varying in time and space along and across the loop heating flux. We show that such 2D models are an extreme borderline case of a multithread internal structure of the flaring loop, with a filling factor equal to 1. Nevertheless, these simple models ensure the general correctness of the obtained results and can be adopted as a correct approximation of the real flaring structures.
Yogurtcu, Osman N.; Johnson, Margaret E.
2015-01-01
The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute
NASA Technical Reports Server (NTRS)
Shie, Chung-Lin; Tao, Wei-Kuo; Simpson, Joanne
2003-01-01
The 1999 Kwajalein Atoll field experiment (KWAJEX), one of several major TRMM (Tropical Rainfall Measuring Mission) field experiments, has successfully obtained a wealth of information and observation data on tropical convective systems over the western Central Pacific region. In this paper, clouds and convective systems that developed during three active periods (Aug 7-12, Aug 17-21, and Aug 29-Sep 13) around Kwajalein Atoll site are simulated using both 2D and 3D Goddard Cumulus Ensemble (GCE) models. Based on numerical results, the clouds and cloud systems are generally unorganized and short lived. These features are validated by radar observations that support the model results. Both the 2D and 3D simulated rainfall amounts and their stratiform contribution as well as the heat, water vapor, and moist static energy budgets are examined for the three convective episodes. Rainfall amounts are quantitatively similar between the two simulations, but the stratiform contribution is considerably larger in the 2D simulation. Regardless of dimension, fo all three cases, the large-scale forcing and net condensation are the two major physical processes that account for the evolution of the budgets with surface latent heat flux and net radiation solar and long-wave radiation)being secondary processes. Quantitative budget differences between 2D and 3D as well as between various episodes will be detailed.Morover, simulated radar signatures and Q1/Q2 fields from the three simulations are compared to each other and with radar and sounding observations.
Mathematical models of malaria - a review
2011-01-01
Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease PMID:21777413
On the uniqueness of quantitative DNA difference descriptors in 2D graphical representation models
NASA Astrophysics Data System (ADS)
Nandy, A.; Nandy, P.
2003-01-01
The rapid growth in additions to databases of DNA primary sequence data have led to searches for methods to numerically characterize these data and help in fast identification and retrieval of relevant sequences. The DNA descriptors derived from the 2D graphical representation technique have already been proposed to index chemical toxicity and single nucleotide polymorphic (SNP) genes but the inherent degeneracies in this representation have given rise to doubts about their suitability. We prove in this paper that such degeneracies will exist only in very restricted cases and that the method can be relied upon to provide unique descriptors for, in particular, the SNP genes and several other classes of DNA sequences.
An Experimental Approach to Mathematical Modeling in Biology
ERIC Educational Resources Information Center
Ledder, Glenn
2008-01-01
The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…
Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.
ERIC Educational Resources Information Center
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.
ERIC Educational Resources Information Center
Swetz, Frank
1991-01-01
Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)
NASA Astrophysics Data System (ADS)
Ivy, D. J.; Rigby, M. L.; Prinn, R. G.; Muhle, J.; Weiss, R. F.
2009-12-01
We present optimized annual global emissions from 1973-2008 of nitrogen trifluoride (NF3), a powerful greenhouse gas which is not currently regulated by the Kyoto Protocol. In the past few decades, NF3 production has dramatically increased due to its usage in the semiconductor industry. Emissions were estimated through the 'pulse-method' discrete Kalman filter using both a simple, flexible 2-D 12-box model used in the Advanced Global Atmospheric Gases Experiment (AGAGE) network and the Model for Ozone and Related Tracers (MOZART v4.5), a full 3-D atmospheric chemistry model. No official audited reports of industrial NF3 emissions are available, and with limited information on production, a priori emissions were estimated using both a bottom-up and top-down approach with two different spatial patterns based on semiconductor perfluorocarbon (PFC) emissions from the Emission Database for Global Atmospheric Research (EDGAR v3.2) and Semiconductor Industry Association sales information. Both spatial patterns used in the models gave consistent results, showing the robustness of the estimated global emissions. Differences between estimates using the 2-D and 3-D models can be attributed to transport rates and resolution differences. Additionally, new NF3 industry production and market information is presented. Emission estimates from both the 2-D and 3-D models suggest that either the assumed industry release rate of NF3 or industry production information is still underestimated.
NASA Astrophysics Data System (ADS)
Blitz, Celine; Komatitsch, Dimitri; Lognonné, Philippe; Martin, Roland; Le Goff, Nicolas
The understanding of the interior structure of Near Earth Objects (NEOs) is a fundamental issue to determine their evolution and origin, and also, to design possible mitigation techniques (Walker and Huebner, 2004). Indeed, if an oncoming Potentially Hazardous Object (PHO) were to threaten the Earth, numerous methods are suggested to prevent it from colliding our planet. Such mitigation techniques may involve nuclear explosives on or below the object surface, impact by a projectile, or concentration of solar energy using giant mirrors (Holsapple, 2004). The energy needed in such mitigation techniques highly depends on the porosity of the hazardous threatening object (asteroid or comet), as suggested by Holsapple, 2004. Thus, for a given source, the seismic response of a coherent homogeneous asteroid should be very different from the seismic response of a fractured or rubble-pile asteroid. To assess this hypothesis, we performed numerical simulations of wave propagation in different interior models of the Near Earth Asteroid 433 Eros. The simulations of wave propagation required a shape model of asteroid Eros, kindly provided by A. Cheng and O. Barnouin-Jha (personal communication). A cross-section along the longest axis has been chosen to define our 2D geometrical model, and we study two models of the interior: a homogeneous one, and a complex one characterized by fault networks below the main crosscut craters, and covered by a regolith layer of thickness ranging from 50 m to 150 m. To perform the numerical simulations we use the spectral-element method, which solves the variational weak form of the seismic wave equation (Komatitsch and Tromp, 1999) on the meshes of the 2D models of asteroid Eros. The homogeneous model is composed of an elastic material characterized by a pressure wave velocity Vp = 3000 m.s-1 , a shear wave velocity Vs = 1700 m.s-1 and a density of 2700 kg.m-3 . The fractured model possesses the same characteristics except for the presence of
Lindenschmidt, Karl-Erich; Huang, Shaochun; Baborowski, Martina
2008-07-01
In flood modeling, many one-dimensional (1D) hydrodynamic and water quality models are too restricted in capturing the spatial differentiation of processes within a polder or system of polders and two-dimensional (2D) models are too demanding in data requirements and computational resources, especially if Monte-Carlo techniques are to be used for model uncertainty analyses. The first goal of this paper is to show the successful development of a quasi-2D modeling approach which still calculates the dynamic wave in 1D but the discretisation of the computational units is in 2D, allowing a better spatial representation of the flow and substance transport processes in the polders without a large additional expenditure on data pre-processing and simulation processing. The models DYNHYD (1D hydrodynamics) and TOXI (sediment and micro-pollutant transport) were used as a basis for the hydrodynamic and water quality simulations. An extreme flood event on the Elbe River, Germany, with a proposed polder system variant was used as a test case. The results show a plausible differentiation of suspended sediment and zinc concentrations within the polders both spatially and temporally. This fulfills the second goal of this research. The third goal of this work is to provide an example methodology of carrying out an environmental risk assessment in inundated areas by flood waters, as required by the European Union floods directive. The deposition of zinc in polders was used for this example, due to its high contamination potential in the Elbe River. The extended quasi-2D modeling system incorporates a Monte-Carlo uncertainty analysis to assess the environmental impact of heavy metal deposition in the polders during extreme flooding. The environmental risk computed gives a 48% chance of exceeding the inspection value of 500 mg zinc/kg sediment for a flood such as the August 2002 event.
Voters' Fickleness:. a Mathematical Model
NASA Astrophysics Data System (ADS)
Boccara, Nino
This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.
Mathematical Modelling of Turbidity Currents
NASA Astrophysics Data System (ADS)
Fay, G. L.; Fowler, A.; Howell, P.
2011-12-01
A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.
Mathematical Models of College Myopia
Greene, Peter R.; Grill, Zachary W.; Medina, Antonio
2015-01-01
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia. PMID:26709316
3D/2D registration and segmentation of scoliotic vertebrae using statistical models.
Benameur, Said; Mignotte, Max; Parent, Stefan; Labelle, Hubert; Skalli, Wafa; de Guise, Jacques
2003-01-01
We propose a new 3D/2D registration method for vertebrae of the scoliotic spine, using two conventional radiographic views (postero-anterior and lateral), and a priori global knowledge of the geometric structure of each vertebra. This geometric knowledge is efficiently captured by a statistical deformable template integrating a set of admissible deformations, expressed by the first modes of variation in Karhunen-Loeve expansion, of the pathological deformations observed on a representative scoliotic vertebra population. The proposed registration method consists of fitting the projections of this deformable template with the preliminary segmented contours of the corresponding vertebra on the two radiographic views. The 3D/2D registration problem is stated as the minimization of a cost function for each vertebra and solved with a gradient descent technique. Registration of the spine is then done vertebra by vertebra. The proposed method efficiently provides accurate 3D reconstruction of each scoliotic vertebra and, consequently, it also provides accurate knowledge of the 3D structure of the whole scoliotic spine. This registration method has been successfully tested on several biplanar radiographic images and validated on 57 scoliotic vertebrae. The validation results reported in this paper demonstrate that the proposed statistical scheme performs better than other conventional 3D reconstruction methods.
Mathematical Models Of Turbulence In Transonic Flow
NASA Technical Reports Server (NTRS)
Rubesin, Morris W.; Viegas, John R.
1989-01-01
Predictions of several models compared with measurements of well-documented flow. Report reviews performances of variety of mathematical models of turbulence in transonic flow. Predictions of models compared with measurements of flow in wind tunnel along outside of cylinder having axisymmetric bump of circular-arc cross section in meridional plane. Review part of continuing effort to calibrate and verify computer codes for prediction of transonic flows about airfoils. Johnson-and-King model proved superior in predicting transonic flow over bumpy cylinder.
Stock, Kristin; Estrada, Marta F.; Vidic, Suzana; Gjerde, Kjersti; Rudisch, Albin; Santo, Vítor E.; Barbier, Michaël; Blom, Sami; Arundkar, Sharath C.; Selvam, Irwin; Osswald, Annika; Stein, Yan; Gruenewald, Sylvia; Brito, Catarina; van Weerden, Wytske; Rotter, Varda; Boghaert, Erwin; Oren, Moshe; Sommergruber, Wolfgang; Chong, Yolanda; de Hoogt, Ronald; Graeser, Ralph
2016-01-01
Two-dimensional (2D) cell cultures growing on plastic do not recapitulate the three dimensional (3D) architecture and complexity of human tumors. More representative models are required for drug discovery and validation. Here, 2D culture and 3D mono- and stromal co-culture models of increasing complexity have been established and cross-comparisons made using three standard cell carcinoma lines: MCF7, LNCaP, NCI-H1437. Fluorescence-based growth curves, 3D image analysis, immunohistochemistry and treatment responses showed that end points differed according to cell type, stromal co-culture and culture format. The adaptable methodologies described here should guide the choice of appropriate simple and complex in vitro models. PMID:27364600
Building Mathematical Models of Simple Harmonic and Damped Motion.
ERIC Educational Resources Information Center
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Livezey, Mara; Nagy, Leslie D; Diffenderfer, Laura E; Arthur, Evan J; Hsi, David J; Holton, Jeffrey M; Furge, Laura Lowe
2012-03-01
Human cytochrome P450 2D6 (CYP2D6) is involved in metabolism of approximately 25% of pharmaceutical drugs. Inactivation of CYP2D6 can lead to adverse drug interactions. Four inactivators of CYP2D6 have previously been identified: 5-Fluoro-2-[4-[(2-phenyl-1H-imidazol-5-yl)methyl]-1-piperazinyl]pyrimidine(SCH66712), (1-[(2-ethyl- 4-methyl-1H-imidazol-5-yl)-methyl]-4-[4-(trifluoromethyl)-2-pyridinyl]piperazine(EMTPP), paroxetine, and 3,4- methylenedioxymethamphetamine (MDMA). All four contain planar, aromatic groups as well as basic nitrogens common to CYP2D6 substrates. SCH66712 and EMTPP also contain piperazine groups and substituted imidazole rings that are common in pharmaceutical agents, though neither of these compounds is clinically relevant. Paroxetine and MDMA contain methylenedioxyphenyls. SCH66712 and EMTPP are both known protein adductors while paroxetine and MDMA are probable heme modifiers. The current study shows that each inactivator displays Type I binding with Ks values that vary by 2-orders of magnitude with lower Ks values associated with greater inactivation. Comparison of KI, kinact, and partition ratio values shows SCH66712 is the most potent inactivator. Molecular modeling experiments using AutoDock identify Phe120 as a key interaction for all four inactivators with face-to-face and edge-to-face pi interactions apparent. Distance between the ligand and heme iron correlates with potency of inhibition. Ligand conformations were scored according to their binding energies as calculated by AutoDock and correlation was observed between molecular models and Ks values.
MOLECULAR ANALYSIS AND MODELING OF INACTIVATION OF HUMAN CYP2D6 BY FOUR MECHANISM BASED INACTIVATORS
Livezey, Mara; Nagy, Leslie D.; Diffenderfer, Laura E.; Arthur, Evan J.; Hsi, David J.; Holton, Jeffrey M.; Furge, Laura Lowe
2014-01-01
Human cytochrome P450 2D6 (CYP2D6) is involved in metabolism of approximately 25% of pharmaceutical drugs. Inactivation of CYP2D6 can lead to adverse drug interactions. Four inactivators of CYP2D6 have previously been identified: 5-Fluoro-2-[4-[(2-phenyl-1H-imidazol-5-yl)methyl]-1-piperazinyl]pyrimidine (SCH66712), (1-[(2-ethyl-4-methyl-1H(-EMTPP-imidazol-5-yl)-methyl]-4-[4-(trifluoromethyl)-2-pyridinyl]piperazine (EMTPP), paroxetine, and 3,4-methylenedioxymethamphetamine (MDMA). All four contain planar, aromatic groups as well as basic nitrogens common to CYP2D6 substrates. SCH66712 and EMTPP also contain piperazine groups and substituted imidazole rings that are common in pharmaceutical agents, though neither of these compounds is clinically relevant. Paroxetine and MDMA contain methylenedioxyphenyls. SCH66712 and EMTPP are both known protein adductors while paroxetine and MDMA are probable heme modifiers. The current study shows that each inactivator displays Type I binding with Ks values that vary by 2-orders of magnitude with lower Ks values associated with greater inactivation. Comparison of KI, kinact, and partition ratio values shows SCH66712 is the most potent inactivator. Molecular modeling experiments using AutoDock identify Phe120 as a key interaction for all four inactivators with face-to-face and edge-to-face pi interactions apparent. Distance between the ligand and heme iron correlates with potency of inhibition. Ligand conformations were scored according to their binding energies as calculated by AutoDock and correlation was observed between molecular models and Ks values. PMID:22372551
Mathematical modeling of vertebrate limb development.
Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A
2013-05-01
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.
Müller, Peter; Messmer, Marie; Bayer, Monika; Pfeilschifter, Josef M; Hintermann, Edith; Christen, Urs
2016-05-01
Non-alcoholic fatty liver disease (NAFLD) and its more severe development non-alcoholic steatohepatitis (NASH) are increasing worldwide. In particular NASH, which is characterized by an active hepatic inflammation, has often severe consequences including progressive fibrosis, cirrhosis, and eventually hepatocellular carcinoma (HCC). Here we investigated how metabolic liver injury is influencing the pathogenesis of autoimmune hepatitis (AIH). We used the CYP2D6 mouse model in which wild type C57BL/6 mice are infected with an Adenovirus expressing the major liver autoantigen cytochrome P450 2D6 (CYP2D6). Such mice display several features of human AIH, including interface hepatitis, formation of LKM-1 antibodies and CYP2D6-specific T cells, as well as hepatic fibrosis. NAFLD was induced with a high-fat diet (HFD). We found that pre-existing NAFLD potentiates the severity of AIH. Mice fed for 12 weeks with a HFD displayed increased cellular infiltration of the liver, enhanced hepatic fibrosis and elevated numbers of liver autoantigen-specific T cells. Our data suggest that a pre-existing metabolic liver injury constitutes an additional risk for the severity of an autoimmune condition of the liver, such as AIH.
ERIC Educational Resources Information Center
Jurow, A. Susan
2004-01-01
Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…
ERIC Educational Resources Information Center
Lim, L. L.; Tso, T. -Y.; Lin, F. L.
2009-01-01
This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…
ERIC Educational Resources Information Center
Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard
2008-01-01
This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…
The Method of Minimal Representations in 2d Ising Model Calculations
1992-05-01
Contact No. "N00014-90-J-1372. "eDepartment of Mathematics and the Computer Science Division of the EECS Department. UniversiTv of California. Berkeley...tiorinalizat ions) (I= f (2- B)/T. i, = ( -BIT aiid C- The attractive propierty of 31i,, i~s that it is a lioliligatiVP irreducible mat rix whom...function,.. For a giveni partitiou f the set of all representable vectors, forms, a sub~space Sj of R2" . We h~ow\\ to thie influjence of computer science
Mathematical modelling of the lower urinary tract.
Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia
2013-03-01
The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.
Mathematical modelling of leprosy and its control.
Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik
2015-03-01
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.
2D full wave modeling for a synthetic Doppler backscattering diagnostic
Hillesheim, J. C.; Schmitz, L.; Kubota, S.; Rhodes, T. L.; Carter, T. A.; Holland, C.
2012-10-15
Doppler backscattering (DBS) is a plasma diagnostic used in tokamaks and other magnetic confinement devices to measure the fluctuation level of intermediate wavenumber (k{sub {theta}}{rho}{sub s}{approx} 1) density fluctuations and the lab frame propagation velocity of turbulence. Here, a synthetic DBS diagnostic is described, which has been used for comparisons between measurements in the DIII-D tokamak and predictions from nonlinear gyrokinetic simulations. To estimate the wavenumber range to which a Gaussian beam would be sensitive, a ray tracing code and a 2D finite difference, time domain full wave code are used. Experimental density profiles and magnetic geometry are used along with the experimental antenna and beam characteristics. An example of the effect of the synthetic diagnostic on the output of a nonlinear gyrokinetic simulation is presented.
A 2-D Self-Consistent DSMC Model for Chemically Reacting Low Pressure Plasma Reactors
Bartel, Timothy J.; Economou, Demetre; Johannes, Justine E.
1999-06-17
This paper will focus on the methodology of using a 2D plasma Direct Simulation Monte Carlo technique to simulate the species transport in an inductively coupled, low pressure, chemically reacting plasma system. The pressure in these systems is typically less than 20 mtorr with plasma densities of approximately 10{sup 17} {number_sign}/m{sup 3} and an ionization level of only 0.1%. This low ionization level tightly couples the neutral, ion, and electron chemistries and interactions in a system where the flow is subsonic. We present our strategy and compare simulation results to experimental data for Cl{sub 2} in a Gaseous Electronics Conference (GEC) reference cell modified with an inductive coil.
2-D Modeling of the Variability of the Solar Interior for Climate Studies
NASA Astrophysics Data System (ADS)
Sofia, S.; Li, L. H.; Spada, F.; Ventura, P.
2012-07-01
To establish the possible influence of solar variability on climate, it is necessary to understand the luminosity changes induced by a variable dynamo magnetic field. To accomplish this, we have developed a 2D code of the structure and evolution of the solar interior (based on the 1D YREC code), that includes rotation, magnetic fields of arbitrary configuration, and turbulence, that can be run on very short time scales (down to 1 year), and that represents all global parameters (R, L, Teff) with a relative accuracy of 1 part per million, or better. This paper discusses the motivation for this work, the structure and the physical components of the code, and its application to interpret the results of the SODISM experiment on the PICARD satellite, and of the balloon-borne Solar Disk Sextant (SDS) experiment.
Mathematical Model For Deposition Of Soot
NASA Technical Reports Server (NTRS)
Makel, Darby B.
1991-01-01
Semiempirical mathematical model predicts deposition of soot in tubular gas generator in which hydrocarbon fuel burned in very-fuel-rich mixture with pure oxygen. Developed in response to concern over deposition of soot in gas generators and turbomachinery of rocket engines. Also of interest in terrestrial applications involving fuel-rich combustion or analogous process; e.g., purposeful deposition of soot to manufacture carbon black pigments.
On mathematical modelling of flameless combustion
Mancini, Marco; Schwoeppe, Patrick; Weber, Roman; Orsino, Stefano
2007-07-15
A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out. The experimental burner features a strong oxidizer jet and two weak natural gas jets. Numerous publications have shown the inability of various RANS-based mathematical models to predict the structure of the weak jet. We have proven that the failure is in error predictions of the entrainment and therefore is not related to any chemistry submodels, as has been postulated. (author)
SU-E-T-05: A 2D EPID Transit Dosimetry Model Based On An Empirical Quadratic Formalism
Tan, Y; Metwaly, M; Glegg, M; Baggarley, S; Elliott, A
2014-06-01
Purpose: To describe a 2D electronic portal imaging device (EPID) transit dosimetry model, based on an empirical quadratic formalism, that can predict either EPID or in-phantom dose distribution for comparisons with EPID captured image or treatment planning system (TPS) dose respectively. Methods: A quadratic equation can be used to relate the reduction in intensity of an exit beam to the equivalent path length of the attenuator. The calibration involved deriving coefficients from a set of dose planes measured for homogeneous phantoms with known thicknesses under reference conditions. In this study, calibration dose planes were measured with EPID and ionisation chamber (IC) in water for the same reference beam (6MV, 100mu, 20×20cm{sup 2}) and set of thicknesses (0–30cm). Since the same calibration conditions were used, the EPID and IC measurements can be related through the quadratic equation. Consequently, EPID transit dose can be predicted from TPS exported dose planes and in-phantom dose can be predicted using EPID distribution captured during treatment as an input. The model was tested with 4 open fields, 6 wedge fields, and 7 IMRT fields on homogeneous and heterogeneous phantoms. Comparisons were done using 2D absolute gamma (3%/3mm) and results were validated against measurements with a commercial 2D array device. Results: The gamma pass rates for comparisons between EPID measured and predicted ranged from 93.6% to 100.0% for all fields and phantoms tested. Results from this study agreed with 2D array measurements to within 3.1%. Meanwhile, comparisons in-phantom between TPS computed and predicted ranged from 91.6% to 100.0%. Validation with 2D array device was not possible for inphantom comparisons. Conclusion: A 2D EPID transit dosimetry model for treatment verification was described and proven to be accurate. The model has the advantage of being generic and allows comparisons at the EPID plane as well as multiple planes in-phantom.
Mathematical Models and the Experimental Analysis of Behavior
ERIC Educational Resources Information Center
Mazur, James E.
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…
Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling
2007-03-01
of Defense, or the United States Government. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR...March 2007 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR FIGHTER...80 x MATHEMATICAL PROGAMMING MODEL FOR FIGHTER TRAINING SQUADRON PILOT
Biology by numbers: mathematical modelling in developmental biology.
Tomlin, Claire J; Axelrod, Jeffrey D
2007-05-01
In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.
2D Radiation MHD K-shell Modeling of Single Wire Array Stainless Steel Experiments on the Z Machine
Thornhill, J. W.; Giuliani, J. L.; Apruzese, J. P.; Chong, Y. K.; Davis, J.; Dasgupta, A.; Whitney, K. G.; Clark, R. W.; Jones, B.; Coverdale, C. A.; Ampleford, D. J.; Cuneo, M. E.; Deeney, C.
2009-01-21
Many physical effects can produce unstable plasma behavior that affect K-shell emission from arrays. Such effects include: asymmetry in the initial density profile, asymmetry in power flow, thermal conduction at the boundaries, and non-uniform wire ablation. Here we consider how asymmetry in the radiation field also contributes to the generation of multidimensional plasma behavior that affects K-shell power and yield. To model this radiation asymmetry, we have incorporated into the MACH2 r-z MHD code a self-consistent calculation of the non-LTE population kinetics based on radiation transport using multi-dimensional ray tracing. Such methodology is necessary for modeling the enhanced radiative cooling that occurs at the anode and cathode ends of the pinch during the run-in phase of the implosion. This enhanced radiative cooling is due to reduced optical depth at these locations producing an asymmetric flow of radiative energy that leads to substantial disruption of large initial diameter (>5 cm) pinches and drives 1D into 2D fluid (i.e., Rayleigh-Taylor like) flows. The impact of this 2D behavior on K-shell power and yield is investigated by comparing 1D and 2D model results with data obtained from a series of single wire array stainless steel experiments performed on the Z generator.
NASA Technical Reports Server (NTRS)
Proffitt, M. H.; Solomon, S.; Loewenstein, M.
1992-01-01
A linear reference relationship between O3 and N2O has been used to estimate polar winter O3 loss from aircraft data taken in the lower stratosphere. Here, this relationship is evaluated at high latitudes by comparing it with a 2D model simulation and with NIMBUS 7 satellite measurements. Although comparisons with satellite measurements are limited to January through May, the model simulations are compared during other seasons. The model simulations and the satellite data are found to be consistent with the winter O3 loss analysis. It is shown that such analyses are likely to be inappropriate during other seasons.
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
Toward IMRT 2D dose modeling using artificial neural networks: A feasibility study
Kalantzis, Georgios; Vasquez-Quino, Luis A.; Zalman, Travis; Pratx, Guillem; Lei, Yu
2011-10-15
Purpose: To investigate the feasibility of artificial neural networks (ANN) to reconstruct dose maps for intensity modulated radiation treatment (IMRT) fields compared with those of the treatment planning system (TPS). Methods: An artificial feed forward neural network and the back-propagation learning algorithm have been used to replicate dose calculations of IMRT fields obtained from PINNACLE{sup 3} v9.0. The ANN was trained with fluence and dose maps of IMRT fields for 6 MV x-rays, which were obtained from the amorphous silicon (a-Si) electronic portal imaging device of Novalis TX. Those fluence distributions were imported to the TPS and the dose maps were calculated on the horizontal midpoint plane of a water equivalent homogeneous cylindrical virtual phantom. Each exported 2D dose distribution from the TPS was classified into two clusters of high and low dose regions, respectively, based on the K-means algorithm and the Euclidian metric in the fluence-dose domain. The data of each cluster were divided into two sets for the training and validation phase of the ANN, respectively. After the completion of the ANN training phase, 2D dose maps were reconstructed by the ANN and isodose distributions were created. The dose maps reconstructed by ANN were evaluated and compared with the TPS, where the mean absolute deviation of the dose and the {gamma}-index were used. Results: A good agreement between the doses calculated from the TPS and the trained ANN was achieved. In particular, an average relative dosimetric difference of 4.6% and an average {gamma}-index passing rate of 93% were obtained for low dose regions, and a dosimetric difference of 2.3% and an average {gamma}-index passing rate of 97% for high dose region. Conclusions: An artificial neural network has been developed to convert fluence maps to corresponding dose maps. The feasibility and potential of an artificial neural network to replicate complex convolution kernels in the TPS for IMRT dose calculations
Mathematical modeling of deformation during hot rolling
Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K.
1994-12-31
The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
A novel simple procedure to consider seismic soil structure interaction effects in 2D models
NASA Astrophysics Data System (ADS)
Jaramillo, Juan Diego; Gómez, Juan David; Restrepo, Doriam; Rivera, Santiago
2014-09-01
A method is proposed to estimate the seismic soil-structure-interaction (SSI) effects for use in engineering practice. It is applicable to 2D structures subjected to vertically incident shear waves supported by homogenous half-spaces. The method is attractive since it keeps the simplicity of the spectral approach, overcomes some of the difficulties and inaccuracies of existing classical techniques and yet it considers a physically consistent excitation. This level of simplicity is achieved through a response spectra modification factor that can be applied to the free-field 5%-damped response spectra to yield design spectral ordinates that take into account the scattered motions introduced by the interaction effects. The modification factor is representative of the Transfer Function (TF) between the structural relative displacements and the free-field motion, which is described in terms of its maximum amplitude and associated frequency. Expressions to compute the modification factor by practicing engineers are proposed based upon a parametric study using 576 cases representative of actual structures. The method is tested in 10 cases spanning a wide range of common fundamental vibration periods.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Aircraft engine mathematical model - linear system approach
NASA Astrophysics Data System (ADS)
Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ
2016-06-01
This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.
NASA Astrophysics Data System (ADS)
Chen, T.; Wang, P.; Fehler, M.; Zhang, Y.; Burns, D.
2009-12-01
Localizing subsurface fractures and estimating their mechanical parameters and geometric properties are very important in oil and gas industry as well as geothermal energy research. It is essential to quantitatively understand how the elastic wave propagation is affected by these fractures. In this paper, an analytical expression for the scattered P- and SV waves from a 2D fracture is formulated based on a normal mode method, where the 2D fracture is modeled by a low-aspect ratio elliptical cylinder. The scatter function of this 2D fracture are expressed in terms of the incident angle, the orientation and aspect ratio of the fracture as well as the elastic impedance contrast between the surrounding medium and the inhomogeneity inside the fracture. Results from this analytical solution match well with those from a finite-difference approach. Solutions of this analytical model at two limiting cases (a circular cylinder with aspect ratio equal to one and a strip with aspect ratio equal to zero) are also compared to analytical solutions directly derived for the circular cylinder and strip by other studies.
Lin, Shangchao; Shih, Chih-Jen; Sresht, Vishnu; Govind Rajan, Ananth; Strano, Michael S; Blankschtein, Daniel
2016-08-03
The colloidal dispersion stability of 1D and 2D materials in the liquid phase is critical for scalable nano-manufacturing, chemical modification, composites production, and deployment as conductive inks or nanofluids. Here, we review recent computational and theoretical studies carried out by our group to model the dispersion stability of 1D and 2D materials, including single-walled carbon nanotubes, graphene, and graphene oxide in aqueous surfactant solutions or organic solvents. All-atomistic (AA) molecular dynamics (MD) simulations can probe the molecular level details of the adsorption morphology of surfactants and solvents around these materials, as well as quantify the interaction energy between the nanomaterials mediated by surfactants or solvents. Utilizing concepts from reaction kinetics and diffusion, one can directly predict the rate constants for the aggregation kinetics and dispersion life times using MD outputs. Furthermore, the use of coarse-grained (CG) MD simulations allows quantitative prediction of surfactant adsorption isotherms. Combined with the Poisson-Boltzmann equation, the Langmuir isotherm, and the DLVO theory, one can directly use CGMD outputs to: (i) predict electrostatic potentials around the nanomaterial, (ii) correlate surfactant surface coverages with surfactant concentrations in the bulk dispersion medium, and (iii) determine energy barriers against coagulation. Finally, we discuss challenges associated with studying emerging 2D materials, such as, hexagonal boron nitride (h-BN), phosphorene, and transition metal dichalcogenides (TMDCs), including molybdenum disulfide (MoS2). An outlook is provided to address these challenges with plans to develop force-field parameters for MD simulations to enable predictive modeling of emerging 2D materials in the liquid phase.
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
ERIC Educational Resources Information Center
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Assessment of Primary 5 Students' Mathematical Modelling Competencies
ERIC Educational Resources Information Center
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Declarative representation of uncertainty in mathematical models.
Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Mathematical Modeling of an Oscillating Droplet
NASA Technical Reports Server (NTRS)
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
2D soil and engineering-seismic bedrock modeling of eastern part of Izmir inner bay/Turkey
NASA Astrophysics Data System (ADS)
Pamuk, Eren; Akgün, Mustafa; Özdağ, Özkan Cevdet; Gönenç, Tolga
2017-02-01
Soil-bedrock models are used as a base when the earthquake-soil common behaviour is defined. Moreover, the medium which is defined as bedrock is classified as engineering and seismic bedrock in itself. In these descriptions, S-wave velocity is (Vs) used as a base. The mediums are called soil where the Vs is < 760 m/s, the bigger ones are called bedrock as well. Additionally, the parts are called engineering bedrock where the Vs is between 3000 m/s and 760 m/s, the parts where are bigger than 3000 m/s called seismic bedrock. The interfacial's horizontal topography where is between engineering and seismic bedrock is effective on earthquake's effect changing on the soil surface. That's why, 2D soil-bedrock models must be used to estimate the earthquake effect that could occur on the soil surface. In this research, surface wave methods and microgravity method were used for occuring the 2D soil-bedrock models in the east of İzmir bay. In the first stage, velocity values were obtained by the studies using surface wave methods. Then, density values were calculated from these velocity values by the help of the empiric relations. 2D soil-bedrock models were occurred based upon both Vs and changing of density by using these density values in microgravity model. When evaluating the models, it was determined that the soil is 300-400 m thickness and composed of more than one layers in parts where are especially closer to the bay. Moreover, it was observed that the soil thickness changes in the direction of N-S. In the study area, geologically, it should be thought the engineering bedrock is composed of Bornova melange and seismic bedrock unit is composed of Menderes massif. Also, according to the geophysical results, Neogene limestone and andesite units at between 200 and 400 m depth show that engineering bedrock characteristic.
Sparsity and level set regularization for diffuse optical tomography using a transport model in 2D
NASA Astrophysics Data System (ADS)
Prieto, Kernel; Dorn, Oliver
2017-01-01
In this paper we address an inverse problem for the time-dependent linear transport equation (or radiative transfer equation) in 2D having in mind applications in diffuse optical tomography (DOT). We propose two new reconstruction algorithms which so far have not been applied to such a situation and compare their performances in certain practically relevant situations. The first of these reconstruction algorithms uses a sparsity promoting regularization scheme, whereas the second one uses a simultaneous level set reconstruction scheme for two parameters of the linear transport equation. We will also compare the results of both schemes with a third scheme which is a more traditional L 2-based Landweber-Kaczmarz scheme. We focus our attention on the DOT application of imaging the human head of a neonate where the simpler diffusion approximation is not well-suited for the inversion due to the presence of a clear layer beneath the skull which is filled with ‘low-scattering’ cerebrospinal fluid. This layer, even if its location and characteristics are known a priori, poses significant difficulties for most reconstruction schemes due to its ‘wave-guiding’ property which reduces sensitivity of the data to the interior regions. A further complication arises due to the necessity to reconstruct simultaneously two different parameters of the linear transport equation, the scattering and the absorption cross-section, from the same data set. A significant ‘cross-talk’ between these two parameters is usually expected. Our numerical experiments indicate that each of the three considered reconstruction schemes do have their merits and perform differently but reasonably well when the clear layer is a priori known. We also demonstrate the behavior of the three algorithms in the particular situation where the clear layer is unknown during the reconstruction.
Kraloua, B.; Hennad, A.
2008-09-23
The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.
NASA Astrophysics Data System (ADS)
Autovino, Dario; Negm, Amro; Rallo, Giovanni; Provenzano, Giuseppe
2016-04-01
In Mediterranean countries characterized by limited water resources for agricultural and societal sectors, irrigation management plays a major role to improve water use efficiency at farm scale, mainly where irrigation systems are correctly designed to guarantee a suitable application efficiency and the uniform water distribution throughout the field. In the last two decades, physically-based agro-hydrological models have been developed to simulate mass and energy exchange processes in the soil-plant-atmosphere (SPA) system. Mechanistic models like HYDRUS 2D/3D (Šimunek et al., 2011) have been proposed to simulate all the components of water balance, including actual crop transpiration fluxes estimated according to a soil potential-dependent sink term. Even though the suitability of these models to simulate the temporal dynamics of soil and crop water status has been reported in the literature for different horticultural crops, a few researches have been considering arboreal crops where the higher gradients of root water uptake are the combination between the localized irrigation supply and the three dimensional root system distribution. The main objective of the paper was to assess the performance of HYDRUS-2D model to evaluate soil water contents and transpiration fluxes of an olive orchard irrigated with two different water distribution systems. Experiments were carried out in Castelvetrano (Sicily) during irrigation seasons 2011 and 2012, in a commercial farm specialized in the production of table olives (Olea europaea L., var. Nocellara del Belice), representing the typical variety of the surrounding area. During the first season, irrigation water was provided by a single lateral placed along the plant row with four emitters per plant (ordinary irrigation), whereas during the second season a grid of emitters laid on the soil was installed in order to irrigate the whole soil surface around the selected trees. The model performance was assessed based on the
Leblanc, M D; Whitehead, J P; Plumer, M L
2013-05-15
A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J' and intergrain exchange J on the ordering temperature T(C) and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.
NASA Astrophysics Data System (ADS)
Leblanc, M. D.; Whitehead, J. P.; Plumer, M. L.
2013-05-01
A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J‧ and intergrain exchange J on the ordering temperature TC and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.
A New Cluster Updating for 2-D SU(2) × SU(2) Chiral Model
NASA Astrophysics Data System (ADS)
Zhang, Jianbo; Ji, Daren
1993-09-01
We propose a variant version of Wolff's cluster algorithm, which may be extended to SU(N) × SU(N) chiral model, and test it in 2-dimensional SU(2) × SU(2) chiral model. The results show that the new method can efficiently reduce the critical slowing down in SU(2) × SU(2) chiral model.
A Cluster Algorithm for the 2-D SU(3) × SU(3) Chiral Model
NASA Astrophysics Data System (ADS)
Ji, Da-ren; Zhang, Jian-bo
1996-07-01
To extend the cluster algorithm to SU(N) × SU(N) chiral models, a variant version of Wolff's cluster algorithm is proposed and tested for the 2-dimensional SU(3) × SU(3) chiral model. The results show that the new method can reduce the critical slowing down in SU(3) × SU(3) chiral model.
Mathematical modelling of submarine landslide motion
NASA Astrophysics Data System (ADS)
Burminskij, A.
2012-04-01
Mathematical modelling of submarine landslide motion The paper presents a mathematical model to calculate dynamic parameters of a submarine landslide. The problem of estimation possible submarine landslides dynamic parameters and run-out distances as well as their effect on submarine structures becomes more and more actual because they can have significant impacts on infrastructure such as the rupture of submarine cables and pipelines, damage to offshore drilling platforms, cause a tsunami. In this paper a landslide is considered as a viscoplastic flow and is described by continuum mechanics equations, averaged over the flow depth. The model takes into account friction at the bottom and at the landslide-water boundary, as well as the involvement of bottom material in motion. A software was created and series of test calculations were performed. Calculations permitted to estimate the contribution of various model coefficients and initial conditions. Motion down inclined bottom was studied both for constant and variable slope angle. Examples of typical distributions of the flow velocity, thickness and density along the landslide body at different stages of motion are given.
Mathematical Modeling of Extinction of Inhomogeneous Populations
Karev, G.P.; Kareva, I.
2016-01-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
2-1/2-D electromagnetic modeling of nodular defects in high-power multilayer optical coatings
Molau, N.E.; Brand, H.R.; Kozlowski, M.R.; Shang, C.C.
1996-07-01
Advances in the design and production of high damage threshold optical coatings for use in mirrors and polarizers have been driven by the design requirements of high-power laser systems such as the proposed 1.8-MJ National Ignition Facility (NIF) and the prototype 12- kJ Beamlet laser system. The present design of the NIF will include 192 polarizers and more than 1100 mirrors. Currently, the material system of choice for high-power multilayer optical coatings with high damage threshold applications near 1.06 {mu}m are e-beam deposited HfO{sub 2}/Si0{sub 2} coatings. However, the optical performance and laser damage thresholds of these coatings are limited by micron-scale defects and insufficient control over layer thickness. In this report, we will discuss the results of our 2-1/2-D finite-element time- domain (FDTD) EM modeling effort for rotationally-symmetric nodular defects in multilayer dielectric HR coatings. We have added a new diagnostic to the 2-1/2-D FDTD EM code, AMOS, that enables us to calculate the peak steady-state electric fields throughout a 2-D planar region containing a 2-D r-z cross-section of the axisymmetric nodular defect and surrounding multilayer dielectric stack. We have also generated a series of design curves to identify the range of loss tangents for Si0{sub 2} and HfO{sub 2} consistent with the experimentally determined power loss of the HR coatings. In addition, we have developed several methods to provide coupling between the EM results and the thermal-mechanical simulation effort.
Calibration of a 1D/1D urban flood model using 1D/2D model results in the absence of field data.
Leandro, J; Djordjević, S; Chen, A S; Savić, D A; Stanić, M
2011-01-01
Recently increased flood events have been prompting researchers to improve existing coupled flood-models such as one-dimensional (1D)/1D and 1D/two-dimensional (2D) models. While 1D/1D models simulate sewer and surface networks using a one-dimensional approach, 1D/2D models represent the surface network by a two-dimensional surface grid. However their application raises two issues to urban flood modellers: (1) stormwater systems planning/emergency or risk analysis demands for fast models, and the 1D/2D computational time is prohibitive, (2) and the recognized lack of field data (e.g. Hunter et al. (2008)) causes difficulties for the calibration/validation of 1D/1D models. In this paper we propose to overcome these issues by calibrating a 1D/1D model with the results of a 1D/2D model. The flood-inundation results show that: (1) 1D/2D results can be used to calibrate faster 1D/1D models, (2) the 1D/1D model is able to map the 1D/2D flood maximum extent well, and the flooding limits satisfactorily in each time-step, (3) the 1D/1D model major differences are the instantaneous flow propagation and overestimation of the flood-depths within surface-ponds, (4) the agreement in the volume surcharged by both models is a necessary condition for the 1D surface-network validation and (5) the agreement of the manholes discharge shapes measures the fitness of the calibrated 1D surface-network.
Mathematical modeling of the coating process.
Toschkoff, Gregor; Khinast, Johannes G
2013-12-05
Coating of tablets is a common unit operation in the pharmaceutical industry. In most cases, the final product must meet strict quality requirements; to meet them, a detailed understanding of the coating process is required. To this end, numerous experiment studies have been performed. However, to acquire a mechanistic understanding, experimental data must be interpreted in the light of mathematical models. In recent years, a combination of analytical modeling and computational simulations enabled deeper insights into the nature of the coating process. This paper presents an overview of modeling and simulation approaches of the coating process, covering various relevant aspects from scale-up considerations to coating mass uniformity investigations and models for drop atomization. The most important analytical and computational concepts are presented and the findings are compared.
Mathematical modelling of hepatic lipid metabolism.
Pratt, Adrian C; Wattis, Jonathan A D; Salter, Andrew M
2015-04-01
The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile. One counter-intuitive observation to arise from simulations is that liver triglyceride initially decreases when a high fat meal is ingested, a phenomenon potentially explained by the carbohydrate portion of the meal raising plasma insulin.
Predictive mathematical models of cancer signalling pathways.
Bachmann, J; Raue, A; Schilling, M; Becker, V; Timmer, J; Klingmüller, U
2012-02-01
Complex intracellular signalling networks integrate extracellular signals and convert them into cellular responses. In cancer cells, the tightly regulated and fine-tuned dynamics of information processing in signalling networks is altered, leading to uncontrolled cell proliferation, survival and migration. Systems biology combines mathematical modelling with comprehensive, quantitative, time-resolved data and is most advanced in addressing dynamic properties of intracellular signalling networks. Here, we introduce different modelling approaches and their application to medical systems biology, focusing on the identifiability of parameters in ordinary differential equation models and their importance in network modelling to predict cellular decisions. Two related examples are given, which include processing of ligand-encoded information and dual feedback regulation in erythropoietin (Epo) receptor signalling. Finally, we review the current understanding of how systems biology could foster the development of new treatment strategies in the context of lung cancer and anaemia.
Mathematical Models of Continuous Flow Electrophoresis
NASA Technical Reports Server (NTRS)
Saville, D. A.; Snyder, R. S.
1985-01-01
Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.
Kolkoori, S R; Rahman, M-U; Chinta, P K; Ktreutzbruck, M; Rethmeier, M; Prager, J
2013-02-01
Ultrasound propagation in inhomogeneous anisotropic materials is difficult to examine because of the directional dependency of elastic properties. Simulation tools play an important role in developing advanced reliable ultrasonic non destructive testing techniques for the inspection of anisotropic materials particularly austenitic cladded materials, austenitic welds and dissimilar welds. In this contribution we present an adapted 2D ray tracing model for evaluating ultrasonic wave fields quantitatively in inhomogeneous anisotropic materials. Inhomogeneity in the anisotropic material is represented by discretizing into several homogeneous layers. According to ray tracing model, ultrasonic ray paths are traced during its energy propagation through various discretized layers of the material and at each interface the problem of reflection and transmission is solved. The presented algorithm evaluates the transducer excited ultrasonic fields accurately by taking into account the directivity of the transducer, divergence of the ray bundle, density of rays and phase relations as well as transmission coefficients. The ray tracing model is able to calculate the ultrasonic wave fields generated by a point source as well as a finite dimension transducer. The ray tracing model results are validated quantitatively with the results obtained from 2D Elastodynamic Finite Integration Technique (EFIT) on several configurations generally occurring in the ultrasonic non destructive testing of anisotropic materials. Finally, the quantitative comparison of ray tracing model results with experiments on 32mm thick austenitic weld material and 62mm thick austenitic cladded material is discussed.
Development of 2D dynamic model for hydrogen-fed and methane-fed solid oxide fuel cells
NASA Astrophysics Data System (ADS)
Luo, X. J.; Fong, K. F.
2016-10-01
A new two-dimensional (2D) dynamic model is developed in Fortran to study the mass and energy transport, the velocity field and the electrochemical phenomena of high-temperature solid oxide fuel cell (SOFC). The key feature of this model is that gas properties, reaction heat, open circuit voltage, ohmic voltage and exchange current density are temperature-dependent. Based on this, the change of gas temperature and related characteristics can be evaluated in this study. The transient performances of SOFC, like heat-up and start-up processes, are therefore assessed accordingly. In this 2D dynamic SOFC model, chemical and electrochemical reaction, flow field, mass and energy transfer models are coupled in order to determine the current density, the mass fraction and the temperature of gas species. Mass, momentum and energy balance equations are discretized by finite difference method. Performance evaluation in current density, electrical efficiency and overall efficiency is conducted for the effects of different operating parameters in SOFC. The present model can serve as a valuable tool for in-depth performance evaluation of other design and operating parameters of SOFC unit, as well as further dynamic simulation and optimization of SOFC as a prime mover in cogeneration or trigeneration system.
NASA Technical Reports Server (NTRS)
Fleming, Eric L.; Jackman, Charles H.; Considine, David B.; Stolarski, Richard S.
1999-01-01
In this study, we examine the sensitivity of long lived tracers to changes in the base transport components in our 2-D model. Changes to the strength of the residual circulation in the upper troposphere and stratosphere and changes to the lower stratospheric K(sub zz) had similar effects in that increasing the transport rates decreased the overall stratospheric mean age, and increased the rate of removal of material from the stratosphere. Increasing the stratospheric K(sub yy) increased the mean age due to the greater recycling of air parcels through the middle atmosphere, via the residual circulation, before returning to the troposphere. However, increasing K(sub yy) along with self-consistent increases in the corresponding planetary wave drive, which leads to a stronger residual circulation, more than compensates for the K(sub yy)-effect, and produces significantly younger ages throughout the stratosphere. Simulations with very small tropical stratospheric K(sub yy) decreased the globally averaged age of air by as much as 25% in the middle and upper stratosphere, and resulted in substantially weaker vertical age gradients above 20 km in the extratropics. We found only very small stratospheric tracer sensitivity to the magnitude of the horizontal mixing across the tropopause, and to the strength of the mesospheric gravity wave drag and diffusion used in the model. We also investigated the transport influence on chemically active tracers and found a strong age-tracer correlation, both in concentration and calculated lifetimes. The base model transport gives the most favorable overall comparison with a variety of inert tracer observations, and provides a significant improvement over our previous 1995 model transport. Moderate changes to the base transport were found to provide modest agreement with some of the measurements. Transport scenarios with residence times ranging from moderately shorter to slightly longer relative to the base case simulated N2O lifetimes
NASA Astrophysics Data System (ADS)
Barker, J. R.; Pasternack, G. B.; Bratovich, P.; Massa, D.; Reedy, G.; Johnson, T.
2010-12-01
Two-dimensional (depth-averaged) hydrodynamic models have existed for decades and are used to study a variety of hydrogeomorphic processes as well as to design river rehabilitation projects. Rapid computer and coding advances are revolutionizing the size and detail of 2D models. Meanwhile, advances in topo mapping and environmental informatics are providing the data inputs to drive large, detailed simulations. Million-element computational meshes are in hand. With simulations of this size and detail, the primary challenge has shifted to finding rapid and inexpensive means for testing model predictions against observations. Standard methods for collecting velocity data include boat-mounted ADCP and point-based sensors on boats or wading rods. These methods are labor intensive and often limited to a narrow flow range. Also, they generate small datasets at a few cross-sections, which is inadequate to characterize the statistical structure of the relation between predictions and observations. Drawing on the long-standing oceanographic method of using drogues to track water currents, previous studies have demonstrated the potential of small dGPS units to obtain surface velocity in rivers. However, dGPS is too inaccurate to test 2D models. Also, there is financial risk in losing drogues in rough currents. In this study, an RTK GPS unit was mounted onto a manned whitewater kayak. The boater positioned himself into the current and used floating debris to maintain a speed and heading consistent with the ambient surface flow field. RTK GPS measurements were taken ever 5 sec. From these positions, a 2D velocity vector was obtained. The method was tested over ~20 km of the lower Yuba River in California in flows ranging from 500-5000 cfs, yielding 5816 observations. To compare velocity magnitude against the 2D model-predicted depth-averaged value, kayak-based surface values were scaled down by an optimized constant (0.72), which had no negative effect on regression analysis
3D/2D model-to-image registration applied to TIPS surgery.
Jomier, Julien; Bullitt, Elizabeth; Van Horn, Mark; Pathak, Chetna; Aylward, Stephen R
2006-01-01
We have developed a novel model-to-image registration technique which aligns a 3-dimensional model of vasculature with two semiorthogonal fluoroscopic projections. Our vascular registration method is used to intra-operatively initialize the alignment of a catheter and a preoperative vascular model in the context of image-guided TIPS (Transjugular, Intrahepatic, Portosystemic Shunt formation) surgery. Registration optimization is driven by the intensity information from the projection pairs at sample points along the centerlines of the model. Our algorithm shows speed, accuracy and consistency given clinical data.
A program for 2D modeling (cross) correlogram tables using fast Fourier transform
NASA Astrophysics Data System (ADS)
Ma, Xianlin; Yao, Tingting
2001-08-01
An alternative to the traditional fitting of analytical correlogram models or of a linear model of coregionalization has been recently proposed, whereby the conditions for permissibility of a set of (cross) correlogram tables are imposed on their Fourier transforms, that is on the corresponding set of (cross) spectrum tables. The resulting model is entirely non-parametric and consists of a set of permissible (cross) correlogram tables from which gridded correlogram values can be read directly. This paper gives the suite of GSLIB-type programs to implement this correlogram modeling approach. Presentation of the program is backed by a case study using actual petroleum reservoir data (porosity and seismic reflection energy).
Mathematical model of laser PUVA psoriasis treatment
NASA Astrophysics Data System (ADS)
Medvedev, Boris A.; Tuchin, Valery V.; Yaroslavsky, Ilya V.
1991-05-01
In order to optimize laser PUVA psoriasis treatment we develop the mathematical model of the dynamics of cell processes within epidermis. We consider epidermis as a structure consisting of N cell monolayers. There are four kinds of cells that correspond to four epidermal strata. The different kinds of cells can exist within a given monolayer. We assume that the following cell processes take place: division, death and transition from one stratum to the following. Discrete transition of cells from stratum j to j + 1 approximates to real differentiation.
Mathematical modelling of risk reduction in reinsurance
NASA Astrophysics Data System (ADS)
Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.
2017-01-01
The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.
A mathematical model of aortic aneurysm formation
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412
Mathematical modeling of human brain physiological data
NASA Astrophysics Data System (ADS)
Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.
2013-12-01
Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.
Mathematical modeling of infectious disease dynamics
Siettos, Constantinos I.; Russo, Lucia
2013-01-01
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814
A mathematical model of aortic aneurysm formation.
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient's aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient's abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material.
Collective Flocking Dynamics: Long Rang Order in a Non-Equilibrium 2D XY Model
NASA Astrophysics Data System (ADS)
Tu, Yuhai
1996-03-01
We propose and study a non-equilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, schools of fishs, etc.) (J. Toner and Y. Tu, Phys. Rev. Lett.), 75(23), 4326(1995) Our model becomes highly non-trivial, and different from the equilibrium model, for d
NASA Astrophysics Data System (ADS)
Filipović, Vilim; Romić, Davor; Romić, Marija; Matijević, Lana; Mallmann, Fábio J. K.; Robinson, David A.
2016-04-01
Growing vegetables commercially requires intensive management and involves high irrigation demands and input of agrochemicals. Plastic mulch application in combination with drip irrigation is a common agricultural management technique practiced due to variety of benefits to the crop, mostly vegetable biomass production. However, the use of these techniques can result in various impacts on water and nutrient distribution in underlying soil and consequently affect nutrient leaching towards groundwater resources. The aim of this work is to estimate the effect of plastic mulch cover in combination with drip irrigation on water and nitrate dynamics in soil using HYDRUS-2D model. The field site was located in Croatian costal karst area on a Gleysol (WRB). The experiment was designed according to the split-plot design in three repetitions and was divided into plots with plastic mulch cover (MULCH) and control plots with bare soil (CONT). Each of these plots received applications of three levels of nitrogen fertilizer: 70, 140, and 210 kg per ha. All plots were equipped with drip irrigation and cropped with bell pepper (Capsicum annuum L. cv. Bianca F1). Lysimeters were installed at 90 cm depth in all plots and were used for monitoring the water and nitrate outflow. HYDRUS-2D was used for modeling the water and nitrogen outflow in the MULCH and CONT plots, implementing the proper boundary conditions. HYDRUS-2D simulated results showed good fitting to the field site observed data in both cumulative water and nitrate outflow, with high level of agreement. Water flow simulations produced model efficiency of 0.84 for CONT and 0.56 for MULCH plots, while nitrate simulations showed model efficiency ranging from 0.67 to 0.83 and from 0.70 to 0.93, respectively. Additional simulations were performed with the absence of the lysimeter, revealing faster transport of nitrates below drip line in the CONT plots, mostly because of the increased surface area subjected to precipitation
A hydrodynamically-consistent MRT lattice Boltzmann model on a 2D rectangular grid
NASA Astrophysics Data System (ADS)
Peng, Cheng; Min, Haoda; Guo, Zhaoli; Wang, Lian-Ping
2016-12-01
A multiple-relaxation time (MRT) lattice Boltzmann (LB) model on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LB model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the Navier-Stokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the two-dimensional decaying Taylor-Green vortex flow and lid-driven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model (Bouzidi et al. (2001) [28]) are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.
A validated 2-D diffusion-advection model for prediction of drift from ground boom sprayers
NASA Astrophysics Data System (ADS)
Baetens, K.; Ho, Q. T.; Nuyttens, D.; De Schampheleire, M.; Melese Endalew, A.; Hertog, M. L. A. T. M.; Nicolaï, B.; Ramon, H.; Verboven, P.
Correct field drift prediction is a key element in environmental risk assessment of spraying applications. A reduced order drift prediction model based on the diffusion-advection equation is presented. It allows fast assessment of the drift potential of specific ground boom applications under specific environmental wind conditions that obey the logarithmic wind profile. The model was calibrated based on simulations with a validated Computational Fluid Dynamics (CFD) model. Validation of both models against 38 carefully conducted field experiments is successfully performed for distances up to 20 m from the field edge, for spraying on flat pasture land. The reduced order model succeeded in correct drift predictions for different nozzle types, wind velocities, boom heights and spray pressures. It used 4 parameters representing the physical aspects of the drift cloud; the height of the cloud at the field edge, the mass flux crossing the field edge, the settling velocity of the droplets and the turbulence. For the parameter set and range considered, it is demonstrated for the first time that the effect of the droplet diameter distribution of the different nozzle types on the amount of deposition spray drift can be evaluated by a single parameter, i.e., the volume fraction of droplets with a diameter smaller than 191 μm. The reduced order model can be solved more than 4 orders of magnitude faster than the comprehensive CFD model.
FireStem2D--a two-dimensional heat transfer model for simulating tree stem injury in fires.
Chatziefstratiou, Efthalia K; Bohrer, Gil; Bova, Anthony S; Subramanian, Ravishankar; Frasson, Renato P M; Scherzer, Amy; Butler, Bret W; Dickinson, Matthew B
2013-01-01
FireStem2D, a software tool for predicting tree stem heating and injury in forest fires, is a physically-based, two-dimensional model of stem thermodynamics that results from heating at the bark surface. It builds on an earlier one-dimensional model (FireStem) and provides improved capabilities for predicting fire-induced mortality and injury before a fire occurs by resolving stem moisture loss, temperatures through the stem, degree of bark charring, and necrotic depth around the stem. We present the results of numerical parameterization and model evaluation experiments for FireStem2D that simulate laboratory stem-heating experiments of 52 tree sections from 25 trees. We also conducted a set of virtual sensitivity analysis experiments to test the effects of unevenness of heating around the stem and with aboveground height using data from two studies: a low-intensity surface fire and a more intense crown fire. The model allows for improved understanding and prediction of the effects of wildland fire on injury and mortality of trees of different species and sizes.
FireStem2D – A Two-Dimensional Heat Transfer Model for Simulating Tree Stem Injury in Fires
Chatziefstratiou, Efthalia K.; Bohrer, Gil; Bova, Anthony S.; Subramanian, Ravishankar; Frasson, Renato P. M.; Scherzer, Amy; Butler, Bret W.; Dickinson, Matthew B.
2013-01-01
FireStem2D, a software tool for predicting tree stem heating and injury in forest fires, is a physically-based, two-dimensional model of stem thermodynamics that results from heating at the bark surface. It builds on an earlier one-dimensional model (FireStem) and provides improved capabilities for predicting fire-induced mortality and injury before a fire occurs by resolving stem moisture loss, temperatures through the stem, degree of bark charring, and necrotic depth around the stem. We present the results of numerical parameterization and model evaluation experiments for FireStem2D that simulate laboratory stem-heating experiments of 52 tree sections from 25 trees. We also conducted a set of virtual sensitivity analysis experiments to test the effects of unevenness of heating around the stem and with aboveground height using data from two studies: a low-intensity surface fire and a more intense crown fire. The model allows for improved understanding and prediction of the effects of wildland fire on injury and mortality of trees of different species and sizes. PMID:23894599
NASA Astrophysics Data System (ADS)
Sheridan, M. F.; Stinton, A. J.; Patra, A.; Pitman, B.; Bauer, A.; Nichita, C.
2003-04-01
The TITAN2D geophysical mass-flow model that is currently under development is evaluated by comparing simulation results with those obtained from another flow model, FLOW3D, and the published data on the 1963 Little Tahoma Peak avalanches on Mount Rainier, Washington. The avalanches, totaling approximately 10 x 106 m3 of brecciated lava flows and other debris, traveled 6.8 km horizontally and fell 1.8 km vertically (H/L = 0.246). Velocities calculated from run up range from 24-42 m/sec and may have been as high as 130 m/sec as the avalanches moved over Emmons Glacier. The avalanches formed a deposit up to 30 m thick. The FLOW3D model uses a sliding block principle to simulate flow movement over a TIN. Results from this model show similarities in terms of velocity history, location of run up areas, run out length and aerial distribution of deposit, although post-avalanche topography in the TIN affects the latter. The TITAN2D model is appropriate for fluid flow in open channels. It is a 2-D, depth-averaged model that uses a raster grid instead of a TIN for the topography. The model flow initiates as a pile defined as an ellipsoid by a height (z) and a radius in the x and y planes. Flow parameters are the internal friction and bed friction angles. Results from this model are promising. Good comparisons can be drawn early during the simulations when the model results fit closely with the mapped extent of the avalanches. However, as the simulated flows move downstream they deviate more from the mapped extent. An area that needs to be addressed is the incorporation of variable bed friction in the model. Simulations done using a low bed friction angle appropriate for movement on the glacier traveled far beyond the limits of the actual deposits, while a high angle suitable for flow over a gravely surface caused the avalanches to stop well short of the mapped limits, never leaving Emmons Glacier. Incorporation of variable bed friction angles into the model using GIS will
Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model
NASA Technical Reports Server (NTRS)
Biegal, Bryan A.; Rafferty, Connor S.; Yu, Zhiping; Ancona, Mario G.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)
1998-01-01
The continued down-scaling of electronic devices, in particular the commercially dominant MOSFET, will force a fundamental change in the process of new electronics technology development in the next five to ten years. The cost of developing new technology generations is soaring along with the price of new fabrication facilities, even as competitive pressure intensifies to bring this new technology to market faster than ever before. To reduce cost and time to market, device simulation must become a more fundamental, indeed dominant, part of the technology development cycle. In order to produce these benefits, simulation accuracy must improve markedly. At the same time, device physics will become more complex, with the rapid increase in various small-geometry and quantum effects. This work describes both an approach to device simulator development and a physical model which advance the effort to meet the tremendous electronic device simulation challenge described above. The device simulation approach is to specify the physical model at a high level to a general-purpose (but highly efficient) partial differential equation solver (in this case PROPHET, developed by Lucent Technologies), which then simulates the model in 1-D, 2-D, or 3-D for a specified device and test regime. This approach allows for the rapid investigation of a wide range of device models and effects, which is certainly essential for device simulation to catch up with, and then stay ahead of, electronic device technology of the present and future. The physical device model used in this work is the density-gradient (DG) quantum correction to the drift-diffusion model [Ancona, Phys. Rev. B 35(5), 7959 (1987)]. This model adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We used the DG model in 1-D and 2-D (for the first time) to simulate both bipolar and unipolar devices. Simulations of heavily-doped, short-base diodes indicated that the DG quantum
Automatic mathematical modeling for real time simulation program (AI application)
NASA Technical Reports Server (NTRS)
Wang, Caroline; Purinton, Steve
1989-01-01
A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.
An efficient numerical model for hydrodynamic parameterization in 2D fractured dual-porosity media
NASA Astrophysics Data System (ADS)
Fahs, Hassane; Hayek, Mohamed; Fahs, Marwan; Younes, Anis
2014-01-01
This paper presents a robust and efficient numerical model for the parameterization of the hydrodynamic in fractured porous media. The developed model is based upon the refinement indicators algorithm for adaptive multi-scale parameterization. For each level of refinement, the Levenberg-Marquardt method is used to minimize the difference between the measured and predicted data that are obtained by solving the direct problem with the mixed finite element method. Sensitivities of state variables with respect to the parameters are calculated by the sensitivity method. The adjoint-state method is used to calculate the local gradients of the objective function necessary for the computation of the refinement indicators. Validity and efficiency of the proposed model are demonstrated by means of several numerical experiments. The developed numerical model provides encouraging results, even for noisy data and/or with a reduced number of measured heads.
A mathematical model of elastic fin micromotors
NASA Astrophysics Data System (ADS)
Lu, Pin; Lee, Kwok Hong; Piang Lim, Siak; Dong, Shuxiang; Zhong Lin, Wu
2000-08-01
In the present work, a simplified mathematical model of ultrasonic elastic fin micromotors has been developed. According to the operating principle of this type of motor, the motions of a rotor in each cycle of the stator vibration are divided into several stages based on whether the fin tip and the stator are in contact with slip, contact without slip or separation. The equations of motion of the rotor in each stage are derived. The valid range of the model has been discussed through numerical examples. This work provides an initial effort to construct a model for the elastic fin motor by considering the dynamical deformation of the rotor as well as the intermittent contacts.
A mathematical model of leptin resistance.
Jacquier, Marine; Soula, Hédi A; Crauste, Fabien
2015-09-01
Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes the dynamics of leptin, leptin receptors and the regulation of food intake and body weight. It displays two stable equilibria, one representing a healthy state and the other one an obese and leptin resistant state. We show that a constant leptin injection can lead to leptin resistance and that a temporal variation in some parameter values influencing food intake can induce a change of equilibrium and a pathway to leptin resistance and obesity.
Estimating 3D movements from 2D observations using a continuous model of helical swimming.
Gurarie, Eliezer; Grünbaum, Daniel; Nishizaki, Michael T
2011-06-01
Helical swimming is among the most common movement behaviors in a wide range of microorganisms, and these movements have direct impacts on distributions, aggregations, encounter rates with prey, and many other fundamental ecological processes. Microscopy and video technology enable the automated acquisition of large amounts of tracking data; however, these data are typically two-dimensional. The difficulty of quantifying the third movement component complicates understanding of the biomechanical causes and ecological consequences of helical swimming. We present a versatile continuous stochastic model-the correlated velocity helical movement (CVHM) model-that characterizes helical swimming with intrinsic randomness and autocorrelation. The model separates an organism's instantaneous velocity into a slowly varying advective component and a perpendicularly oriented rotation, with velocities, magnitude of stochasticity, and autocorrelation scales defined for both components. All but one of the parameters of the 3D model can be estimated directly from a two-dimensional projection of helical movement with no numerical fitting, making it computationally very efficient. As a case study, we estimate swimming parameters from videotaped trajectories of a toxic unicellular alga, Heterosigma akashiwo (Raphidophyceae). The algae were reared from five strains originally collected from locations in the Atlantic and Pacific Oceans, where they have caused Harmful Algal Blooms (HABs). We use the CVHM model to quantify cell-level and strain-level differences in all movement parameters, demonstrating the utility of the model for identifying strains that are difficult to distinguish by other means.
Towards a predictive vortex model for 2D non-linear aerodynamics
NASA Astrophysics Data System (ADS)
Darakananda, Darwin; Eldredge, Jeff D.
2014-11-01
In previous work (Hemati et al 2014), we presented a framework in which a low-order point vortex model can be optimized to capture the non-linear aerodynamics of a wing undergoing arbitrary rigid body motion. Rather than determine the time-varying vortex strengths with the Kutta condition, these strengths were chosen to minimize the difference between the force predicted by the model and pre-existing empirical data. Here, we present ongoing extensions of this model. With the help of tools from dynamical systems theory, we develop a means to incrementally optimize the model against new data. This opens the possibility for using the model in a dynamic estimator context. Self-sustained vortex shedding from wings is achieved using a criterion based on the leading edge suction parameter. We demonstrate the model on a variety of canonical problems, including pitch-up, oscillatory heaving and pitching, and impulsive translation of a plate at various angles of attack. This work has been supported by AFOSR, under Award FA9550-11-1-0098.
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory
Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun
2010-09-15
We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.
Enhanced Kalman Filtering for a 2D CFD NS Wind Farm Flow Model
NASA Astrophysics Data System (ADS)
Doekemeijer, B. M.; van Wingerden, J. W.; Boersma, S.; Pao, L. Y.
2016-09-01
Wind turbines are often grouped together for financial reasons, but due to wake development this usually results in decreased turbine lifetimes and power capture, and thereby an increased levelized cost of energy (LCOE). Wind farm control aims to minimize this cost by operating turbines at their optimal control settings. Most state-of-the-art control algorithms are open-loop and rely on low fidelity, static flow models. Closed-loop control relying on a dynamic model and state observer has real potential to further decrease wind's LCOE, but is often too computationally expensive for practical use. In this paper two time-efficient Kalman filter (KF) variants are outlined incorporating the medium fidelity, dynamic flow model “WindFarmSimulator” (WFSim). This model relies on a discretized set of Navier-Stokes equations in two dimensions to predict the flow in wind farms at low computational cost. The filters implemented are an Ensemble KF and an Approximate KF. Simulations in which a high fidelity simulation model represents the true wind farm show that these filters are 101 —102 times faster than a regular KF with comparable or better performance, correcting for wake dynamics that are not modeled in WFSim (noticeably, wake meandering and turbine hub effects). This is a first big step towards real-time closed-loop control for wind farms.
Multi-level model for 2D human motion analysis and description
NASA Astrophysics Data System (ADS)
Foures, Thomas; Joly, Philippe
2003-01-01
This paper deals with the proposition of a model for human motion analysis in a video. Its main caracteristic is to adapt itself automatically to the current resolution, the actual quality of the picture, or the level of precision required by a given application, due to its possible decomposition into several hierarchical levels. The model is region-based to address some analysis processing needs. The top level of the model is only defined with 5 ribbons, which can be cut into sub-ribbons regarding to a given (or an expected) level of details. Matching process between model and current picture consists in the comparison of extracted subject shape with a graphical rendering of the model built on the base of some computed parameters. The comparison is processed by using a chamfer matching algorithm. In our developments, we intend to realize a platform of interaction between a dancer and tools synthetizing abstract motion pictures and music in the conditions of a real-time dialogue between a human and a computer. In consequence, we use this model in a perspective of motion description instead of motion recognition: no a priori gestures are supposed to be recognized as far as no a priori application is specially targeted. The resulting description will be made following a Description Scheme compliant with the movement notation called "Labanotation".
2013-01-01
Background Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. Methods We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. Results and conclusion As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods. PMID:24267545
Developing mathematical models of neurobehavioral performance for the "real world".
Dean, Dennis A; Fletcher, Adam; Hursh, Steven R; Klerman, Elizabeth B
2007-06-01
Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.
Progress on the development of a 2-D PIC/Monte Carlo model of glow discharges
NASA Astrophysics Data System (ADS)
Greene, A. E.; Faehl, R. J.; Keinigs, R. K.; Oliphant, T. A., Jr.; Shanahan, W. R.
There are several computational approaches that have been and are being implemented for the investigation of plasma processing discharges. One-dimensional electrostatic PIC calculations have proven useful in modeling the bulk properties of discharges far from the edges and have yielded good agreement with experiment for ion distributions in the sheath region. The value of PIC methods is that they follow the evolution of an N-body system unconstrained by equilibrium requirements. Gaseous discharges are in general far from equilibrium. Electrons in the bulk region and ions in the sheath can have energies greatly exceeding the neutral gas temperature and can be distributed in a highly non-Maxwellian fashion. One dimensional models are incapable of treating flow and transport of reactants in reactors properly. Geometrical features are also neglected. Modeling the more recently developed high density reactors, such as the Hitachi ECRH source, requires at least two-dimensional and possibly three-dimensional electromagnetic models. Therefore, at Los Alamos we have chosen to address these problems with the MERLIN code. In this paper we will discuss our progress toward developing this code. We will describe, briefly the physics that we are including in this model. We will discuss a test problem that is being used to exercise most of the new features that have recently been added to MERLIN. Finally, we will discuss our future efforts.
Tropical Oceanic Precipitation Processes Over Warm Pool: 2D and 3D Cloud Resolving Model Simulations
NASA Technical Reports Server (NTRS)
Tao, W.-K.; Johnson, D.; Simpson, J.; Einaudi, Franco (Technical Monitor)
2001-01-01
Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere. The vertical distribution of convective latent-heat release modulates the large-scale circulations of the topics. Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate model simulate processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMs) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and clouds systems. The major objective of this paper is to investigate the latent heating, moisture and momentum budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (GCE) model which includes a 3-class ice-phase microphysics scheme.
Application of a 2D air flow model to soil vapor extraction and bioventing case studies
Mohr, D.H.; Merz, P.H.
1995-05-01
Soil vapor extraction (SVE) is frequently the technology of choice to clean up hydrocarbon contamination in unsaturated soil. A two-dimensional air flow model provides a practical tool to evaluate pilot test data and estimate remediation rates for soil vapor extraction systems. The model predictions of soil vacuum versus distance are statistically compared to pilot test data for 65 SVE wells at 44 sites. For 17 of 21 sites where there was asphalt paving, the best agreement was obtained for boundary conditions with no barrier to air flow at the surface. The model predictions of air flow rates and stream lines around the well allow an estimate of the gasoline removal rates by both evaporation and bioremediation. The model can be used to quickly estimate the effective radius of influence, defined here as the maximum distance from the well where there is enough air flow to remove the contaminant present within the allowable time. The effective radius of influence is smaller than a radius of influence defined by soil vacuum only. For a case study, in situ bioremediation rates were estimated using the air flow model and compared to independent estimates based on changes in soil temperature. These estimate bioremediation rates for heavy fuel oil ranged from 2.5 to 11 mg oil degraded per kg soil per day, in agreement with values in the literature.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
ERIC Educational Resources Information Center
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Calibrating OPC model with full CD profile data for 2D and 3D patterns using scatterometry
NASA Astrophysics Data System (ADS)
Dave, Aasutosh D.; Kritsun, Oleg; Deng, Yunfei; Yoshimoto, Kenji; Li, Jie; Hu, Jiangtao
2009-03-01
The ability to manage critical dimensions (CDs) of structures on IC devices is vital to improving product yield and performance. It is challenging to achieve accurate metrology data as the geometries shrink beyond 40 nm features. At this technology node CDSEM noise and resist LER are of significant concerns1. This paper examines the extendibility of scatterometry techniques to characterize structures that are close to limits of lithographic printing and to extract full profile information for 2D and 3D features for OPC model calibration2. The resist LER concerns are diminished because of the automatic averaging that scatterometry provides over the measurement pad; this represents a significant added value for proper OPC model calibration and verification. This work develops a comparison matrix to determine the impact of scatterometry data on OPC model calibration with conventional CDSEM measurements. The paper will report test results for the OPC model through process data for accuracy and predictability.
Romero, V.J.; Ingber, M.S.
1995-07-01
A numerical model for simulating the transient nonlinear behavior of 2-D viscous sloshing flows in rectangular containers subjected to arbitrary horizontal accelerations is presented. The potential-flow formulation uses Rayleigh damping to approximate the effects of viscosity, and Lagrangian node movement is used to accommodate violent sloshing motions. A boundary element approach is used to efficiently handle the time-changing fluid geometry. Additionally, a corrected equation is presented for the constraint condition relating normal and tangential derivatives of the velocity potential where the fluid free surface meets the rigid container wall. The numerical model appears to be more accurate than previous sloshing models, as determined by comparison against exact analytic solutions and results of previously published models.
ERIC Educational Resources Information Center
Congress of the U.S., Washington, DC. Senate Committee on Labor and Human Resources.
This document contains the transcript of a Senate hearing on the crisis in science and math education. The document includes mathematics, science, and engineering education; enhance the scientific and technical literacy of the U.S. public; stimulate the professional from the state of Oregon; Carl Sagan, Cornell women and minorities in careers in…
Pangolin v1.0, a conservative 2-D transport model for large scale parallel calculation
NASA Astrophysics Data System (ADS)
Praga, A.; Cariolle, D.; Giraud, L.
2014-07-01
To exploit the possibilities of parallel computers, we designed a large-scale bidimensional atmospheric transport model named Pangolin. As the basis for a future chemistry-transport model, a finite-volume approach was chosen both for mass preservation and to ease parallelization. To overcome the pole restriction on time-steps for a regular latitude-longitude grid, Pangolin uses a quasi-area-preserving reduced latitude-longitude grid. The features of the regular grid are exploited to improve parallel performances and a custom domain decomposition algorithm is presented. To assess the validity of the transport scheme, its results are compared with state-of-the-art models on analytical test cases. Finally, parallel performances are shown in terms of strong scaling and confirm the efficient scalability up to a few hundred of cores.
An inexpensive 2-D and 3-D model of the sarcomere as a teaching aid.
Rios, Vitor Passos; Bonfim, Vanessa Maria Gomes
2013-12-01
To address a common problem of teaching the sliding filament theory (that is, students have difficulty in visualizing how the component proteins of the sarcomere differ, how they organize themselves into a single working unit, and how they function in relation to each other), we have devised a simple model, with inexpensive materials, to be built by students in the fourth year of an undergraduate biology course. This model can be quickly built by the students themselves and is functional enough to allow visualization of the filaments and their properties. The model uses cheap, simple materials, mostly party and craft supplies, to simulate the component proteins of the sarcomere, and the proposed materials can be readily replaced by more available ones.
2D modeling of silicon based thin film dual and triple junction solar cells
NASA Astrophysics Data System (ADS)
Xiao, Y. G.; Uehara, K.; Lestrade, M.; Li, Z. Q.; Li, Z. M. S.
2009-08-01
Based on Crosslight APSYS, thin film amorphous Si (a-Si:H)/microcrystalline (μc-Si) dual-junction (DJ) and a- Si:H/amorphous SiGe:H (a-SiGe:H)/μc-Si triple-junction (TJ) solar cells are modeled. Basic physical quantities like band diagrams, optical absorption and generation are obtained. Quantum efficiency and I-V curves for individual junctions are presented for current matching analyses. The whole DJ and TJ cell I-V curves are also presented and the results are discussed with respect to the top surface ZnO:Al TCO layer affinity. The interface texture effect is modeled with FDTD (finite difference time domain) module and results for top junction are presented. The modeling results give possible clues to achieve high efficiency for DJ and TJ thin film solar cells.
Unsteady separation experiments on 2-D airfoils, 3-D wings, and model helicopter rotors
NASA Technical Reports Server (NTRS)
Lorber, Peter F.; Carta, Franklin O.
1992-01-01
Information on unsteady separation and dynamic stall is being obtained from two experimental programs that have been underway at United Technologies Research Center since 1984. The first program is designed to obtain detailed surface pressure and boundary layer condition information during high amplitude pitching oscillations of a large (17.3 in. chord) model wing in a wind tunnel. The second program involves the construction and testing of a pressure-instrumented model helicopter rotor. This presentation describes some of the results of these experiments, and in particular compares the detailed dynamic stall inception information obtained from the oscillating wing with the unsteady separation and reverse flow results measured on the retreating blade side of the model rotor during wind tunnel testing.
Simulating HFIR Core Thermal Hydraulics Using 3D-2D Model Coupling
Travis, Adam R; Freels, James D; Ekici, Kivanc
2013-01-01
A model utilizing interdimensional variable coupling is presented for simulating the thermal hydraulic interactions of the High Flux Isotope Reactor (HFIR) core at Oak Ridge National Laboratory (ORNL). The model s domain consists of a single, explicitly represented three-dimensional fuel plate and a simplified two-dimensional coolant channel slice. In simplifying the coolant channel, and thus the number of mesh points in which the Navier-Stokes equations must be solved, the computational cost and solution time are both greatly reduced. In order for the reduced-dimension coolant channel to interact with the explicitly represented fuel plate, however, interdimensional variable coupling must be enacted along all shared boundaries. The primary focus of this paper is in detailing the collection, storage, passage, and application of variables across this interdimensional interface. Comparisons are made showing the general speed-up associated with this simplified coupled model.
A simple 2-D model for the evolution of an island-arc system
NASA Astrophysics Data System (ADS)
Zharinov, S. E.; Demin, S. S.
1990-07-01
Slow seismotectonic movements along inclined deep fault planes under compressive horizontal stresses are supposed to be the principal mechanism controlling the structure and processes in island-arc systems. In order to treat the stress variations caused by this mechanism, a simple geomechanical model is investigated. We consider a shearing surface crack embedded in a homogeneous elastic half-space. The key element of the model is viscous interaction between the sides of the crack, the viscosity varying with depth. The model differs from the classical steady-state mode of subduction by nonstationary creep processes on deep faults and possibly by cyclical evolution of island-arc systems. The results of our numerical analysis are in good agreement with geological, geophysical and seismological data. (i) Vertical displacements of the free surface in the model fit well with the typical topography of a trench—arc-basement rise—back-arc basin system. (ii) The Benioff seismic zone is supposed to be formed due to the concentration of shear stresses near the fault plane. The characteristic patterns of seismicity, the fine geometry of Benioff zones, and their double-planed structure can be explained in terms of our model. (iii) A zone of considerable heat generation caused by viscous dissipation along the fault plane is found within a narrow area in the depth range 100-200 km. Moreover, the island-arc basement rise is characterized in the model by a relative tension of a few tens or even hundreds of bars, while at depths of 100-150 km below the surface, additional compression of the same order of magnitude acts. The magmatic plumbing system may be visualised as a "toothpaste tube" or a sponge filled with magma which is squeezed from the depths to the surface due to the redistribution of the tectonic stresses only. This can explain the physical origin of island-arc magmatism and the typical position of volcanic belts.
Bindu, G; Semenov, S
2013-01-01
This paper describes an efficient two-dimensional fused image reconstruction approach for Microwave Tomography (MWT). Finite Difference Time Domain (FDTD) models were created for a viable MWT experimental system having the transceivers modelled using thin wire approximation with resistive voltage sources. Born Iterative and Distorted Born Iterative methods have been employed for image reconstruction with the extremity imaging being done using a differential imaging technique. The forward solver in the imaging algorithm employs the FDTD method of solving the time domain Maxwell's equations with the regularisation parameter computed using a stochastic approach. The algorithm is tested with 10% noise inclusion and successful image reconstruction has been shown implying its robustness.
Modeling the kinematics of multi-axial composite laminates as a stacking of 2D TIF plies
NASA Astrophysics Data System (ADS)
Ibañez, Ruben; Abisset-Chavanne, Emmanuelle; Chinesta, Francisco; Huerta, Antonio
2016-10-01
Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to sheet forming of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When the stacking sequence involves plies with different orientations the kinematics of each ply during the laminate deformation varies significantly through the composite thickness. In our former works we considered two different approaches when simulating the squeeze flow induced by the laminate compression, the first based on a penalty formulation and the second one based on the use of Lagrange multipliers. In the present work we propose an alternative approach that consists in modeling each ply involved in the laminate as a transversally isotropic fluid - TIF - that becomes 2D as soon as incompressibility constraint and plane stress assumption are taken into account. Thus, composites laminates can be analyzed as a stacking of 2D TIF models that could eventually interact by using adequate friction laws at the inter-ply interfaces.
Analysis of Projections of the Transfer Matrix in 2d Ising Models
1992-01-01
Review, 60:252-262,263-276, 1941. [Ons44] Lars Onsager . Crystal statistics I. A two-dimensional model with an order-disorder transition. Physical Review...lattices but the subject really came to life in 1944 when Onsager [Ons44] derived an exact closed form expression for the partition ,unction (see below
A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1998-01-01
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
A 2D multiring model of blood flow in elastic arteries
NASA Astrophysics Data System (ADS)
Ghigo, Arthur; Lagrée, Pierre-Yves; Fullana, Jose-Maria
2016-11-01
Three-dimensional simulations of blood flow in elastic arteries are difficult and costly due to the complex fluid-structure interactions between the motion of the fluid and the displacement of the wall. We propose a two-dimensional multiring model to overcome those difficulties and obtain at a reasonable computational cost an asymptotically valid description of blood flow in large elastic arteries. The multiring equations are derived by integrating over concentric rings of fluid a simplified system of equations based on a long wave approximation of the axisymmetric Navier-Stokes equations and a thin-cylinder description of the arterial wall. Contrary to classical one-dimensional models, obtained by integrating the same system over a single ring, the multiring model computes the velocity profile as well as the wall shear stress and requires no a priori estimation of model coefficients. We show that by numerically solving the multiring system of equations, we are able to compute a large range of classical blood flow solutions, ranging from the elastic Womersley solution to the rigid tube Poiseuille solution.
An Inexpensive 2-D and 3-D Model of the Sarcomere as a Teaching Aid
ERIC Educational Resources Information Center
Rios, Vitor Passos; Bonfim, Vanessa Maria Gomes
2013-01-01
To address a common problem of teaching the sliding filament theory (that is, students have difficulty in visualizing how the component proteins of the sarcomere differ, how they organize themselves into a single working unit, and how they function in relation to each other), we have devised a simple model, with inexpensive materials, to be built…
Dynamic Linkages Between the Transition Zone & Surface Plate Motions in 2D Models of Subduction
NASA Astrophysics Data System (ADS)
Arredondo, K.; Billen, M. I.
2013-12-01
While slab pull is considered the dominant force controlling plate motion and speed, its magnitude is controlled by slab behavior in the mantle, where tomographic studies show a wide range of possibilities from direct penetration to folding, or stagnation directly above the lower mantle (e.g. Fukao et al., 2009). Geodynamic studies have investigated various parameters, such as plate age and two phase transitions, to recreate observed behavior (e.g. Běhounková and Cízková, 2008). However, past geodynamic models have left out known slab characteristics that may have a large impact on slab behavior and our understanding of subduction processes. Mineral experiments and seismic observations have indicated the existence of additional phase transitions in the mantle transition zone that may produce buoyancy forces large enough to affect the descent of a subducting slab (e.g. Ricard et al., 2005). The current study systematically tests different common assumptions used in geodynamic models: kinematic versus free-slip boundary conditions, the effects of adiabatic heating, viscous dissipation and latent heat, compositional layering and a more complete suite of phase transitions. Final models have a complete energy equation, with eclogite, harzburgite and pyrolite lithosphere compositional layers, and seven composition-dependent phase transitions within the olivine, pyroxene and garnet polymorph minerals. Results show important feedback loops between different assumptions and new behavior from the most complete models. Kinematic models show slab weakening or breaking above the 660 km boundary and between compositional layers. The behavior in dynamic models with a free-moving trench and overriding plate is compared to the more commonly found kinematic models. The new behavior may have important implications for the depth distribution of deep earthquakes within the slab. Though the thermodynamic parameters of certain phase transitions may be uncertain, their presence and
Accurate 2D/3D electromagnetic modeling for time-domain airborne EM systems
NASA Astrophysics Data System (ADS)
Yin, C.; Hodges, G.
2012-12-01
The existing industry software cannot deliver correct results for 3D time-domain airborne EM responses. In this paper, starting from the Fourier transform and convolution, we compare the stability of different modeling techniques and analyze the reason for instable calculations of the time-domain airborne EM responses. We find that the singularity of the impulse responses of EM systems at very early time that are used in the convolution is responsible for the instability of the modeling (Fig.1). Based on this finding, we put forward an algorithm that uses step response rather than impulse response of the airborne EM system for the convolution and create a stable algorithm that delivers precise results and maintains well the integral/derivative relationship between the magnetic field B and the magnetic induction dB/dt. A three-step transformation procedure for the modeling is proposed: 1) output the frequency-domain EM response data from the existing software; 2) transform into step-response by digital Fourier/Hankel transform; 3) convolve the step response with the transmitting current or its derivatives. The method has proved to be working very well (Fig. 2). The algorithm can be extended to the modeling of other time-domain ground and airborne EM system responses.Fig. 1: Comparison of impulse and step responses for an airborne EM system Fig. 2: Bz and dBz/dt calculated from step (middle panel) and impulse responses (lower panel) for the same 3D model as in Fig.1.
Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method
Waewcharoen, Sribudh; Boonyapibanwong, Supachai; Koonprasert, Sanoe
2008-09-01
One of the most important questions in tsunami modeling is the estimation of tsunami run-up heights at different points along a coastline. Methods for numerical simulation of tsunami wave propagation in deep and shallow seas are well developed and have been widely used by many scientists (2001-2008). In this paper, we consider a two-dimensional nonlinear shallow water model of tsunami given by Tivon Jacobson is work [1]. u{sub t}+uu{sub x}+{nu}u{sub y} -c{sup 2}(h{sub x}+(h{sub b}){sub x}) {nu}{sub t}+u{nu}{sub x}+{nu}{nu}{sub y} = -c{sup 2}(h{sub y}+(h{sub b}){sub y}) h{sub t}+(hu){sub x}+(h{nu}){sub y} = 0 g-shore, h is surface elevation and s, t is time, u is velocity of cross-shore, {nu} is velocity of along-shore, h is surface elevation and h{sub b} is function of shore. This is a nondimensionalized model with the gravity g and constant reference depth H factored into c = {radical}(gH). We apply the Adomian Decompostion Method (ADM) to solve the tsunami model. This powerful method has been used to obtain explicit and numerical solutions of three types of diffusion-convection-reaction (DECR) equations. The ADM results for the tsunami model yield analytical solutions in terms of a rapidly convergent infinite power series. Symbolic computation, numerical results and graphs of solutions are obtained by Maple program.
Artificial neural networks and model-based recognition of 3-D objects from 2-D images
NASA Astrophysics Data System (ADS)
Chao, Chih-Ho; Dhawan, Atam P.
1992-09-01
A computer vision system is developed for 3-D object recognition using artificial neural networks and a knowledge-based top-down feedback analysis system. This computer vision system can adequately analyze an incomplete edge map provided by a low-level processor for 3-D representation and recognition using key features. The key features are selected using a priority assignment and then used in an artificial neural network for matching with model key features. The result of such matching is utilized in generating the model-driven top-down feedback analysis. From the incomplete edge map we try to pick a candidate pattern utilizing the key feature priority assignment. The highest priority is given for the most connected node and associated features. The features are space invariant structures and sets of orientation for edge primitives. These features are now mapped into real numbers. A Hopfield network is then applied with two levels of matching to reduce the search time. The first match is to choose the class of possible model, the second match is then to find the model closest to the data patterns. This model is then rotated in 3-D to find the best match with the incomplete edge patterns and to provide the additional features in 3-D. In the case of multiple objects, a dynamically interconnected search strategy is designed to recognize objects using one pattern at a time. This strategy is also useful in recognizing occluded objects. The experimental results presented show the capability and effectiveness of this system.
Magmatism vs mushmatism: 2D thermo-mechanical modelling of crustal mush processes
NASA Astrophysics Data System (ADS)
Roele, K.; Morgan, J. V.; Jackson, M.
2015-12-01
The concept of 'mushmatism'- that a magma chamber resides in a crystalline state for the majority of its life, has been suggested as a plausible mechanism for observed crustal melt evolution. It is proposed that as melt is generated, its composition evolves as it rises buoyantly, reacting chemically with the surrounding crystal mush at progressively lower temperatures. It is therefore possible to explain formation of granitic melts and observed mafic-felsic layering in the crust using mush processes. It has previously been assumed that a high influx rate of molten material is required for large volumes of crustal melt to be produced. This has been modelled in the past with repetitive sill intrusion at unrealistically high rates (>3x107 m3a-1) to cause a large enough thermal perturbation of the geotherm to sustain eruptible melt in the shallow crust. However, these models are purely thermal and neglect the effects of melt segregation and mush processes on longevity of melt volumes in the crust. We have developed an axisymmetric thermo-mechanical model that includes mass transport described by coupled matrix compaction and buoyant melt segregation during repeated sill intrusion. Results are consistent with thermal models in that they demonstrate dominance of crystalline mush processes in the transient magma chamber at low-to-moderate intrusion rates. However, addition of buoyant segregation leads to formation of discrete high melt fraction layers as melt ascends through the emplacement zone. This causes a decoupling in location of maximum temperature and melt fraction not observed by purely thermal models. Our results therefore have significant implications for current methods of interpretation of geophysical data, in particular, calculating melt volumes and determining the depth of the magma chamber. In addition, transient reservoirs are produced at lower emplacement rates by the thermo-mechanical model because accumulated magma is evolved and able to remain liquid
Modeling and characterization of 2-D and 3-D textile structural composites
Yang, J.M.
1986-01-01
This dissertation studies the analytical modeling and experimental characterization of various two-dimensional and three-dimensional textile structure composites. In the analytical approach, various theoretical models were established to predict the stiffness, strength, nonlinear deformation, and failure behavior of triaxial woven-fabric composites, 3-D braided composites, and multilayer multidirectional warp knit fabric composites in polymer and metal matrices. The structure performance maps of various textile structural composites were also established, based upon these analytical methods. In the experimental approach, extensive mechanical testing and microstructural characterization were performed to investigate the thermomechanical properties and failure behavior of 3-D braided FP/Al composites. Results of this research will serve as the basis for assessing the potential of textile composites for structural applications.
Delocalization of two interacting particles in the 2D Harper model
NASA Astrophysics Data System (ADS)
Frahm, Klaus M.; Shepelyansky, Dima L.
2016-01-01
We study the problem of two interacting particles in a two-dimensional quasiperiodic potential of the Harper model. We consider an amplitude of the quasiperiodic potential such that in absence of interactions all eigenstates are exponentially localized while the two interacting particles are delocalized showing anomalous subdiffusive spreading over the lattice with the spreading exponent b ≈ 0.5 instead of a usual diffusion with b = 1. This spreading is stronger than in the case of a correlated disorder potential with a one particle localization length as for the quasiperiodic potential. At the same time we do not find signatures of ballistic pairs existing for two interacting particles in the localized phase of the one-dimensional Harper model.
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation
Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...
1995-01-01
In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less
Critical Casimir forces between defects in the 2D Ising model
NASA Astrophysics Data System (ADS)
Nowakowski, P.; Maciołek, A.; Dietrich, S.
2016-12-01
An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.
A 2D Particle in Cell model for ion extraction and focusing in electrostatic accelerators.
Veltri, P; Cavenago, M; Serianni, G
2014-02-01
Negative ions are fundamental to produce intense and high energy neutral beams used to heat the plasma in fusion devices. The processes regulating the ion extraction involve the formation of a sheath on a scale comparable to the Debye length of the plasma. On the other hand, the ion acceleration as a beam is obtained on distances greater than λD. The paper presents a model for both the phases of ion extraction and acceleration of the ions and its implementation in a numerical code. The space charge of particles is deposited following usual Particle in Cell codes technique, while the field is solved with finite element methods. Some hypotheses on the beam plasma transition are described, allowing to model both regions at the same time. The code was tested with the geometry of the NIO1 negative ions source, and the results are compared with existing ray tracing codes and discussed.
A Survey on Model Based Approaches for 2D and 3D Visual Human Pose Recovery
Perez-Sala, Xavier; Escalera, Sergio; Angulo, Cecilio; Gonzàlez, Jordi
2014-01-01
Human Pose Recovery has been studied in the field of Computer Vision for the last 40 years. Several approaches have been reported, and significant improvements have been obtained in both data representation and model design. However, the problem of Human Pose Recovery in uncontrolled environments is far from being solved. In this paper, we define a general taxonomy to group model based approaches for Human Pose Recovery, which is composed of five main modules: appearance, viewpoint, spatial relations, temporal consistence, and behavior. Subsequently, a methodological comparison is performed following the proposed taxonomy, evaluating current SoA approaches in the aforementioned five group categories. As a result of this comparison, we discuss the main advantages and drawbacks of the reviewed literature. PMID:24594613
Stability of Solitary Waves and Vortices in a 2D Nonlinear Dirac Model.
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G; Saxena, Avadh; Comech, Andrew; Lan, Ruomeng
2016-05-27
We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These conclusions are found not to be restricted to the case of cubic two-dimensional nonlinearities but are found to be extended to the case of quintic nonlinearity, as well as to that of three spatial dimensions. Our results also reveal nontrivial differences with respect to the better understood nonrelativistic analogue of the model, namely the nonlinear Schrödinger equation.
Carbonate fracture stratigraphy: An integrated outcrop and 2D discrete element modelling study
NASA Astrophysics Data System (ADS)
Spence, Guy; Finch, Emma
2013-04-01
Constraining fracture stratigraphy is important as natural fractures control primary fluid flow in low matrix permeability naturally fractured carbonate hydrocarbon reservoirs. Away from the influence of folds and faults, stratigraphic controls are known to be the major control on fracture networks. The fracture stratigraphy of carbonate nodular-chert rhythmite successions are investigated using a Discrete Element Modelling (DEM) technique and validated against observations from outcrops. Comparisons are made to the naturally fractured carbonates of the Eocene Thebes Formation exposed in the west central Sinai of Egypt, which form reservoir rocks in the nearby East Ras Budran Field. DEM allows mechanical stratigraphy to be defined as the starting conditions from which forward numerical modelling can generate fracture stratigraphy. DEM can incorporate both stratigraphic and lateral heterogeneity, and enable mechanical and fracture stratigraphy to be characterised separately. Stratally bound stratified chert nodules below bedding surfaces generate closely spaced lateral heterogeneity in physical properties at stratigraphic mechanical interfaces. This generates extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. A series of representative geologically appropriate synthetic mechanical stratigraphic models were tested. Fracture networks generated in 15 DEM experiments designed to isolate and constrain the effects of nodular chert rhythmites on carbonate fracture stratigraphy are presented. The discrete element media used to model the elastic strengths of rocks contain 72,866 individual elements. Mechanical stratigraphies and the fracture networks generated are placed in a sequence stratigraphic framework. Nodular chert rhythmite successions are shown to be a distinct type of naturally fractured carbonate reservoir. Qualitative stratigraphic rules for predicting the distribution, lengths, spacing
A hierarchical lattice spring model to simulate the mechanics of 2-D materials-based composites
NASA Astrophysics Data System (ADS)
Brely, Lucas; Bosia, Federico; Pugno, Nicola
2015-07-01
In the field of engineering materials, strength and toughness are typically two mutually exclusive properties. Structural biological materials such as bone, tendon or dentin have resolved this conflict and show unprecedented damage tolerance, toughness and strength levels. The common feature of these materials is their hierarchical heterogeneous structure, which contributes to increased energy dissipation before failure occurring at different scale levels. These structural properties are the key to exceptional bioinspired material mechanical properties, in particular for nanocomposites. Here, we develop a numerical model in order to simulate the mechanisms involved in damage progression and energy dissipation at different size scales in nano- and macro-composites, which depend both on the heterogeneity of the material and on the type of hierarchical structure. Both these aspects have been incorporated into a 2-dimensional model based on a Lattice Spring Model, accounting for geometrical nonlinearities and including statistically-based fracture phenomena. The model has been validated by comparing numerical results to continuum and fracture mechanics results as well as finite elements simulations, and then employed to study how structural aspects impact on hierarchical composite material properties. Results obtained with the numerical code highlight the dependence of stress distributions on matrix properties and reinforcement dispersion, geometry and properties, and how failure of sacrificial elements is directly involved in the damage tolerance of the material. Thanks to the rapidly developing field of nanocomposite manufacture, it is already possible to artificially create materials with multi-scale hierarchical reinforcements. The developed code could be a valuable support in the design and optimization of these advanced materials, drawing inspiration and going beyond biological materials with exceptional mechanical properties.
Intermittent Turbulence and SOC Dynamics in a 2-D Driven Current-Sheet Model
NASA Technical Reports Server (NTRS)
Klimas, A. J.; Uritsky, V.; Vinas, A. F.; Vassiliasdis, D.; Baker, D. N.
2005-01-01
Borovsky et al. have shown that Earth's magnetotail plasma sheet is strongly turbulent. More recently, Borovsky and Funsten have shown that eddy turbulence dominates and have suggested that the eddy turbulence is driven by fast flows that act as jets in the plasma. Through basic considerations of energy and magnetic flux conservation, these fast flows are thought to be localized to small portions of the total plasma sheet and to be generated by magnetic flux reconnection that is similarly localized. Angelopoulos et al., using single spacecraft Geotail data, have shown that the plasma sheet turbulence exhibits signs of intermittence and Weygand et al., using four spacecraft Cluster data, have confirmed and expanded on this conclusion. Uritsky et al., using Polar UVI image data, have shown that the evolution of bright, nightside, UV auroral emission regions is consistent with many of the properties of systems in self-organized criticality (SOC). Klimas et al. have suggested that the auroral dynamics is a reflection of the dynamics of the fast flows in the plasma. sheet. Their hypothesis is that the transport of magnetic fludenergy through the magnetotail is enabled by scale-free avalanches of localized reconnection whose SOC dynamics are reflected in the auroral UV emission dynamics. A corollary of this hypothesis is that the strong, intermittent, eddy turbulence of the plasma sheet is closely related to its critical dynamics. The question then arises: Can in situ evidence for the SOC dynamics be found in the properties of the plasma sheet turbulence? A 2-dimensional numerical driven current-sheet model of the central plasma sheet has been developed that incorporates an idealized current-driven instability with a resistive MHD system. It has been shown that the model can evolve into SOC in a physically relevant parameter regime. Initial results from a study of intermittent turbulence in this model and the relationship of this turbulence to the model's known SOC
Region-Based Feature Interpretation for Recognizing 3D Models in 2D images
1991-06-01
Likewise, if two model lines are colinear or are connected at their endpoints, they must do the same in the image (again, within some bounds, to account...not well defined. Is a flowerpot part of the plant object? The answer depends on the vision task, and even then may be ambiguous or allow overlapping...However, not all have been tried, either in psychological tests or in vision systems. Proximity: Features are close to each other. Edge Connectivity
Mathematical modeling of a thermovoltaic cell
NASA Technical Reports Server (NTRS)
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Missing the Promise of Mathematical Modeling
ERIC Educational Resources Information Center
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Teaching Mathematical Modelling for Earth Sciences via Case Studies
NASA Astrophysics Data System (ADS)
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Using a Functional Model to Develop a Mathematical Formula
ERIC Educational Resources Information Center
Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.
2008-01-01
The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…
NASA Astrophysics Data System (ADS)
Yu, Ting; Chaix, Jean-François; Komatitsch, Dimitri; Garnier, Vincent; Audibert, Lorenzo; Henault, Jean-Marie
2017-02-01
Multiple scattering is important when ultrasounds propagate in a heterogeneous medium such as concrete, the scatterer size of which is in the order of the wavelength. The aim of this work is to build a 2D numerical model of ultrasonic wave propagation integrating the multiple scattering phenomena in SPECFEM software. The coherent field of multiple scattering could be obtained by averaging numerical wave fields, and it is used to determine the effective phase velocity and attenuation corresponding to an equivalent homogeneous medium. After the creation of numerical model under several assumptions, its validation is completed in a case of scattering by one cylinder through the comparison with analytical solution. Two cases of multiple scattering by a set of cylinders at different concentrations are simulated to perform a parametric study (of frequency, scatterer concentration, scatterer size). The effective properties are compared with the predictions of Waterman-Truell model as well, to verify its validity.
Mathematical modeling of acid-base physiology
Occhipinti, Rossana; Boron, Walter F.
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697
Superconducting correlations and thermodynamic properties in 2D square and triangular t-J model
NASA Astrophysics Data System (ADS)
Ogata, Masao
2006-03-01
Equal-time superconducting correlation functions of the two-dimensional t-J model on the square lattice are studied using high-temperature expansion method.[1] The sum of the pairing correlation, its spatial dependence and correlation length are obtained down to T ˜0.2t. By comparison of single-particle contributions in the correlation functions, we find effective attractive interactions between quasi-particles in dx^2-y^2-wave channel. It is shown that d-wave correlation grows rapidly at low temperatures for the doping 0.1 < δ< 0.5. The temperature for this growth is roughly scaled by J/2. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there are few numerical evidences of superconductivity. We also study the possible d- and f-wave pairing in the triangular t-J model.[2] When t>0 with hole doping, a rapid growth of effective d-wave paring interaction is found that indicates the resonating-valence-bond superconductivity. In contrast, when t<0, where the ferromagnetic- and antiferromagnetic correlation compete, correlation lengths of the f-wave triplet paring tends to diverge around δ=0.6, although its effective interaction is small. This result is compared and discussed with the recently discovered superconductor, NaxCoO2.yH2O, where Co atoms form a triangular lattice. Specific heat in low temperatures are also obtained in the high-temperature expansion method. We will discuss that the doping dependence of the specific heat coefficient, γ, agrees with experimental data. [1] T. Koretsune and M. Ogata, J. Phys. Soc. Japan 74, 1390 (2005). [2] T. Koretsune and M. Ogata, Phys. Rev. Lett. 89, 116401 (2002), and Phys. Rev. B72, 134513 (2005).
An Asymptotic Analysis of a 2-D Model of Dynamically Active Compartments Coupled by Bulk Diffusion
NASA Astrophysics Data System (ADS)
Gou, J.; Ward, M. J.
2016-08-01
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum-sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling cells of a common small radius ɛ ≪ 1 are coupled through a passive bulk diffusion field. For this coupled system, the method of matched asymptotic expansions is used to construct steady-state solutions and to formulate a spectral problem that characterizes the linear stability properties of the steady-state solutions, with the aim of predicting whether temporal oscillations can be triggered by the cell-bulk coupling. Phase diagrams in parameter space where such collective oscillations can occur, as obtained from our linear stability analysis, are illustrated for two specific choices of the intracellular kinetics. In the limit of very large bulk diffusion, it is shown that solutions to the ODE-PDE cell-bulk system can be approximated by a finite-dimensional dynamical system. This limiting system is studied both analytically, using a linear stability analysis and, globally, using numerical bifurcation software. For one illustrative example of the theory, it is shown that when the number of cells exceeds some critical number, i.e., when a quorum is attained, the passive bulk diffusion field can trigger oscillations through a Hopf bifurcation that would otherwise not occur without the coupling. Moreover, for two specific models for the intracellular dynamics, we show that there are rather wide regions in parameter space where these triggered oscillations are synchronous in nature. Unless the bulk diffusivity is asymptotically large, it is shown that a diffusion-sensing behavior is possible whereby more clustered spatial configurations of cells inside the domain lead to larger regions in parameter space where synchronous collective oscillations between the small cells can occur. Finally, the linear stability analysis for these cell
NASA Astrophysics Data System (ADS)
Mahmood, T.; Shahzad, A.; Iqbal, Z.; Ahmed, J.; Khan, M.
A study is presented for the flow and heat transfer of Sisko fluid model over an unsteady stretching sheet in the presence of uniform magnetic field. While taking newly developed similarity transformations, the governing time dependent partial differential equations are reduced to nonlinear ordinary differential equations. Numerical solutions of the reduced nonlinear differential equations are found by employing Shooting method. The influence of physical parameters of interest on the velocity and temperature profiles are highlighted graphically and examined in detail. Moreover, the skin friction coefficient and Nusselt number are tabulated against influential parameters. Skin friction coefficient increases with unsteadiness parameter, magnetic field and suction parameter.
Incorporating neurophysiological concepts in mathematical thermoregulation models
NASA Astrophysics Data System (ADS)
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
NASA Astrophysics Data System (ADS)
Kasperski, Adam; Rżysko, Wojciech; Szabelski, Paweł
2016-12-01
The ability of capturing guest molecules in a selective way is one of desirable properties of modern structured adsorbents. This refers to a wide class of guest molecules, especially to those which are chiral and whose enantiomers are to be efficiently separated. In this contribution, using Monte Carlo modeling, we show how simple molecular building blocks with cruciform shape can be used to create 2D porous matrices with tunable adsorptive properties. To that end we consider different self-assembled structures comprising cross-shaped molecules and probe their ability to retain model guest molecules differing in size and shape. In particular we focus on the adsorption of enantiomeric pairs on these substrates and quantify the associated selectivity. The obtained results show that a suitable choice of the building block, including size and aspect ratio allows for the creation of 2D functional matrices with programmed adsorption performance. The findings of our theoretical investigations can be helpful in designing molecular guest-host systems with potential applications in separations, sensing and heterogeneous catalysis.
NASA Astrophysics Data System (ADS)
Kalisperakis, I.; Stentoumis, Ch.; Grammatikopoulos, L.; Karantzalos, K.
2015-08-01
The indirect estimation of leaf area index (LAI) in large spatial scales is crucial for several environmental and agricultural applications. To this end, in this paper, we compare and evaluate LAI estimation in vineyards from different UAV imaging datasets. In particular, canopy levels were estimated from i.e., (i) hyperspectral data, (ii) 2D RGB orthophotomosaics and (iii) 3D crop surface models. The computed canopy levels have been used to establish relationships with the measured LAI (ground truth) from several vines in Nemea, Greece. The overall evaluation indicated that the estimated canopy levels were correlated (r2 > 73%) with the in-situ, ground truth LAI measurements. As expected the lowest correlations were derived from the calculated greenness levels from the 2D RGB orthomosaics. The highest correlation rates were established with the hyperspectral canopy greenness and the 3D canopy surface models. For the later the accurate detection of canopy, soil and other materials in between the vine rows is required. All approaches tend to overestimate LAI in cases with sparse, weak, unhealthy plants and canopy.
Competition Among Reputations in the 2D Sznajd Model: Spontaneous Emergence of Democratic States
NASA Astrophysics Data System (ADS)
Crokidakis, Nuno; Forgerini, Fabricio L.
2012-04-01
We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation—a mechanism limiting the agents' persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents' reputation increases for each persuaded neighbor, and case 2, in which the agents' reputation increases for each persuasion and decreases when a neighbor keeps his opinion. Our results show that the introduction of reputation avoids full consensus even for initial densities of up spins greater than 1/2. The relaxation times follow a log-normal-like distribution in both cases, but they are larger in case 2 due to the competition among reputations. In addition, we show that the usual phase transition occurs and depends on the initial concentration d of individuals with the same opinion, but the critical points d c in the two cases are different.
Enhanced Doppler reflectometry power response: physical optics and 2D full wave modelling
NASA Astrophysics Data System (ADS)
Pinzón, J. R.; Happel, T.; Blanco, E.; Conway, G. D.; Estrada, T.; Stroth, U.
2017-03-01
The power response of a Doppler reflectometer is investigated by means of the physical optics model; a simple model which considers basic scattering processes at the reflection layer. Apart from linear and saturated scattering regimes, non-linear regimes with an enhanced backscattered power are found. The different regimes are characterized and understood based on analytical calculations. The power response is also studied with two-dimensional full wave simulations, where the enhanced backscattered power regimes are also found in qualitative agreement with the physical optics results. The ordinary and extraordinary modes are compared for the same angle of incidence, with the conclusion that the ordinary mode is better suited for Doppler reflectometry turbulence level measurements due to the linearity of its response. The scattering efficiency is studied and a first approximation to describe it is proposed. At the end, the application of the physical optics results to experimental data analysis is discussed. In particular, a formula to assess the linearity of Doppler reflectometry measurements is provided.
Phase Diagram of a 2-D Plane Rotator Model with Integer and Half-Integer Vortices
NASA Astrophysics Data System (ADS)
de Souza, Adauto J. F.; Landau, D. P.
1996-03-01
A two-dimensional plane rotator spin model is simulated by employing the single cluster embeding Monte Carlo technique and the re-weighting histogram analysis. The system is described by the Hamiltonian^1 \\cal H = -J1 sum_< i,j > Si \\cdot Sj - J2 sum_< i,j > ( Si \\cdot Sj )^2. In adition to the familiar integer vortices, this model possesses half-integer vortex excitations as well. The system exhibits three low-temperature phases which may be identified by the behavior of suitably defined two-point correlation functions. The half- and integer-vortex densities as a function of temperature are calculated for several values of the parameter α = J_2/J_1. The phase boundaries are determined and the nature of the phase transitions is investigated. Research supported in part by the CNPq and the NSF. Permanent address: Departmento de Física e Matemática, Universidade Federal Rural de Pernambuco, 52171-900, Recife, Pernambuco, Brazil ^1 D.H. Lee and G. Grinstein Phys. Rev. Lett. \\underline55, 541, (1985)
Modeling Selective Local Interactions with Memory: Motion on a 2D Lattice.
Weinberg, Daniel; Levy, Doron
2014-06-15
We consider a system of particles that simultaneously move on a two-dimensional periodic lattice at discrete times steps. Particles remember their last direction of movement and may either choose to continue moving in this direction, remain stationary, or move toward one of their neighbors. The form of motion is chosen based on predetermined stationary probabilities. Simulations of this model reveal a connection between these probabilities and the emerging patterns and size of aggregates. In addition, we develop a reaction diffusion master equation from which we derive a system of ODEs describing the dynamics of the particles on the lattice. Simulations demonstrate that solutions of the ODEs may replicate the aggregation patterns produced by the stochastic particle model. We investigate conditions on the parameters that influence the locations at which particles prefer to aggregate. This work is a two-dimensional generalization of [Galante & Levy, Physica D, http://dx.doi.org/10.1016/j.physd.2012.10.010], in which the corresponding one-dimensional problem was studied.
Manifest: A computer program for 2-D flow modeling in Stirling machines
NASA Technical Reports Server (NTRS)
Gedeon, David
1989-01-01
A computer program named Manifest is discussed. Manifest is a program one might want to use to model the fluid dynamics in the manifolds commonly found between the heat exchangers and regenerators of Stirling machines; but not just in the manifolds - in the regenerators as well. And in all sorts of other places too, such as: in heaters or coolers, or perhaps even in cylinder spaces. There are probably nonStirling uses for Manifest also. In broad strokes, Manifest will: (1) model oscillating internal compressible laminar fluid flow in a wide range of two-dimensional regions, either filled with porous materials or empty; (2) present a graphics-based user-friendly interface, allowing easy selection and modification of region shape and boundary condition specification; (3) run on a personal computer, or optionally (in the case of its number-crunching module) on a supercomputer; and (4) allow interactive examination of the solution output so the user can view vector plots of flow velocity, contour plots of pressure and temperature at various locations and tabulate energy-related integrals of interest.
NASA Astrophysics Data System (ADS)
Sheridan, M. F.; Stinton, A. J.; Patra, A.; Pitman, E. B.; Bauer, A.; Nichita, C. C.
2005-01-01
The Titan2D geophysical mass-flow model is evaluated by comparing its simulation results and those obtained from another flow model, FLOW3D, with published data on the 1963 Little Tahoma Peak avalanches on Mount Rainier, Washington. The avalanches, totaling approximately 10×10 6 m 3 of broken lava blocks and other debris, traveled 6.8 km horizontally and fell 1.8 km vertically ( H/ L=0.246). Velocities calculated from runup range from 24 to 42 m/s and may have been as high as 130 m/s while the avalanches passed over Emmons Glacier. Titan2D is a code for an incompressible Coulomb continuum; it is a depth-averaged, 'shallow-water', granular-flow model. The conservation equations for mass and momentum are solved with a Coulomb-type friction term at the basal interface. The governing equations are solved on multiple processors using a parallel, adaptive mesh, Godunov scheme. Adaptive gridding dynamically concentrates computing power in regions of special interest; mesh refinement and coarsening key on the perimeter of the moving avalanche. The model flow initiates as a pile defined as an ellipsoid by a height ( z) and an elliptical base defined by radii in the x and y planes. Flow parameters are the internal friction angle and bed friction angle. Results from the model are similar in terms of velocity history, lateral spreading, location of runup areas, and final distribution of the Little Tahoma Peak deposit. The avalanches passed over the Emmons Glacier along their upper flow paths, but lower in the valley they traversed stream gravels and glacial outwash deposits. This presents difficulty in assigning an appropriate bed friction angle for the entire deposit. Incorporation of variable bed friction angles into the model using GIS will help to resolve this issue.
NASA Astrophysics Data System (ADS)
Hayden-Lesmeister, A.; Remo, J. W.; Piazza, B.
2015-12-01
The Atchafalaya River (AR) in Louisiana is the principal distributary of the Mississippi River (MR), and its basin contains the largest contiguous area of baldcypress-water tupelo swamp forests in North America. After designation of the Atchafalaya River Basin (ARB) as a federal floodway following the destructive 1927 MR flood, it was extensively modified to accommodate a substantial portion of the MR flow (~25%) to mitigate flooding in southern Louisiana. These modifications and increased flows resulted in substantial incision along large portions of the AR, altering connectivity between the river and its associated waterbodies. As a result of incision, the hydroperiod has been substantially altered, which has contributed to a decline in ecological health of the ARB's baldcypress-water tupelo forests. While it is recognized that the altered hydroperiod has negatively affected natural baldcypress regeneration, it is unclear whether proposed projects designed to enhance flow connectivity will increase long-term survival of these forests. In this study, we have constructed a 1D2D hydrodynamic model using SOBEK 2.12 to realistically model key physical parameters such as residence times, inundation extent, water-surface elevations (WSELs), and flow velocities to increase our understanding of the ARB's altered hydroperiod and the consequences for baldcypress-water tupelo forests. While the model encompasses a majority of the ARB, our modeling effort is focused on the Flat Lake Water Management Unit located in the southern portion of the ARB, where it will also be used to evaluate flow connectivity enhancement projects within the management unit. We believe our 1D2D hybrid hydraulic modeling approach will provide the flexibility and accuracy needed to guide connectivity enhancement efforts in the ARB and may provide a model framework for guiding similar efforts along other highly-altered river systems.
Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D
NASA Astrophysics Data System (ADS)
Tóth, Gyula I.; Tegze, György; Pusztai, Tamás; Tóth, Gergely; Gránásy, László
2010-09-01
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, and determine the line free energy in 2D and the height of the nucleation barrier in 2D and 3D for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that, in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from the sphere to specific faceted shapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic; this anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggregation in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simulations. An oscillatory effective pair potential resembling those for model glass formers has been evaluated from structural data of the amorphous phase obtained by instantaneous quenching. Finally, we present results for eutectic solidification in a binary PFC model.
Subsurface Gas Flow and Ice Grain Acceleration within Enceladus and Europa Fissures: 2D DSMC Models
NASA Astrophysics Data System (ADS)
Tucker, O. J.; Combi, M. R.; Tenishev, V.
2014-12-01
The ejection of material from geysers is a ubiquitous occurrence on outer solar system bodies. Water vapor plumes have been observed emanating from the southern hemispheres of Enceladus and Europa (Hansen et al. 2011, Roth et al. 2014), and N2plumes carrying ice and ark particles on Triton (Soderblom et al. 2009). The gas and ice grain distributions in the Enceladus plume depend on the subsurface gas properties and the geometry of the fissures e.g., (Schmidt et al. 2008, Ingersoll et al. 2010). Of course the fissures can have complex geometries due to tidal stresses, melting, freezing etc., but directly sampled and inferred gas and grain properties for the plume (source rate, bulk velocity, terminal grain velocity) can be used to provide a basis to constrain characteristic dimensions of vent width and depth. We used a 2-dimensional Direct Simulation Monte Carlo (DSMC) technique to model venting from both axi-symmetric canyons with widths ~2 km and narrow jets with widths ~15-40 m. For all of our vent geometries, considered the water vapor source rates (1027 - 1028 s-1) and bulk gas velocities (~330 - 670 m/s) obtained at the surface were consistent with inferred values obtained by fits of the data for the plume densities (1026 - 1028 s-1, 250 - 1000 m/s) respectively. However, when using the resulting DSMC gas distribution for the canyon geometries to integrate the trajectories of ice grains we found it insufficient to accelerate submicron ice grains to Enceladus' escape speed. On the other hand, the gas distributions in the jet like vents accelerated grains > 10 μm significantly above Enceladus' escape speed. It has been suggested that micron-sized grains are ejected from the vents with speeds comparable to the Enceladus escape speed. Here we report on these results including comparisons to results obtained from 1D models as well as discuss the implications of our plume model results. We also show preliminary results for similar considerations applied to Europa
Directional 2D functions as models for fast layout pattern transfer verification
NASA Astrophysics Data System (ADS)
Torres, J. Andres; Hofmann, Mark; Otto, Oberdan
2009-03-01
results are analyzed from the point of view of runtime and matching with respect to a complete verification process that uses full mask data preparation followed by production-quality contour simulations under a variety of process variations, including perturbations to focus, mask bias and exposure. One of the main concerns with using an empirical model is its ability to predict topologies that were not part of the original calibration. While there is indeed a dependency on the model in regard to the data used for calibration, the results indicate that this dependency is weak and that such models are able to provide sufficient accuracy with much more tolerable computation times.
NASA Astrophysics Data System (ADS)
Savin, Daniel
Molecules play an important role in the modern universe where they are a key component for a wide range of sources including diffuse, translucent, and dense molecular clouds; hot cores; photon dominated regions (PDRs); protostellar disks; protoplanetary disks; planetary and satellite ionospheres; cometary comae; and circumstellar envelopes around dying stars. As we strive to improve our understanding of these objects, it is necessary to be able to model and interpret their chemical composition, charge balance, emission and/or absorption spectra, and thermal structure. This, in turn, requires reliable knowledge of the underlying molecular collisions which control these properties. Of particular astrophysical importance is dissociative recombination (DR) which is the primary neutralizing reaction for molecules in cosmic plasmas. For chemical networks involving ion-molecule reactions, this process is often the terminating step for particular synthesis pathways. Knowing branching ratios for final products is critical as they can determine the viability of the pathway in question as well as whether or not a compound can be produced in the gas phase or if unknown surface chemistry must be invoked. The end products of DR may be energetic, in which case they can collisionally heat the plasma. Or they may be in excited states, in which case they can cool the gas through radiative relaxation. Here we propose a series of DR studies for selected ions of importance to the various NASA Astrophysics missions. Our work is designed to improve the DR data used in astrophysical and astrochemical models for the molecular objects listed above and thereby improve our understanding of these sources. We will deepen our understanding of halogen chemistry in the cold interstellar medium (ISM). This will enable the development of new proxies for H2 abundance determinations in the cold ISM. Based on knowledge gained from our previous DR studies, we will extend current models for ISM heating