Modeling and simulation of the flow field in the electrolysis of magnesium

NASA Astrophysics Data System (ADS)

Sun, Ze; Zhang, He-Nan; Li, Ping; Li, Bing; Lu, Gui-Min; Yu, Jian-Guo

2009-05-01

A three-dimensional mathematical model was developed to describe the flow field in the electrolysis cell of the molten magnesium salt, where the model of the three-phase flow was coupled with the electric field force. The mathematical model was validated against the experimental data of the cold model in the electrolysis cell of zinc sulfate with 2 mol/L concentration. The flow field of the cold model was measured by particle image velocimetry, a non-intrusive visualization experimental technique. The flow field in the advanced diaphragmless electrolytic cell of the molten magnesium salt was investigated by the simulations with the mathematical model.

Analysis of spatial thermal field in a magnetic bearing

NASA Astrophysics Data System (ADS)

Wajnert, Dawid; Tomczuk, Bronisław

2018-03-01

This paper presents two mathematical models for temperature field analysis in a new hybrid magnetic bearing. Temperature distributions have been calculated using a three dimensional simulation and a two dimensional one. A physical model for temperature testing in the magnetic bearing has been developed. Some results obtained from computer simulations were compared with measurements.

Mathematical model and software for investigation of internal ballistic processes in high-speed projectile installations

NASA Astrophysics Data System (ADS)

Diachkovskii, A. S.; Zykova, A. I.; Ishchenko, A. N.; Kasimov, V. Z.; Rogaev, K. S.; Sidorov, A. D.

2017-11-01

This paper describes a software package that allows to explore the interior ballistics processes occurring in a shot scheme with bulk charges using propellant pasty substances at various loading schemes, etc. As a mathematical model, a model of a polydisperse mixture of non-deformable particles and a carrier gas phase is used in the quasi-one-dimensional approximation. Writing the equations of the mathematical model allows to use it to describe a broad class of interior ballistics processes. Features of the using approach are illustrated by calculating the ignition period for the charge of tubular propellant.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

Mathematical models for determining the protected spaces of the vertical lightning rod

NASA Technical Reports Server (NTRS)

Mladenovic, I.; Vorgucic, A.

1991-01-01

Two mathematical models are presented for determining the protected spaces of the vertical lightning-rod. In the first model there was applied the circular approximation. Through the introduction of the modified striking distance in the second improved approximation there was obtained a new model for the protected space of the lightning-rod. The models are of general type, foreseen for the three-dimensional space and they are simply applied on solving the practical problems.

Two-Dimensional Versus Three-Dimensional Conceptualization in Astronomy Education

NASA Astrophysics Data System (ADS)

Reynolds, Michael David

Numerous science conceptual issues are naturally three-dimensional. Classroom presentations are often two -dimensional or at best multidimensional. Several astronomy topics are of this nature, e. g. mechanics of the phases of the moon. Textbooks present this three-dimensional topic in two-dimensions; such is often the case in the classroom. This study was conducted to examine conceptions exhibited by pairs of like-sex 11th grade standard physics students as they modeled the lunar phases. Student pairs, 13 male and 13 female, were randomly selected and assigned. Pairing comes closer to classroom emulation, minimizes needs for direct probes, and pair discussion is more likely to display variety and depth. Four hypotheses were addressed: (1) Participants who model three-dimensionally will more likely achieve a higher explanation score. (2) Students who experienced more earth or physical science exposure will more likely model three-dimensionally. (3) Pairs that exhibit a strong science or mathematics preference will more likely model three-dimensionally. (4) Males will model in three dimensions more than females. Students provided background information, including science course exposure and subject preference. Each pair laid out a 16-card set representing two complete lunar phase changes. The pair was asked to explain why the phases occur. Materials were provided for use, including disks, spheres, paper and pen, and flashlight. Activities were videotaped for later evaluation. Statistics of choice was a correlation determination between course preference and model type and ANOVA for the other hypotheses. It was determined that pairs who modeled three -dimensionally achieved a higher score on their phases mechanics explanation at p <.05 level. Pairs with earth science or physical science exposure, those who prefer science or mathematics, and male participants were not more likely to model three-dimensionally. Possible reasons for lack of significance was small sample size and in the case of course preferences, small differences in course preference means. Based on this study, instructors should be aware of dimensionality and student misconceptions. Whenever possible, three-dimensional concepts should be modeled as such. Authors and publishers should consider modeling suggestions and three-dimensional ancillaries.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, Jong Hoon; Faghri, Amir; Chang, Won Soon; Mahefkey, Edward T.

1989-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, J. H.; Faghri, A.; Chang, W. S.; Mahefkey, E. T.

1990-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Xiao, Ruo-Xiu; Zhao, Zhe; Zhang, Li-Hai; Zhang, Li-Cheng; Tang, Pei-Fu

2016-11-01

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse

ERIC Educational Resources Information Center

Straehler-Pohl, Hauke; Gellert, Uwe

2013-01-01

This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein's conceptualisation of power in classification, we develop a three-dimensional model that operationalises the…

Modeling and experimental examination of water level effects on radon exhalation from fragmented uranium ore.

PubMed

Ye, Yong-Jun; Dai, Xin-Tao; Ding, De-Xin; Zhao, Ya-Li

2016-12-01

In this study, a one-dimensional steady-state mathematical model of radon transport in fragmented uranium ore was established according to Fick's law and radon transfer theory in an air-water interface. The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula. We also designed a one-dimensional experimental apparatus for simulating radon diffusion migration in the uranium ore with various water levels to verify the mathematical model. The predicted results were in close agreement with the measured results, suggesting that the proposed model can be readily used to determine radon concentrations and exhalation rates in fragmented uranium ore with varying water levels. Copyright © 2016. Published by Elsevier Ltd.

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise

PubMed Central

Lau, Kevin D.; Asrress, Kaleab N.; Redwood, Simon R.; Figueroa, C. Alberto

2016-01-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. PMID:26945076

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise.

PubMed

Arthurs, Christopher J; Lau, Kevin D; Asrress, Kaleab N; Redwood, Simon R; Figueroa, C Alberto

2016-05-01

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit. Copyright © 2016 the American Physiological Society.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

towards a theory-based multi-dimensional framework for assessment in mathematics: The "SEA" framework

NASA Astrophysics Data System (ADS)

Anku, Sitsofe E.

1997-09-01

Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Quantitative three-dimensional analysis of root canal curvature in maxillary first molars using micro-computed tomography.

PubMed

Lee, Jong-Ki; Ha, Byung-Hyun; Choi, Jeong-Ho; Heo, Seok-Mo; Perinpanayagam, Hiran

2006-10-01

In endodontic therapy, access and instrumentation are strongly affected by root canal curvature. However, the few studies that have actually measured curvature are mostly from two-dimensional radiographs. The purpose of this study was to measure the three-dimensional (3D) canal curvature in maxillary first molars using micro-computed tomography (microCT) and mathematical modeling. Extracted maxillary first molars (46) were scanned by microCT (502 image slices/tooth, 1024 X 1024 pixels, voxel size of 19.5 x 19.5 x 39.0 microm) and their canals reconstructed by 3D modeling software. The intersection of major and minor axes in the canal space of each image slice were connected to create an imaginary central axis for each canal. The radius of curvature of the tangential circle was measured and inverted as a measure of curvature using custom-made mathematical modeling software. Root canal curvature was greatest in the apical third and least in the middle third for all canals. The greatest curvatures were in the mesiobuccal (MB) canal (0.76 +/- 0.48 mm(-1)) with abrupt curves, and the least curvatures were in the palatal (P) canal (0.38 +/- 0.34 mm(-1)) with a gradual curve. This study has measured the 3D curvature of root canals in maxillary first molars and reinforced the value of microCT with mathematical modeling.

Gender Differences in Lunar-Related Scientific and Mathematical Understandings

ERIC Educational Resources Information Center

Wilhelm, Jennifer

2009-01-01

This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle-level students interacted with the Moon through observations, sketching, journalling, two-dimensional and three-dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic…

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Development of mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The data assimilation problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three-dimensional concentration fields from atmospheric diffusion models. General conditions were derived for the reconstructability of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data was developed.

Development of mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three dimensional concentration fields from atmospheric diffusion models. General conditions are derived for the "reconstructability' of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data is developed.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2018-04-01

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.

DNA denaturation through a model of the partition points on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Mejdani, R.; Huseini, H.

1994-08-01

We have shown that by using a model of the partition points gas on a one-dimensional lattice, we can study, besides the saturation curves obtained before for the enzyme kinetics, also the denaturation process, i.e. the breaking of the hydrogen bonds connecting the two strands, under treatment by heat of DNA. We think that this model, as a very simple model and mathematically transparent, can be advantageous for pedagogic goals or other theoretical investigations in chemistry or modern biology.

Dimensional analysis, similarity, analogy, and the simulation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davis, A.A.

1978-01-01

Dimensional analysis, similarity, analogy, and cybernetics are shown to be four consecutive steps in application of the simulation theory. This paper introduces the classes of phenomena which follow the same formal mathematical equations as models of the natural laws and the interior sphere of restraints groups of phenomena in which one can introduce simplfied nondimensional mathematical equations. The simulation by similarity in a specific field of physics, by analogy in two or more different fields of physics, and by cybernetics in nature in two or more fields of mathematics, physics, biology, economics, politics, sociology, etc., appears as a unique theorymore » which permits one to transport the results of experiments from the models, convenably selected to meet the conditions of researches, constructions, and measurements in the laboratories to the originals which are the primary objectives of the researches. Some interesting conclusions which cannot be avoided in the use of simplified nondimensional mathematical equations as models of natural laws are presented. Interesting limitations on the use of simulation theory based on assumed simplifications are recognized. This paper shows as necessary, in scientific research, that one write mathematical models of general laws which will be applied to nature in its entirety. The paper proposes the extent of the second law of thermodynamics as the generalized law of entropy to model life and its activities. This paper shows that the physical studies and philosophical interpretations of phenomena and natural laws cannot be separated in scientific work; they are interconnected and one cannot be put above the others.« less

Modeling of the financial market using the two-dimensional anisotropic Ising model

NASA Astrophysics Data System (ADS)

Lima, L. S.

2017-09-01

We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

Verification and transfer of thermal pollution model. Volume 6: User's manual for 1-dimensional numerical model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter.

Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

ERIC Educational Resources Information Center

Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

2016-01-01

Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

An Invitation to the Mathematics of Topological Quantum Computation

NASA Astrophysics Data System (ADS)

Rowell, E. C.

2016-03-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials.

Projection multiplex recording of computer-synthesised one-dimensional Fourier holograms for holographic memory systems: mathematical and experimental modelling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Betin, A Yu; Bobrinev, V I; Verenikina, N M

A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

NASA Astrophysics Data System (ADS)

Neustupa, Tomáš

2017-07-01

The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

Verification and transfer of thermal pollution model. Volume 4: User's manual for three-dimensional rigid-lid model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Nwadike, E. V.; Sinha, S. E.

1982-01-01

The theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model are described. Model verification at two sites, a separate user's manual for each model are included. The 3-D model has two forms: free surface and rigid lid. The former allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth, estuaries and coastal regions. The latter is suited for small surface wave heights compared to depth because surface elevation was removed as a parameter. These models allow computation of time dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions. The free surface model also provides surface height variations with time.

Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zabaras, Nicolas J.

2016-11-08

Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.

Unsteady flow model for circulation-control airfoils

NASA Technical Reports Server (NTRS)

Rao, B. M.

1979-01-01

An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.

A Long-Term Mathematical Model for Mining Industries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Giraud, Pierre-Noel; Lasry, Jean-Michel

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In somemore » cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.« less

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Use of mathematic modeling to compare and predict hemodynamic effects of the modified Blalock-Taussig and right ventricle-pulmonary artery shunts for hypoplastic left heart syndrome.

PubMed

Bove, Edward L; Migliavacca, Francesco; de Leval, Marc R; Balossino, Rossella; Pennati, Giancarlo; Lloyd, Thomas R; Khambadkone, Sachin; Hsia, Tain-Yen; Dubini, Gabriele

2008-08-01

Stage one reconstruction (Norwood operation) for hypoplastic left heart syndrome can be performed with either a modified Blalock-Taussig shunt or a right ventricle-pulmonary artery shunt. Both methods have certain inherent characteristics. It is postulated that mathematic modeling could help elucidate these differences. Three-dimensional computer models of the Blalock-Taussig shunt and right ventricle-pulmonary artery shunt modifications of the Norwood operation were developed by using the finite volume method. Conduits of 3, 3.5, and 4 mm were used in the Blalock-Taussig shunt model, whereas conduits of 4, 5, and 6 mm were used in the right ventricle-pulmonary artery shunt model. The hydraulic nets (lumped resistances, compliances, inertances, and elastances) were identical in the 2 models. A multiscale approach was adopted to couple the 3-dimensional models with the circulation net. Computer simulations were compared with postoperative catheterization data. Good correlation was found between predicted and observed data. For the right ventricle-pulmonary artery shunt modification, there was higher aortic diastolic pressure, decreased pulmonary artery pressure, lower Qp/Qs ratio, and higher coronary perfusion pressure. Mathematic modeling predicted minimal regurgitant flow in the right ventricle-pulmonary artery shunt model, which correlated with postoperative Doppler measurements. The right ventricle-pulmonary artery shunt demonstrated lower stroke work and a higher mechanical efficiency (stroke work/total mechanical energy). The close correlation between predicted and observed data supports the use of mathematic modeling in the design and assessment of surgical procedures. The potentially damaging effects of a systemic ventriculotomy in the right ventricle-pulmonary artery shunt modification of the Norwood operation have not been analyzed.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

PubMed

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

2015-01-01

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

A new prospect in magnetic nanoparticle-based cancer therapy: Taking credit from mathematical tissue-mimicking phantom brain models.

PubMed

Saeedi, Mostafa; Vahidi, Omid; Goodarzi, Vahabodin; Saeb, Mohammad Reza; Izadi, Leila; Mozafari, Masoud

2017-11-01

Distribution patterns/performance of magnetic nanoparticles (MNPs) was visualized by computer simulation and experimental validation on agarose gel tissue-mimicking phantom (AGTMP) models. The geometry of a complex three-dimensional mathematical phantom model of a cancer tumor was examined by tomography imaging. The capability of mathematical model to predict distribution patterns/performance in AGTMP model was captured. The temperature profile vs. hyperthermia duration was obtained by solving bio-heat equations for four different MNPs distribution patterns and correlated with cell death rate. The outcomes indicated that bio-heat model was able to predict temperature profile throughout the tissue model with a reasonable precision, to be applied for complex tissue geometries. The simulation results on the cancer tumor model shed light on the effectiveness of the studied parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

Verification and transfer of thermal pollution model. Volume 2: User's manual for 3-dimensional free-surface model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Tuann, S. Y.; Lee, C. R.

1982-01-01

The six-volume report: describes the theory of a three-dimensional (3-D) mathematical thermal discharge model and a related one-dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth. These models allow computation of time-dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions.

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Two-dimensional models as testing ground for principles and concepts of local quantum physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schroer, Bert

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated localmore » covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125.« less

Two-dimensional models as testing ground for principles and concepts of local quantum physics

NASA Astrophysics Data System (ADS)

Schroer, Bert

2006-02-01

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff( S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular "Euclideanization" is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an "Encyclopedia of Mathematical Physics" contribution hep-th/0502125.

Improved method for calibration of exchange flows for a physical transport box model of Tampa Bay, FL USA

EPA Science Inventory

Results for both sequential and simultaneous calibration of exchange flows between segments of a 10-box, one-dimensional, well-mixed, bifurcated tidal mixing model for Tampa Bay are reported. Calibrations were conducted for three model options with different mathematical expressi...

Mathematical modeling of transformation process of structurally unstable magnetic configurations into structurally stable ones in two-dimensional and three-dimensional geometry

NASA Astrophysics Data System (ADS)

Inovenkov, Igor; Echkina, Eugenia; Ponomarenko, Loubov

Magnetic reconnection is a fundamental process in astrophysical, space and laboratory plasma. In essence, it represents a change of topology of the magnetic field caused by readjustment of the structure of the magnetic field lines. This change leads to release of energy accumulated in the field. We consider transformation process of structurally unstable magnetic configurations into the structurally steady ones from the point of view of the Catastrophe theory. Special attention is paid to modeling of evolution of the structurally unstable three-dimensional magnetic fields.

Hydrodynamic water impact. [Apollo spacecraft waterlanding

NASA Technical Reports Server (NTRS)

Kettleborough, C. F.

1972-01-01

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Optimization of the lithium/thionyl chloride battery

NASA Technical Reports Server (NTRS)

White, Ralph E.

1987-01-01

The progress which has been made in modeling the lithium/thionyl chloride cell over the past year and proposed research for the coming year are discussed. A one-dimensional mathematical model for a lithium/thionyl chloride cell has been developed and used to investigate methods of improving cell performance. During the course of the work a problem was detected with the banded solver being used. It was replaced with one more reliable. Future work may take one of two directions. The one-dimensional model could be augmented to include additional features and to investigate in more detail the cell temperature behavior, or a simplified two-dimensional model for the spirally wound design of this battery could be developed to investigate the heat flow within the cell.

Feasibility of High Energy Lasers for Interdiction Activities

DTIC Science & Technology

2017-12-01

2.3.2 Power in the Bucket Another parameter we will use in this study is the power-in-the-bucket. The “bucket” is defined as the area on the target we...the heat diffusion equation for a one -dimensional case (where the x-direction is into the target) and assuming a semi-infinite slab of material. The... studied and modeled. One of the approaches to describe these interactions is by making a one -dimensional mathematical model assuming [8]: 1. A semi

Meta-modelling, visualization and emulation of multi-dimensional data for virtual production intelligence

NASA Astrophysics Data System (ADS)

Schulz, Wolfgang; Hermanns, Torsten; Al Khawli, Toufik

2017-07-01

Decision making for competitive production in high-wage countries is a daily challenge where rational and irrational methods are used. The design of decision making processes is an intriguing, discipline spanning science. However, there are gaps in understanding the impact of the known mathematical and procedural methods on the usage of rational choice theory. Following Benjamin Franklin's rule for decision making formulated in London 1772, he called "Prudential Algebra" with the meaning of prudential reasons, one of the major ingredients of Meta-Modelling can be identified finally leading to one algebraic value labelling the results (criteria settings) of alternative decisions (parameter settings). This work describes the advances in Meta-Modelling techniques applied to multi-dimensional and multi-criterial optimization by identifying the persistence level of the corresponding Morse-Smale Complex. Implementations for laser cutting and laser drilling are presented, including the generation of fast and frugal Meta-Models with controlled error based on mathematical model reduction Reduced Models are derived to avoid any unnecessary complexity. Both, model reduction and analysis of multi-dimensional parameter space are used to enable interactive communication between Discovery Finders and Invention Makers. Emulators and visualizations of a metamodel are introduced as components of Virtual Production Intelligence making applicable the methods of Scientific Design Thinking and getting the developer as well as the operator more skilled.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

NASA Astrophysics Data System (ADS)

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies.

PubMed

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

PubMed Central

Lu, Gui-Min; Yu, Jian-Guo

2018-01-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study. PMID:29892347

Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters

NASA Astrophysics Data System (ADS)

Bischi, G. I.; Tramontana, F.

2010-10-01

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka-Volterra prey-predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka-Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka-Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.

Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies

NASA Astrophysics Data System (ADS)

Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration

Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

2014-07-01

Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

A comparison of analog and digital modeling techniques for simulating three-dimensional ground-water flow on Long Island, New York

USGS Publications Warehouse

Reilly, Thomas E.; Harbaugh, Arlen W.

1980-01-01

A three-dimensional electric-analog model of the Long Island, NY , groundwater system constructed by the U.S. Geological Survey in the early 1970 's was used as the basis for developing a digital, three-dimensional finite-difference model. The digital model was needed to provide faster modifications and more rapid solutions to water-management questions. Results generated by the two models are depicted as potentiometric-surface maps of the upper glacial and Magothy aquifers. Results compare favorably for all parts of Long Island except the northwestern part, where hydrologic discontinuities are most prevalent and which the two models represent somewhat differently. The mathematical and hydrologic principles used in development of ground-water models, and the procedures for calibration and acceptance, are presented in nontechnical terms. (USGS)

A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

NASA Astrophysics Data System (ADS)

Prybytak, Dzmitry; Zima, Piotr

2017-12-01

The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

A thermal analysis of a spirally wound battery using a simple mathematical model

NASA Technical Reports Server (NTRS)

Evans, T. I.; White, R. E.

1989-01-01

A two-dimensional thermal model for spirally wound batteries has been developed. The governing equation of the model is the energy balance. Convective and insulated boundary conditions are used, and the equations are solved using a finite element code called TOPAZ2D. The finite element mesh is generated using a preprocessor to TOPAZ2D called MAZE. The model is used to estimate temperature profiles within a spirally wound D-size cell. The model is applied to the lithium/thionyl chloride cell because of the thermal management problems that this cell exhibits. Simplified one-dimensional models are presented that can be used to predict best and worst temperature profiles. The two-dimensional model is used to predict the regions of maximum temperature within the spirally wound cell. Normal discharge as well as thermal runaway conditions are investigated.

Development of an Unstructured, Three-Dimensional Material Response Design Tool

NASA Technical Reports Server (NTRS)

Schulz, Joseph; Stern, Eric; Palmer, Grant; Muppidi, Suman; Schroeder, Olivia

2017-01-01

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. The extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries as well as multi-dimensional physics, which have been shown to be important in some scenarios and are not captured by one-dimensional models. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

NAPL: SIMULATOR DOCUMENTATION

EPA Science Inventory

A mathematical and numerical model is developed to simulate the transport and fate of NAPLs (Non-Aqueous Phase Liquids) in near-surface granular soils. The resulting three-dimensional, three phase simulator is called NAPL. The simulator accommodates three mobile phases: water, NA...

Verification and transfer of thermal pollution model. Volume 3: Verification of 3-dimensional rigid-lid model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.; Sinha, S. K.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter. These models allow computation of time-dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions. The free-surface model also provides surface height variations with time.

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

Modeling and Visualization Process of the Curve of Pen Point by GeoGebra

ERIC Educational Resources Information Center

Aktümen, Muharem; Horzum, Tugba; Ceylan, Tuba

2013-01-01

This study describes the mathematical construction of a real-life model by means of parametric equations, as well as the two- and three-dimensional visualization of the model using the software GeoGebra. The model was initially considered as "determining the parametric equation of the curve formed on a plane by the point of a pen, positioned…

Three-dimensional dynamics of scientific balloon systems in response to sudden gust loadings. [including a computer program user manual

NASA Technical Reports Server (NTRS)

Dorsey, D. R., Jr.

1975-01-01

A mathematical model was developed of the three-dimensional dynamics of a high-altitude scientific research balloon system perturbed from its equilibrium configuration by an arbitrary gust loading. The platform is modelled as a system of four coupled pendula, and the equations of motion were developed in the Lagrangian formalism assuming a small-angle approximation. Three-dimensional pendulation, torsion, and precessional motion due to Coriolis forces are considered. Aerodynamic and viscous damping effects on the pendulatory and torsional motions are included. A general model of the gust field incident upon the balloon system was developed. The digital computer simulation program is described, and a guide to its use is given.

Verification and transfer of thermal pollution model. Volume 5: Verification of 2-dimensional numerical model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorate (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter. These models allow computation of time dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions.

Two dimensional analytical model for a reconfigurable field effect transistor

NASA Astrophysics Data System (ADS)

Ranjith, R.; Jayachandran, Remya; Suja, K. J.; Komaragiri, Rama S.

2018-02-01

This paper presents two-dimensional potential and current models for a reconfigurable field effect transistor (RFET). Two potential models which describe subthreshold and above-threshold channel potentials are developed by solving two-dimensional (2D) Poisson's equation. In the first potential model, 2D Poisson's equation is solved by considering constant/zero charge density in the channel region of the device to get the subthreshold potential characteristics. In the second model, accumulation charge density is considered to get above-threshold potential characteristics of the device. The proposed models are applicable for the device having lightly doped or intrinsic channel. While obtaining the mathematical model, whole body area is divided into two regions: gated region and un-gated region. The analytical models are compared with technology computer-aided design (TCAD) simulation results and are in complete agreement for different lengths of the gated regions as well as at various supply voltage levels.

Applying the Inverse Maximum Ratio- Λ to 3-Dimensional Surfaces

NASA Astrophysics Data System (ADS)

Chandran, Avinash; Brown, Derek; DiPietro, Loretta; Danoff, Jerome

2016-06-01

The question of contour uniformity on a three-dimensional surface arises in various fields of study. Although many questions related to surface uniformity exist, there is a lack of standard methodology to quantify uniformity of a three-dimensional surface. Therefore, a sound mathematical approach to this question could prove to be useful in various areas of study. The purpose of this paper is to expand the previously validated mathematical concept of the inverse maximum ratio over a three-dimensional surface and assess its robustness. We will describe the mathematical approach used to accomplish this and use several simulated examples to validate the metric.

Three-Dimensional Model for Preservation and Restoration of Architectural Heritage

NASA Technical Reports Server (NTRS)

Marchis, Elena

2011-01-01

Thc aim of the research will be to create a model, three-dimensional mathematical. implementation. consultation and assistance to "large" restoration projects that will assist the structural analysis, allowing easier display of dynamic strain. analysis and lighting noise. It could also be a valuable tool for decision support. therefore. may simulate several possible scenarios for intervention, This model appears therefore an excellent support for recovering. ordering and monitoring information about materials and data (stage of restoration. photographs. sampling points. results of diagnostic tests, etc.) collected dynamically during the "life" of the cultural heritage. allowing to document its complete history

Modelling and calculation of flotation process in one-dimensional formulation

NASA Astrophysics Data System (ADS)

Amanbaev, Tulegen; Tilleuov, Gamidulla; Tulegenova, Bibigul

2016-08-01

In the framework of the assumptions of the mechanics of the multiphase media is constructed a mathematical model of the flotation process in the dispersed mixture of liquid, solid and gas phases, taking into account the degree of mineralization of the surface of the bubbles. Application of the constructed model is demonstrated on the example of one-dimensional stationary flotation and it is shown that the equations describing the process of ascent of the bubbles are singularly perturbed ("rigid"). The effect of size and concentration of bubbles and the volumetric content of dispersed particles on the flotation process are analyzed.

Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

NASA Astrophysics Data System (ADS)

Jimbo, Michio

2013-03-01

Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

Chronoamperometric study of the films formed by 4,4'-bipyridyl cation radical salts on mercury in the presence of iodide ions: consecutive two-dimensional phase transitions.

PubMed

Gómez, L; Ruiz, J J; Camacho, L; Rodríguez-Amaro, R

2005-01-04

This paper reports a new mathematical model for consecutive two-dimensional phase transitions that accounts for the chronoamperometric behavior observed in the formation of electrochemical phases by 4,4'-bipyridyl cation radical (BpyH(2)(*)(+)) on mercury in aqueous iodide solutions. Also, a new interpretation for the induction time is proposed.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

An experimental and theoretical evaluation of increased thermal diffusivity phase change devices

NASA Technical Reports Server (NTRS)

White, S. P.; Golden, J. O.; Stermole, F. J.

1972-01-01

This study was to experimentally evaluate and mathematically model the performance of phase change thermal control devices containing high thermal conductivity metal matrices. Three aluminum honeycomb filters were evaluated at five different heat flux levels using n-oct-adecane as the test material. The system was mathematically modeled by approximating the partial differential equations with a three-dimensional implicit alternating direction technique. The mathematical model predicts the system quite well. All of the phase change times are predicted. The heating of solid phase is predicted exactly while there is some variation between theoretical and experimental results in the liquid phase. This variation in the liquid phase could be accounted for by the fact that there are some heat losses in the cell and there could be some convection in the experimental system.

Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

PubMed

Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

2016-08-01

Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.

Computing Reliabilities Of Ceramic Components Subject To Fracture

NASA Technical Reports Server (NTRS)

Nemeth, N. N.; Gyekenyesi, J. P.; Manderscheid, J. M.

1992-01-01

CARES calculates fast-fracture reliability or failure probability of macroscopically isotropic ceramic components. Program uses results from commercial structural-analysis program (MSC/NASTRAN or ANSYS) to evaluate reliability of component in presence of inherent surface- and/or volume-type flaws. Computes measure of reliability by use of finite-element mathematical model applicable to multiple materials in sense model made function of statistical characterizations of many ceramic materials. Reliability analysis uses element stress, temperature, area, and volume outputs, obtained from two-dimensional shell and three-dimensional solid isoparametric or axisymmetric finite elements. Written in FORTRAN 77.

Three Dimensional Flow and Pressure Patterns in a Hydrostatic Journal Bearing

NASA Technical Reports Server (NTRS)

Braun, M. Jack; Dzodzo, Milorad B.

1996-01-01

The flow in a hydrostatic journal bearing (HJB) is described by a mathematical model that uses the three dimensional non-orthogonal form of the Navier-Stokes equations. Using the u, v, w, and p, as primary variables, a conservative formulation, finite volume multi-block method is applied through a collocated, body fitted grid. The HJB has four shallow pockets with a depth/length ratio of 0.067. This paper represents a natural extension to the two and three dimensional studies undertaken prior to this project.

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

One-dimensional cold cap model for melters with bubblers

DOE PAGES

Pokorny, Richard; Hilliard, Zachary J.; Dixon, Derek R.; ...

2015-07-28

The rate of glass production during vitrification in an all-electrical melter greatly impacts the cost and schedule of nuclear waste treatment and immobilization. The feed is charged to the melter on the top of the molten glass, where it forms a layer of reacting and melting material, called the cold cap. During the final stages of the batch-to-glass conversion process, gases evolved from reactions produce primary foam, the growth and collapse of which controls the glass production rate. The mathematical model of the cold cap was revised to include functional representation of primary foam behavior and to account for themore » dry cold cap surface. The melting rate is computed as a response to the dependence of the primary foam collapse temperature on the heating rate and melter operating conditions, including the effect of bubbling on the cold cap bottom and top surface temperatures. The simulation results are in good agreement with experimental data from laboratory-scale and pilot-scale melter studies. Lastly, the cold cap model will become part of the full three-dimensional mathematical model of the waste glass melter.« less

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

3D digital image processing for biofilm quantification from confocal laser scanning microscopy: Multidimensional statistical analysis of biofilm modeling

NASA Astrophysics Data System (ADS)

Zielinski, Jerzy S.

The dramatic increase in number and volume of digital images produced in medical diagnostics, and the escalating demand for rapid access to these relevant medical data, along with the need for interpretation and retrieval has become of paramount importance to a modern healthcare system. Therefore, there is an ever growing need for processed, interpreted and saved images of various types. Due to the high cost and unreliability of human-dependent image analysis, it is necessary to develop an automated method for feature extraction, using sophisticated mathematical algorithms and reasoning. This work is focused on digital image signal processing of biological and biomedical data in one- two- and three-dimensional space. Methods and algorithms presented in this work were used to acquire data from genomic sequences, breast cancer, and biofilm images. One-dimensional analysis was applied to DNA sequences which were presented as a non-stationary sequence and modeled by a time-dependent autoregressive moving average (TD-ARMA) model. Two-dimensional analyses used 2D-ARMA model and applied it to detect breast cancer from x-ray mammograms or ultrasound images. Three-dimensional detection and classification techniques were applied to biofilm images acquired using confocal laser scanning microscopy. Modern medical images are geometrically arranged arrays of data. The broadening scope of imaging as a way to organize our observations of the biophysical world has led to a dramatic increase in our ability to apply new processing techniques and to combine multiple channels of data into sophisticated and complex mathematical models of physiological function and dysfunction. With explosion of the amount of data produced in a field of biomedicine, it is crucial to be able to construct accurate mathematical models of the data at hand. Two main purposes of signal modeling are: data size conservation and parameter extraction. Specifically, in biomedical imaging we have four key problems that were addressed in this work: (i) registration, i.e. automated methods of data acquisition and the ability to align multiple data sets with each other; (ii) visualization and reconstruction, i.e. the environment in which registered data sets can be displayed on a plane or in multidimensional space; (iii) segmentation, i.e. automated and semi-automated methods to create models of relevant anatomy from images; (iv) simulation and prediction, i.e. techniques that can be used to simulate growth end evolution of researched phenomenon. Mathematical models can not only be used to verify experimental findings, but also to make qualitative and quantitative predictions, that might serve as guidelines for the future development of technology and/or treatment.

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

NASA Astrophysics Data System (ADS)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Underwater striling engine design with modified one-dimensional model

NASA Astrophysics Data System (ADS)

Li, Daijin; Qin, Kan; Luo, Kai

2015-09-01

Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.

The Bean model in suprconductivity: Variational formulation and numerical solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prigozhin, L.

The Bean critical-state model describes the penetration of magnetic field into type-II superconductors. Mathematically, this is a free boundary problem and its solution is of interest in applied superconductivity. We derive a variational formulation for the Bean model and use it to solve two-dimensional and axially symmetric critical-state problems numerically. 25 refs., 9 figs., 1 tab.

Research of MPPT for photovoltaic generation based on two-dimensional cloud model

NASA Astrophysics Data System (ADS)

Liu, Shuping; Fan, Wei

2013-03-01

The cloud model is a mathematical representation to fuzziness and randomness in linguistic concepts. It represents a qualitative concept with expected value Ex, entropy En and hyper entropy He, and integrates the fuzziness and randomness of a linguistic concept in a unified way. This model is a new method for transformation between qualitative and quantitative in the knowledge. This paper is introduced MPPT (maximum power point tracking, MPPT) controller based two- dimensional cloud model through analysis of auto-optimization MPPT control of photovoltaic power system and combining theory of cloud model. Simulation result shows that the cloud controller is simple and easy, directly perceived through the senses, and has strong robustness, better control performance.

Modeling snow-crystal growth: a three-dimensional mesoscopic approach.

PubMed

Gravner, Janko; Griffeath, David

2009-01-01

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

Prosthetic avian vocal organ controlled by a freely behaving bird based on a low dimensional model of the biomechanical periphery.

PubMed

Arneodo, Ezequiel M; Perl, Yonatan Sanz; Goller, Franz; Mindlin, Gabriel B

2012-01-01

Because of the parallels found with human language production and acquisition, birdsong is an ideal animal model to study general mechanisms underlying complex, learned motor behavior. The rich and diverse vocalizations of songbirds emerge as a result of the interaction between a pattern generator in the brain and a highly nontrivial nonlinear periphery. Much of the complexity of this vocal behavior has been understood by studying the physics of the avian vocal organ, particularly the syrinx. A mathematical model describing the complex periphery as a nonlinear dynamical system leads to the conclusion that nontrivial behavior emerges even when the organ is commanded by simple motor instructions: smooth paths in a low dimensional parameter space. An analysis of the model provides insight into which parameters are responsible for generating a rich variety of diverse vocalizations, and what the physiological meaning of these parameters is. By recording the physiological motor instructions elicited by a spontaneously singing muted bird and computing the model on a Digital Signal Processor in real-time, we produce realistic synthetic vocalizations that replace the bird's own auditory feedback. In this way, we build a bio-prosthetic avian vocal organ driven by a freely behaving bird via its physiologically coded motor commands. Since it is based on a low-dimensional nonlinear mathematical model of the peripheral effector, the emulation of the motor behavior requires light computation, in such a way that our bio-prosthetic device can be implemented on a portable platform.

Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

PubMed

Adamson, M W; Morozov, A Y; Kuzenkov, O A

2016-09-01

Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2018-03-01

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.

NAPL: SIMULATOR DOCUMENTATION (EPA/600/SR-97/102)

EPA Science Inventory

A mathematical and numerical model is developed to simulate the transport and fate of NAPLs (Non-Aqueous Phase Liquids) in near-surface granular soils. The resulting three-dimensional, three phase simulator is called NAPL. The simulator accommodates three mobile phases: water, NA...

Scaling for Dynamical Systems in Biology.

PubMed

Ledder, Glenn

2017-11-01

Asymptotic methods can greatly simplify the analysis of all but the simplest mathematical models and should therefore be commonplace in such biological areas as ecology and epidemiology. One essential difficulty that limits their use is that they can only be applied to a suitably scaled dimensionless version of the original dimensional model. Many books discuss nondimensionalization, but with little attention given to the problem of choosing the right scales and dimensionless parameters. In this paper, we illustrate the value of using asymptotics on a properly scaled dimensionless model, develop a set of guidelines that can be used to make good scaling choices, and offer advice for teaching these topics in differential equations or mathematical biology courses.

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,…

The experiment of cooperative learning model type team assisted individualization (TAI) on three-dimensional space subject viewed from spatial intelligence

NASA Astrophysics Data System (ADS)

Manapa, I. Y. H.; Budiyono; Subanti, S.

2018-03-01

The aim of this research is to determine the effect of TAI or direct learning (DL) on student’s mathematics achievement viewed from spatial intelligence. This research was quasi experiment. The population was 10th grade senior high school students in Alor Regency on academic year of 2015/2016 chosen by stratified cluster random sampling. The data were collected through achievement and spatial intelligence test. The data were analyzed by two ways, ANOVA with unequal cell and scheffe test. This research showed that student’s mathematics achievement used in TAI had better results than DL models one. In spatial intelligence category, student’s mathematics achievement with high spatial intelligence has better result than the other spatial intelligence category and students with high spatial intelligence have better results than those with middle spatial intelligence category. At TAI, student’s mathematics achievement with high spatial intelligence has better result than those with the other spatial intelligence category and students with middle spatial intelligence have better results than students with low spatial intelligence. In DL model, student’s mathematics achievement with high and middle spatial intelligence has better result than those with low spatial intelligence, but students with high spatial intelligence and middle spatial intelligence have no significant difference. In each category of spatial intelligence and learning model, mathematics achievement has no significant difference.

Thermal Pollution Mathematical Model. Volume 5: User's Manual for Three-Dimensional Rigid-Lid Model. [environment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.; Sinha, S. K.

1980-01-01

A user's manual for a three dimensional, rigid lid model used for hydrothermal predictions of closed basins subjected to a heated discharge together with various other inflows and outflows is presented. The model has the capability to predict (1) wind driven circulation; (2) the circulation caused by inflows and outflows to the domain; and (3) the thermal effects in the domain, and to combine the above processes. The calibration procedure consists of comparing ground truth corrected airborne radiometer data with surface isotherms predicted by the model. The model was verified for accuracy at various sites and results are found to be fairly accurate in all verification runs.

Thermal Pollution Mathematical Model. Volume 6; Verification of Three-Dimensional Free-Surface Model at Anclote Anchorage; [environment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Tuann, S. Y.; Lee, C. R.

1980-01-01

The free-surface model presented is for tidal estuaries and coastal regions where ambient tidal forces play an important role in the dispersal of heated water. The model is time dependent, three dimensional, and can handle irregular bottom topography. The vertical stretching coordinate is adopted for better treatment of kinematic condition at the water surface. The results include surface elevation, velocity, and temperature. The model was verified at the Anclote Anchorage site of Florida Power Company. Two data bases at four tidal stages for winter and summer conditions were used to verify the model. Differences between measured and predicted temperatures are on an average of less than 1 C.

An asymptotic membrane model for wrinkling of very thin films

NASA Astrophysics Data System (ADS)

Battista, Antonio; Hamdouni, Aziz; Millet, Olivier

2018-05-01

In this work, a formal deduction of a two-dimensional membrane theory, similar to Landau-Lifshitz model, is performed via an asymptotic development of the weak formulation of the three-dimensional equations of elasticity. Some interesting aspects of the deduced model are investigated, in particular the property of obtaining a hyperbolic equation for the out-of-plane displacement under a certain class of boundary conditions and loads. Some simple cases are analyzed to show the relevant aspects of the model and the phenomenology that can be addressed. In particular, it is shown how this mathematical formulation is capable to describe instabilities well known as wrinkling, often observed for the buckling of very thin membranes.

Ephaptic conduction in a cardiac strand model with 3D electrodiffusion

PubMed Central

Mori, Yoichiro; Fishman, Glenn I.; Peskin, Charles S.

2008-01-01

We study cardiac action potential propagation under severe reduction in gap junction conductance. We use a mathematical model of cellular electrical activity that takes into account both three-dimensional geometry and ionic concentration effects. Certain anatomical and biophysical parameters are varied to see their impact on cardiac action potential conduction velocity. This study uncovers quantitative features of ephaptic propagation that differ from previous studies based on one-dimensional models. We also identify a mode of cardiac action potential propagation in which the ephaptic and gap-junction-mediated mechanisms alternate. Our study demonstrates the usefulness of this modeling approach for electrophysiological systems especially when detailed membrane geometry plays an important role. PMID:18434544

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

Connecting Functions in Geometry and Algebra

ERIC Educational Resources Information Center

Steketee, Scott; Scher, Daniel

2016-01-01

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

Semianalytical Solutions for Transport in Aquifer and Fractured Clay Matrix System

EPA Science Inventory

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of analytical solutions is derived based on specific initial and boundary conditions as well as ...

Simulation of Power Collection Dynamics for Simply Supported Power Rail

DOT National Transportation Integrated Search

1972-11-01

The mathematical model of a sprung mass moving along a simply supported beam is used to analyze the dynamics of a power-collection system. A computer simulation of one-dimensional motion is used to demonstrate the phenomenon of collector-power rail i...

Towing Tank Tests on a Ram Wing in a Rectangular Guideway

DOT National Transportation Integrated Search

1973-07-01

The object of the study was to set the theoretical and experimental basis for a preliminary design of a ram wing vehicle. A simplified one-dimensional mathematical model is developed in an attempt to estimate the stability derivatives of this type of...

Finite fringe hologram

NASA Technical Reports Server (NTRS)

Heflinger, L. O.

1970-01-01

In holographic interferometry a small movement of apparatus between exposures causes the background of the reconstructed scene to be covered with interference fringes approximately parallel to each other. The three-dimensional quality of the holographic image is allowable since a mathematical model will give the location of the fringes.

SIMPLE METHOD FOR THE REPRESENTATION, QUANTIFICATION, AND COMPARISON OF THE VOLUMES AND SHAPES OF CHEMICAL COMPOUNDS

EPA Science Inventory

A conceptually and computationally simple method for the definition, display, quantification, and comparison of the shapes of three-dimensional mathematical molecular models is presented. Molecular or solvent-accessible volume and surface area can also be calculated. Algorithms, ...

Dynamic behaviour of thin composite plates for different boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprintu, Iuliana, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com

2014-12-10

In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin.more » This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.« less

Modes of self-organization of diluted bubbly liquids in acoustic fields: One-dimensional theory.

PubMed

Gumerov, Nail A; Akhatov, Iskander S

2017-02-01

The paper is dedicated to mathematical modeling of self-organization of bubbly liquids in acoustic fields. A continuum model describing the two-way interaction of diluted polydisperse bubbly liquids and acoustic fields in weakly-nonlinear approximation is studied analytically and numerically in the one-dimensional case. It is shown that the regimes of self-organization of monodisperse bubbly liquids can be controlled by only a few dimensionless parameters. Two basic modes, clustering and propagating shock waves of void fraction (acoustically induced transparency), are identified and criteria for their realization in the space of parameters are proposed. A numerical method for solving of one-dimensional self-organization problems is developed. Computational results for mono- and polydisperse systems are discussed.

Proceedings of the Advanced Seminar on one-dimensional, open-channel Flow and transport modeling

USGS Publications Warehouse

Schaffranek, Raymond W.

1989-01-01

In view of the increased use of mathematical/numerical simulation models, of the diversity of both model investigations and informational project objectives, and of the technical demands of complex model applications by U.S. Geological Survey personnel, an advanced seminar on one-dimensional open-channel flow and transport modeling was organized and held on June 15-18, 1987, at the National Space Technology Laboratory, Bay St. Louis, Mississippi. Principal emphasis in the Seminar was on one-dimensional flow and transport model-implementation techniques, operational practices, and application considerations. The purposes of the Seminar were to provide a forum for the exchange of information, knowledge, and experience among model users, as well as to identify immediate and future needs with respect to model development and enhancement, user support, training requirements, and technology transfer. The Seminar program consisted of a mix of topical and project presentations by Geological Survey personnel. This report is a compilation of short papers that summarize the presentations made at the Seminar.

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

USGS Publications Warehouse

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Mathematical Modeling in Support of Military Operational Medicine

DTIC Science & Technology

2006-07-01

of PBPK models in toxicol- ogy research and chemical risk assessment today is pri- marily related to their ability to make more quantitative ...derived earlier. The biomechanical basis of SFC is established by its correlation with strain. (a) Pretest Scan (b) Posttest Fracture...Three-Dimensional Reconstruction of Pretest and Posttest CT Scans Cited References Vander Vorst, M., Stuhmiller, J., et al., (2003). Biomechanically

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

A numerical solution of the problem of crown forest fire initiation and spread

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires.

Study of Three-Dimensional Pressure-Driven Turbulent Boundary Layer

DTIC Science & Technology

1990-08-31

614)-)) the flow development rate should be comparable with that of the flows used in practice. In the rest of the Chapter, first the governing...to develop these models will be briefly discussed. The available turbulence models used INTRODUCTION 2 for the mathematically closure of the of...equations, assumptions made for each model and the quantities to be measured for the further development of these models are also going to be pointed out

Mathematical methods for protein science

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Prosthetic Avian Vocal Organ Controlled by a Freely Behaving Bird Based on a Low Dimensional Model of the Biomechanical Periphery

PubMed Central

Arneodo, Ezequiel M.; Perl, Yonatan Sanz; Goller, Franz; Mindlin, Gabriel B.

2012-01-01

Because of the parallels found with human language production and acquisition, birdsong is an ideal animal model to study general mechanisms underlying complex, learned motor behavior. The rich and diverse vocalizations of songbirds emerge as a result of the interaction between a pattern generator in the brain and a highly nontrivial nonlinear periphery. Much of the complexity of this vocal behavior has been understood by studying the physics of the avian vocal organ, particularly the syrinx. A mathematical model describing the complex periphery as a nonlinear dynamical system leads to the conclusion that nontrivial behavior emerges even when the organ is commanded by simple motor instructions: smooth paths in a low dimensional parameter space. An analysis of the model provides insight into which parameters are responsible for generating a rich variety of diverse vocalizations, and what the physiological meaning of these parameters is. By recording the physiological motor instructions elicited by a spontaneously singing muted bird and computing the model on a Digital Signal Processor in real-time, we produce realistic synthetic vocalizations that replace the bird's own auditory feedback. In this way, we build a bio-prosthetic avian vocal organ driven by a freely behaving bird via its physiologically coded motor commands. Since it is based on a low-dimensional nonlinear mathematical model of the peripheral effector, the emulation of the motor behavior requires light computation, in such a way that our bio-prosthetic device can be implemented on a portable platform. PMID:22761555

Heat pipe dynamic behavior

NASA Technical Reports Server (NTRS)

Issacci, F.; Roche, G. L.; Klein, D. B.; Catton, I.

1988-01-01

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

Augmented Computer Mouse Would Measure Applied Force

NASA Technical Reports Server (NTRS)

Li, Larry C. H.

1993-01-01

Proposed computer mouse measures force of contact applied by user. Adds another dimension to two-dimensional-position-measuring capability of conventional computer mouse; force measurement designated to represent any desired continuously variable function of time and position, such as control force, acceleration, velocity, or position along axis perpendicular to computer video display. Proposed mouse enhances sense of realism and intuition in interaction between operator and computer. Useful in such applications as three-dimensional computer graphics, computer games, and mathematical modeling of dynamics.

Computational Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Numerical study of propagation of forest fires in the presence of fire breaks using an averaged setting

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

The forest fires spread in the pine forests have been numerically simulated using a three-dimensional mathematical model. The model was integrated with respect to the vertical coordinate because horizontal sizes of forest are much greater than the heights of trees. In this paper, the assignment and theoretical investigations of the problems of crown forest fires spread pass the firebreaks were carried out. In this context, a study ( mathematical modeling) of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with these fire breaks.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements.

PubMed

Liebi, Marianne; Georgiadis, Marios; Kohlbrecher, Joachim; Holler, Mirko; Raabe, Jörg; Usov, Ivan; Menzel, Andreas; Schneider, Philipp; Bunk, Oliver; Guizar-Sicairos, Manuel

2018-01-01

Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebi et al. [Nature (2015), 527, 349-352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.

Macroscopic balance model for wave rotors

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A mathematical model for multi-port wave rotors is described. The wave processes that effect energy exchange within the rotor passage are modeled using one-dimensional gas dynamics. Macroscopic mass and energy balances relate volume-averaged thermodynamic properties in the rotor passage control volume to the mass, momentum, and energy fluxes at the ports. Loss models account for entropy production in boundary layers and in separating flows caused by blade-blockage, incidence, and gradual opening and closing of rotor passages. The mathematical model provides a basis for predicting design-point wave rotor performance, port timing, and machine size. Model predictions are evaluated through comparisons with CFD calculations and three-port wave rotor experimental data. A four-port wave rotor design example is provided to demonstrate model applicability. The modeling approach is amenable to wave rotor optimization studies and rapid assessment of the trade-offs associated with integrating wave rotors into gas turbine engine systems.

A program to assess a thermal discharge on Trinity Bay, Texas

NASA Technical Reports Server (NTRS)

Zaitzeff, J. B.; Whitehead, V. S.

1972-01-01

The application of a two dimensional mathematical model to the analysis of the thermal discharge to verify its ability to predict the temperature distribution of Trinity Bay in the vicinity of the water outfall. Basic data consist of aerial thermal infrared and in situ measurements.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Three-dimensional Reconstruction of Block Shape Irregularity and its Effects on Block Impacts Using an Energy-Based Approach

NASA Astrophysics Data System (ADS)

Zhang, Yulong; Liu, Zaobao; Shi, Chong; Shao, Jianfu

2018-04-01

This study is devoted to three-dimensional modeling of small falling rocks in block impact analysis in energy view using the particle flow method. The restitution coefficient of rockfall collision is introduced from the energy consumption mechanism to describe rockfall-impacting properties. Three-dimensional reconstruction of falling block is conducted with the help of spherical harmonic functions that have satisfactory mathematical properties such as orthogonality and rotation invariance. Numerical modeling of the block impact to the bedrock is analyzed with both the sphere-simplified model and the 3D reconstructed model. Comparisons of the obtained results suggest that the 3D reconstructed model is advantageous in considering the combination effects of rockfall velocity and rotations during colliding process. Verification of the modeling is carried out with the results obtained from other experiments. In addition, the effects of rockfall morphology, surface characteristics, velocity, and volume, colliding damping and relative angle are investigated. A three-dimensional reconstruction modulus of falling blocks is to be developed and incorporated into the rockfall simulation tools in order to extend the modeling results at block scale to slope scale.

Review on experiment-based two- and three-dimensional models for wound healing

PubMed Central

Gefen, Amit

2016-01-01

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers. PMID:27708762

Mathematics reflecting sensorimotor organization.

PubMed

McCollum, Gin

2003-02-01

This review combines short presentations of several mathematical approaches that conceptualize issues in sensorimotor neuroscience from different perspectives and levels of analysis. The intricate organization of neural structures and sensorimotor performance calls for characterization using a variety of mathematical approaches. This review points out the prospects for mathematical neuroscience: in addition to computational approaches, there is a wide variety of mathematical approaches that provide insight into the organization of neural systems. By starting from the perspective that provides the greatest clarity, a mathematical approach avoids specificity that is inaccurate in characterizing the inherent biological organization. Approaches presented include the mathematics of ordered structures, motion-phase space, subject-coincident coordinates, equivalence classes, topological biodynamics, rhythm space metric, and conditional dynamics. Issues considered in this paper include unification of levels of analysis, response equivalence, convergence, relationship of physics to motor control, support of rhythms, state transitions, and focussing on low-dimensional subspaces of a high-dimensional sensorimotor space.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

A New Interpretation of Effects of the Probabilistic Delayed Start on the One-Dimensional Traffic Flow

NASA Astrophysics Data System (ADS)

Ishibashi, Yoshihiro; Fukui, Minoru

2018-03-01

The effect of the probabilistic delayed start on the one-dimensional traffic flow is investigated on the basis of several models. Analogy with the degeneracy of the states and its resolution, as well as that with the mathematical procedures adopted for them, is utilized. The perturbation is assumed to be proportional to the probability of the delayed start, and the perturbation function is determined so that imposed conditions are fulfilled. The obtained formulas coincide with those previously derived on the basis of the mean-field analyses of the Nagel-Schreckenberg and Fukui-Ishibashi models, and reproduce the cellular automaton simulation results.

The Mathematical Modeling and Computer Simulation of Electrochemical Micromachining Using Ultrashort Pulses

NASA Astrophysics Data System (ADS)

Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.

2009-05-01

The need for complex and accurate three dimensional (3-D) microcomponents is increasing rapidly for many industrial and consumer products. Electrochemical machining process (ECM) has the potential of generating desired crack-free and stress-free surfaces of microcomponents. This paper reports a study of pulse electrochemical micromachining (PECMM) using ultrashort (nanoseconds) pulses for generating complex 3-D microstructures of high accuracy. A mathematical model of the microshaping process with taking into consideration unsteady phenomena in electrical double layer has been developed. The software for computer simulation of PECM has been developed and the effects of machining parameters on anodic localization and final shape of machined surface are presented.

DNN-state identification of 2D distributed parameter systems

NASA Astrophysics Data System (ADS)

Chairez, I.; Fuentes, R.; Poznyak, A.; Poznyak, T.; Escudero, M.; Viana, L.

2012-02-01

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

Simulation Components

DTIC Science & Technology

2006-09-01

groupings such as mathematical , 3-dimensional and process models. Furthermore, one must remain aware of the potential to use or reuse models (or...semi-autonomous forces (SAF), intelligent forces (IFOR), command forces (CFOR), command agents (CA) and many more like terms. One way of looking at...the effective use of SEs within Europe. One element of the SEDEP is the use of generalised wording and definitions so as to not be solely dedicated

The Internal/External Frame of Reference Model of Self-Concept and Achievement Relations: Age-Cohort and Cross-Cultural Differences

ERIC Educational Resources Information Center

Marsh, Herbert W.; Abduljabbar, Adel Salah; Parker, Philip D.; Morin, Alexandre J. S.; Abdelfattah, Faisal; Nagengast, Benjamin; Möller, Jens; Abu-Hilal, Maher M.

2015-01-01

The internal/external frame of reference (I/E) model and dimensional comparison theory posit paradoxical relations between achievement (ACH) and self-concept (SC) in mathematics (M) and verbal (V) domains; ACH in each domain positively affects SC in the matching domain (e.g., MACH to MSC) but negatively in the nonmatching domain (e.g., MACH to…

Dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gravitational waves

NASA Astrophysics Data System (ADS)

Rabinovich, B. I.

2006-01-01

The model problem of the dynamics of a planar plasma ring rotating in the dipole magnetic field of a central body is considered. A finite-dimensional mathematical model of the system is synthesized by the Boubnov-Galerkin method. The class of solutions corresponding to magneto-gravitational waves associated with deformations of the ring boundaries is investigated.

Mathematics Hiding in the Nets for a Cube

ERIC Educational Resources Information Center

Jeon, Kyungsoon

2009-01-01

Whether they are third graders or teacher candidates, students can learn about perimeter and area while having fun manipulating two-dimensional figures into three-dimensional objects. In this article, the author describes a common mathematical activity for geometry students by creating nets for a cube. By making connections between nets in two…

Bursting Transition Dynamics Within the Pre-Bötzinger Complex

NASA Astrophysics Data System (ADS)

Duan, Lixia; Chen, Xi; Tang, Xuhui; Su, Jianzhong

The pre-Bötzinger complex of the mammalian brain stem plays a crucial role in the respiratory rhythms generation. Neurons within the pre-Bötzinger complex have been found experimentally to yield different firing activities. In this paper, we study the spiking and bursting activities related to the respiratory rhythms in the pre-Bötzinger complex based on a mathematical model proposed by Butera. Using the one-dimensional first recurrence map induced by dynamics, we investigate the different bursting patterns and their transition of the pre-Bötzinger complex neurons based on the Butera model, after we derived a one-dimensional map from the dynamical characters of the differential equations, and we obtained conditions for the transition of different bursting patterns. These analytical results were verified through numerical simulations. We conclude that the one-dimensional map contains similar rhythmic patterns as the Butera model and can be used as a simpler modeling tool to study fast-slow models like pre-Bötzinger complex neural circuit.

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

NASA Astrophysics Data System (ADS)

Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

2017-05-01

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

Model based LV-reconstruction in bi-plane x-ray angiography

NASA Astrophysics Data System (ADS)

Backfrieder, Werner; Carpella, Martin; Swoboda, Roland; Steinwender, Clemens; Gabriel, Christian; Leisch, Franz

2005-04-01

Interventional x-ray angiography is state of the art in diagnosis and therapy of severe diseases of the cardiovascular system. Diagnosis is based on contrast enhanced dynamic projection images of the left ventricle. A new model based algorithm for three dimensional reconstruction of the left ventricle from bi-planar angiograms was developed. Parametric super ellipses are deformed until their projection profiles optimally fit measured ventricular projections. Deformation is controlled by a simplex optimization procedure. A resulting optimized parameter set builds the initial guess for neighboring slices. A three dimensional surface model of the ventricle is built from stacked contours. The accuracy of the algorithm has been tested with mathematical phantom data and clinical data. Results show conformance with provided projection data and high convergence speed makes the algorithm useful for clinical application. Fully three dimensional reconstruction of the left ventricle has a high potential for improvements of clinical findings in interventional cardiology.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

[Mathematical model of oblique three-dimensional intertrochanteric detorsion varus-forming osteotomy of the femur by the Bernbeck method in surgical treatment of congenital hip dysplasia in children].

PubMed

Bohatyrewicz, A

1992-01-01

Whenever the conservative procedure fails to bring about congruence of the dysplastic hip joint, an operative procedure becomes indispensable. In Orthopaedic Clinic of the Pomeranian Medical Academy in Szczecin we implement the oblique three-dimensional intertrochanteric detorsion and varus forming osteotomy after Bernbeck in order to correct the proximal end of the femoral bone. Precise determination of the plane to be cut, prior to the operative procedure, simplifies and shortens the operation itself and facilitates the achieving of the planned angular values in all three planes. Mathematical model of osteotomy according to Bernbeck considering required angles of correction as well as angles determining the plane of osteotomy was worked out. In collaboration of the Szczecin Technical University, a simple computer program was elaborated which allowed the presentation of the results in the form of tables. With the help of tables the optimal cutting plane was chosen and created correct biomechanical and anatomical conditions as well as optimal conditions for stable osteosynthesis of dissected fragments of the femoral bone. That type of osteotomy is useful in most operative correcrions of the dysplastic hip joint (not great varus formation connected with relatively extensive detorsion). The achieved congruence in the 22 dysplastic hip joints operated on was the most important condition for their later physiological development. Short post-operative observations confirm the value of described mathematic model.

Control of Stirling engine. Simplified, compressible model

NASA Astrophysics Data System (ADS)

Plotnikov, P. I.; Sokołowski, J.; Żochowski, A.

2016-06-01

A one-dimensional free boundary problem on a motion of a heavy piston in a tube filled with viscous gas is considered. The system of governing equations and boundary conditions is derived. The obtained system of differential equations can be regarded as a mathematical model of an exterior combustion engine. The existence of a weak solution to this model is proved. The problem of maximization of the total work of the engine is considered.

Mathematical Modeling and Optimization Studies on Development of Fuel Cells for Multifarious Applications

DTIC Science & Technology

2010-05-12

multicomponent steady-state model for liquid -feed solid polymer electrolyte DBFCs. These fuel cells use sodium borohydride (NaBH4) in alkaline media...layers, diffusion layers and the polymer electrolyte membrane for a liquid feed DBFC. Diffusion of reactants within and between the pores is accounted...projected for futuristic portable applications. In this project we developed a three- dimensional, multicomponent steady-state model for liquid -feed solid

Error enhancement in geomagnetic models derived from scalar data

NASA Technical Reports Server (NTRS)

Stern, D. P.; Bredekamp, J. H.

1975-01-01

An investigation conducted by Backus (1970) regarding the possible existence of two harmonic functions of certain characteristics in three-dimensional space is considered. The derivation of a model of the main geomagnetic field from scalar data is discussed along with a numerical simulation study. It is found that experimental discrepancies between vector field observations and the predictions of the model may have a mathematical origin, related to the work of Backus.

Self-dual random-plaquette gauge model and the quantum toric code

NASA Astrophysics Data System (ADS)

Takeda, Koujin; Nishimori, Hidetoshi

2004-05-01

We study the four-dimensional Z2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two-dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, pc=0.889972…, and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

Thermal Pollution Mathematical Model. Volume 4: Verification of Three-Dimensional Rigid-Lid Model at Lake Keowee. [envrionment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.; Sinha, S. K.

1980-01-01

The rigid lid model was developed to predict three dimensional temperature and velocity distributions in lakes. This model was verified at various sites (Lake Belews, Biscayne Bay, etc.) and th verification at Lake Keowee was the last of these series of verification runs. The verification at Lake Keowee included the following: (1) selecting the domain of interest, grid systems, and comparing the preliminary results with archival data; (2) obtaining actual ground truth and infrared scanner data both for summer and winter; and (3) using the model to predict the measured data for the above periods and comparing the predicted results with the actual data. The model results compared well with measured data. Thus, the model can be used as an effective predictive tool for future sites.

Decoupling Principle Analysis and Development of a Parallel Three-Dimensional Force Sensor

PubMed Central

Zhao, Yanzhi; Jiao, Leihao; Weng, Dacheng; Zhang, Dan; Zheng, Rencheng

2016-01-01

In the development of the multi-dimensional force sensor, dimension coupling is the ubiquitous factor restricting the improvement of the measurement accuracy. To effectively reduce the influence of dimension coupling on the parallel multi-dimensional force sensor, a novel parallel three-dimensional force sensor is proposed using a mechanical decoupling principle, and the influence of the friction on dimension coupling is effectively reduced by making the friction rolling instead of sliding friction. In this paper, the mathematical model is established by combining with the structure model of the parallel three-dimensional force sensor, and the modeling and analysis of mechanical decoupling are carried out. The coupling degree (ε) of the designed sensor is defined and calculated, and the calculation results show that the mechanical decoupling parallel structure of the sensor possesses good decoupling performance. A prototype of the parallel three-dimensional force sensor was developed, and FEM analysis was carried out. The load calibration and data acquisition experiment system are built, and then calibration experiments were done. According to the calibration experiments, the measurement accuracy is less than 2.86% and the coupling accuracy is less than 3.02%. The experimental results show that the sensor system possesses high measuring accuracy, which provides a basis for the applied research of the parallel multi-dimensional force sensor. PMID:27649194

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Numerical simulation of the baking of porous anode carbon in a vertical flue ring furnace

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacobsen, M.; Melaaen, M.C.

The interaction of pitch pyrolysis in porous anode carbon during heating and volatiles combustion in the flue gas channel has been analyzed to gain insight in the anode baking process. A two-dimensional geometry of a flue gas channel adjacent to a porous flue gas wall, packing coke, and an anode was used for studying the effect of heating rate on temperature gradients and internal gas pressure in the anodes. The mathematical model included porous heat and mass transfer, pitch pyrolysis, combustion of volatiles, radiation, and turbulent channel flow. The mathematical model was developed through source code modification of the computationalmore » fluid dynamics code FLUENT. The model was useful for studying the effects of heating rate, geometry, and anode properties.« less

Experimental Measurements and Mathematical Modeling of Static and Dynamic Characteristics of Water Flow in a Long Pipe

NASA Astrophysics Data System (ADS)

Jablonska, J.; Kozubkova, M.

2017-08-01

Static and dynamic characteristics of flow in technical practice are very important and serious problem and can be solved by experimental measurement or mathematical modeling. Unsteady flow presents time changes of the flow and water hammer can be an example of this phenomenon. Water hammer is caused by rapid changes in the water flow by means the closure or opening of the control valve. The authors deal with by hydraulic hammer at the multiphase flow (water and air), its one-dimensional modeling (Matlab SimHydraulics) and modeling with the use of the finite volume method (Ansys Fluent) in article. The circuit elements are defined by static and dynamic characteristics. The results are verified with measurements. The article evaluates different approaches, their advantages, disadvantages and specifics in solving of water hammer.

Computer design of porous active materials at different dimensional scales

NASA Astrophysics Data System (ADS)

Nasedkin, Andrey

2017-12-01

The paper presents a mathematical and computer modeling of effective properties of porous piezoelectric materials of three types: with ordinary porosity, with metallized pore surfaces, and with nanoscale porosity structure. The described integrated approach includes the effective moduli method of composite mechanics, simulation of representative volumes, and finite element method.

Stationary solutions for the one-dimensional Frémond model of shape memory Effects

NASA Astrophysics Data System (ADS)

Horn, W.

1991-12-01

The objective of this article is to investigate steady state solutions for the Fr'emond theory of shape memory alloys. Special attention is paid to the temperature range where both martensite and austenite appear. We will give a construction of solutions, which involves only elementary mathematical tools.

Modifications to the modular three-dimensional finite-difference ground-water flow model used for the Columbia Plateau Regional Aquifer-System Analysis, Washington, Oregon, and Idaho

USGS Publications Warehouse

Hansen, A.J.

1993-01-01

The report documents modifications to the U.S. Geological Survey's modular three-dimensional finite-difference ground-water flow model used for a regional aquifer-system analysis of the Columbia Plateau. The report, which describes the concepts and mathematical basis for the modifications, is intended for potential users who are familiar with the original modular model. The modifications permit flow from a layer to any adjacent layer, allow the model to retain a cell of a layer that has been cut completely through by a canyon, and allow placing ground-water flow barriers on only specified branch conductances; a special version of the modified model uses a convergent grid. The report describes the data-input items that this modified model must read.

Two-Dimensional Quantum Model of a Nanotransistor

NASA Technical Reports Server (NTRS)

Govindan, T. R.; Biegel, B.; Svizhenko, A.; Anantram, M. P.

2009-01-01

A mathematical model, and software to implement the model, have been devised to enable numerical simulation of the transport of electric charge in, and the resulting electrical performance characteristics of, a nanotransistor [in particular, a metal oxide/semiconductor field-effect transistor (MOSFET) having a channel length of the order of tens of nanometers] in which the overall device geometry, including the doping profiles and the injection of charge from the source, gate, and drain contacts, are approximated as being two-dimensional. The model and software constitute a computational framework for quantitatively exploring such device-physics issues as those of source-drain and gate leakage currents, drain-induced barrier lowering, and threshold voltage shift due to quantization. The model and software can also be used as means of studying the accuracy of quantum corrections to other semiclassical models.

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

NASA Astrophysics Data System (ADS)

Choquet, C.; Diédhiou, M. M.; Rosier, C.

2015-10-01

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phenomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with initial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor.

PubMed

Shakhawath Hossain, Md; Bergstrom, D J; Chen, X B

2015-12-01

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process. © 2015 Wiley Periodicals, Inc.

Estimation of three-dimensional radar tracking using modified extended kalman filter

NASA Astrophysics Data System (ADS)

Aditya, Prima; Apriliani, Erna; Khusnul Arif, Didik; Baihaqi, Komar

2018-03-01

Kalman filter is an estimation method by combining data and mathematical models then developed be extended Kalman filter to handle nonlinear systems. Three-dimensional radar tracking is one of example of nonlinear system. In this paper developed a modification method of extended Kalman filter from the direct decline of the three-dimensional radar tracking case. The development of this filter algorithm can solve the three-dimensional radar measurements in the case proposed in this case the target measured by radar with distance r, azimuth angle θ, and the elevation angle ϕ. Artificial covariance and mean adjusted directly on the three-dimensional radar system. Simulations result show that the proposed formulation is effective in the calculation of nonlinear measurement compared with extended Kalman filter with the value error at 0.77% until 1.15%.

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

PubMed

Carbonell, Felix; Iturria-Medina, Yasser; Evans, Alan C

2018-01-01

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

1975-11-01

A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

Computer-aided-engineering system for modeling and analysis of ECLSS integration testing

NASA Technical Reports Server (NTRS)

Sepahban, Sonbol

1987-01-01

The accurate modeling and analysis of two-phase fluid networks found in environmental control and life support systems is presently undertaken by computer-aided engineering (CAE) techniques whose generalized fluid dynamics package can solve arbitrary flow networks. The CAE system for integrated test bed modeling and analysis will also furnish interfaces and subsystem/test-article mathematical models. Three-dimensional diagrams of the test bed are generated by the system after performing the requisite simulation and analysis.

CFD Modelling Applied to the Co-Combustion of Paper Sludge and Coal in a 130 t/h CFB Boiler

NASA Astrophysics Data System (ADS)

Yu, Z. S.; Ma, X. Q.; Lai, Z. Y.; Xiao, H. M.

Three-dimensional mathematical model has been developed as a tool for co-combustion of paper sludge and coal in a 130 tJh Circulating Fluidized Bed (CFB) boiler. Mathematical methods had been used based on a commercial software FLUENT for combustion. The predicted results of CFB furnace show that the co-combustion of paper sludge/coal is initially intensively at the bottom of bed; the temperature reaches its maximum in the dense-phase zone, around l400K. It indicates that paper sludge spout into furnace from the recycle inlet can increase the furnace maximum temperature (l396.3K), area-weighted average temperature (l109.6K) and the furnace gas outlet area-weighted average temperature(996.8K).The mathematical modeling also predicts that 15 mass% paper sludge co-combustion is the highest temperature at the flue gas outlet, it is 1000.8K. Moreover, it is proved that mathematical models can serve as a tool for detailed analysis of co-combustion of paper sludge and coal processes in a circulating fluidized bed furnace when in view of its convenience. The results gained from numerical simulation show that paper sludge enter into furnace from the recycle inlet excelled than mixing with coal and at the underside of phase interface.

Weather prediction using a genetic memory

NASA Technical Reports Server (NTRS)

Rogers, David

1990-01-01

Kanaerva's sparse distributed memory (SDM) is an associative memory model based on the mathematical properties of high dimensional binary address spaces. Holland's genetic algorithms are a search technique for high dimensional spaces inspired by evolutional processes of DNA. Genetic Memory is a hybrid of the above two systems, in which the memory uses a genetic algorithm to dynamically reconfigure its physical storage locations to reflect correlations between the stored addresses and data. This architecture is designed to maximize the ability of the system to scale-up to handle real world problems.

A statistical formulation of one-dimensional electron fluid turbulence

NASA Technical Reports Server (NTRS)

Fyfe, D.; Montgomery, D.

1977-01-01

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Parameter extraction and transistor models

NASA Technical Reports Server (NTRS)

Rykken, Charles; Meiser, Verena; Turner, Greg; Wang, QI

1985-01-01

Using specified mathematical models of the MOSFET device, the optimal values of the model-dependent parameters were extracted from data provided by the Jet Propulsion Laboratory (JPL). Three MOSFET models, all one-dimensional were used. One of the models took into account diffusion (as well as convection) currents. The sensitivity of the models was assessed for variations of the parameters from their optimal values. Lines of future inquiry are suggested on the basis of the behavior of the devices, of the limitations of the proposed models, and of the complexity of the required numerical investigations.

Fluid structure interaction model for biological systems in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Aziz, Asim; Shoaib, Muhammad

2016-06-01

In the present paper a one-dimensional mathematical model of a cerebral aneurysm is considered. The model combines the interaction between the arterial wall structure, blood pressure and the cerebral spinal fluid (CSF) that is around the aneurysm. CSF is considered electrically conducting in the presence of a uniform magnetic field. Therefore, it may be possible to control pressure and its flow behavior by using an appropriate magnetic field. Hence, such studies have potential for the treatment of Cerebral aneurysms, diseases of heart and blood vessels. The modeled mathematical equations are solved algebraically and the displacement of the arterial wall is plotted to visualize the wall movement. It is evident from the graphs the inclusion of magnetic field reduce the movement of the arterial wall and in turn prevent the rupture of the cerebral aneurysm. The solution is also investigated using computational tools for various other parameters involve in the model.

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.

Three Dimensional Distribution of Sensitive Field and Stress Field Inversion of Force Sensitive Materials under Constant Current Excitation.

PubMed

Zhao, Shuanfeng; Liu, Min; Guo, Wei; Zhang, Chuanwei

2018-02-28

Force sensitive conductive composite materials are functional materials which can be used as the sensitive material of force sensors. However, the existing sensors only use one-dimensional electrical properties of force sensitive conductive materials. Even in tactile sensors, the measurement of contact pressure is achieved by large-scale arrays and the units of a large-scale array are also based on the one-dimensional electrical properties of force sensitive materials. The main contribution of this work is to study the three-dimensional electrical properties and the inversion method of three-dimensional stress field of a force sensitive material (conductive rubber), which pushes the application of force sensitive material from one dimensional to three-dimensional. First, the mathematical model of the conductive rubber current field distribution under a constant force is established by the effective medium theory, and the current field distribution model of conductive rubber with different geometry, conductive rubber content and conductive rubber relaxation parameters is deduced. Secondly, the inversion method of the three-dimensional stress field of conductive rubber is established, which provides a theoretical basis for the design of a new tactile sensor, three-dimensional stress field and space force based on force sensitive materials.

Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations.

PubMed

Safaei, Soroush; Blanco, Pablo J; Müller, Lucas O; Hellevik, Leif R; Hunter, Peter J

2018-01-01

We propose a detailed CellML model of the human cerebral circulation that runs faster than real time on a desktop computer and is designed for use in clinical settings when the speed of response is important. A lumped parameter mathematical model, which is based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, is constructed using a bond graph formulation to ensure mass conservation and energy conservation. The model includes arterial vessels with geometric and anatomical data based on the ADAN circulation model. The peripheral beds are represented by lumped parameter compartments. We compare the hemodynamics predicted by the bond graph formulation of the cerebral circulation with that given by a classical one-dimensional Navier-Stokes model working on top of the whole-body ADAN model. Outputs from the bond graph model, including the pressure and flow signatures and blood volumes, are compared with physiological data.

A continuous mapping of sleep states through association of EEG with a mesoscale cortical model.

PubMed

Lopour, Beth A; Tasoglu, Savas; Kirsch, Heidi E; Sleigh, James W; Szeri, Andrew J

2011-04-01

Here we show that a mathematical model of the human sleep cycle can be used to obtain a detailed description of electroencephalogram (EEG) sleep stages, and we discuss how this analysis may aid in the prediction and prevention of seizures during sleep. The association between EEG data and the cortical model is found via locally linear embedding (LLE), a method of dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates REM and non-REM sleep and maps the EEG data to a low-dimensional output space where the sleep state changes smoothly over time. We also incorporate the concept of strongly connected components and use this as a method of automatic outlier rejection for EEG data. Then, by using LLE on a hybrid data set containing both sleep EEG and signals generated from the mesoscale cortical model, we quantify the relationship between the data and the mathematical model. This enables us to take any sample of sleep EEG data and associate it with a position among the continuous range of sleep states provided by the model; we can thus infer a trajectory of states as the subject sleeps. Lastly, we show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time.

CFD Modeling of Flow, Temperature, and Concentration Fields in a Pilot-Scale Rotary Hearth Furnace

NASA Astrophysics Data System (ADS)

Liu, Ying; Su, Fu-Yong; Wen, Zhi; Li, Zhi; Yong, Hai-Quan; Feng, Xiao-Hong

2014-01-01

A three-dimensional mathematical model for simulation of flow, temperature, and concentration fields in a pilot-scale rotary hearth furnace (RHF) has been developed using a commercial computational fluid dynamics software, FLUENT. The layer of composite pellets under the hearth is assumed to be a porous media layer with CO source and energy sink calculated by an independent mathematical model. User-defined functions are developed and linked to FLUENT to process the reduction process of the layer of composite pellets. The standard k-ɛ turbulence model in combination with standard wall functions is used for modeling of gas flow. Turbulence-chemistry interaction is taken into account through the eddy-dissipation model. The discrete ordinates model is used for modeling of radiative heat transfer. A comparison is made between the predictions of the present model and the data from a test of the pilot-scale RHF, and a reasonable agreement is found. Finally, flow field, temperature, and CO concentration fields in the furnace are investigated by the model.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

A Generalized Quantum-Inspired Decision Making Model for Intelligent Agent

PubMed Central

Loo, Chu Kiong

2014-01-01

A novel decision making for intelligent agent using quantum-inspired approach is proposed. A formal, generalized solution to the problem is given. Mathematically, the proposed model is capable of modeling higher dimensional decision problems than previous researches. Four experiments are conducted, and both empirical experiments results and proposed model's experiment results are given for each experiment. Experiments showed that the results of proposed model agree with empirical results perfectly. The proposed model provides a new direction for researcher to resolve cognitive basis in designing intelligent agent. PMID:24778580

Effect of Using Logo on Pupils' Learning in Two-Dimensional Shapes

ERIC Educational Resources Information Center

Yi, Boo Jia; Eu, Leong Kwan

2016-01-01

The integration of technology in mathematics instruction is an important step in the 21st century learning style. At the primary level, some studies have explored how technology could help in mathematics learning. The purpose of this study is to determine the effect of using Logo on pupils' learning of the properties of two-dimensional shapes. A…

Thermal mathematical modeling and system simulation of Space Shuttle less subsystem

NASA Technical Reports Server (NTRS)

Chao, D. C.; Battley, H. H.; Gallegos, J. J.; Curry, D. M.

1984-01-01

Applications, validation tests, and upgrades of the two- and three-dimensional system level thermal mathematical system simulation models (TMSSM) used for thermal protection system (TPS) analyses are described. The TMSSM were developed as an aid to predicting the performance requirements and configurations of the Shuttle wing leading edge (WLE) and nose cone (NC) TPS tiles. The WLE and its structure were subjected to acoustic, thermal/vacuum, and air loads tests to simulate launch, on-orbit, and re-entry behavior. STS-1, -2 and -5 flight data led to recalibration of on-board instruments and raised estimates of the thermal shock at the NC and WLE. Baseline heating data are now available for the design of future TPS.

Two-dimensional dispersion of magnetostatic volume spin waves

NASA Astrophysics Data System (ADS)

Buijnsters, Frank J.; van Tilburg, Lennert J. A.; Fasolino, Annalisa; Katsnelson, Mikhail I.

2018-06-01

Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of and and refinements thereof. However, solving the two-dimensional dispersion requires the evaluation of a set of coupled transcendental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semi-analytical expression for the dispersion relation of the lowest-frequency mode that is straightforward to evaluate.

A mathematical model of the structure and evolution of small scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, C. E.

1990-01-01

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

Development and validation of a model of bio-barriers for remediation of Cr(VI) contaminated aquifers using laboratory column experiments.

PubMed

Shashidhar, T; Bhallamudi, S Murty; Philip, Ligy

2007-07-16

Bench scale transport and biotransformation experiments and mathematical model simulations were carried out to study the effectiveness of bio-barriers for the containment of hexavalent chromium in contaminated confined aquifers. Experimental results showed that a 10cm thick bio-barrier with an initial biomass concentration of 0.205mg/g of soil was able to completely contain a Cr(VI) plume of 25mg/L concentration. It was also observed that pore water velocity and initial biomass concentration are the most significant parameters in the containment of Cr(VI). The mathematical model developed is based on one-dimensional advection-dispersion reaction equations for Cr(VI) and molasses in saturated, homogeneous porous medium. The transport of Cr(VI) and molasses is coupled with adsorption and Monod's inhibition kinetics for immobile bacteria. It was found that, in general, the model was able to simulate the experimental results satisfactorily. However, there was disparity between the numerically simulated and experimental breakthrough curves for Cr(VI) and molasses in cases where there was high clay content and high microbial activity. The mathematical model could contribute towards improved designs of future bio-barriers for the remediation of Cr(VI) contaminated aquifers.

Cheshire charge in (3+1)-dimensional topological phases

NASA Astrophysics Data System (ADS)

Else, Dominic V.; Nayak, Chetan

2017-07-01

We show that (3 +1 ) -dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to nontrivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3 +1 ) -dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in Z2×Z2 Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category Z (2 VectGω) , thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3 +1 ) -dimensional topological phases.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method

DTIC Science & Technology

1991-02-01

US Army Ballistic Research Laboratories, Aberden Proving Ground , NID, August 1975. [18] Hi1irlimann, T., and .J. lKohlas "LPL: A Structured Language...such systems can prove that (a’ + ab + b2 + ba) = (a + b) 2 . With some effort, since the laws of physical algebra are a minor variant on those of

Using a Polytope to Estimate Efficient Production Functions of Joint Product Processes.

ERIC Educational Resources Information Center

Simpson, William A.

In the last decade, a modeling technique has been developed to handle complex input/output analyses where outputs involve joint products and there are no known mathematical relationships linking the outputs or inputs. The technique uses the geometrical concept of a six-dimensional shape called a polytope to analyze the efficiency of each…

Modeling genome-wide dynamic regulatory network in mouse lungs with influenza infection using high-dimensional ordinary differential equations.

PubMed

Wu, Shuang; Liu, Zhi-Ping; Qiu, Xing; Wu, Hulin

2014-01-01

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.

A global multiscale mathematical model for the human circulation with emphasis on the venous system.

PubMed

Müller, Lucas O; Toro, Eleuterio F

2014-07-01

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers. Copyright © 2014 John Wiley & Sons, Ltd.

Propagation of Cutaneous Thermal Injury: A Mathematical Model

PubMed Central

Xue, Chuan; Chou, Ching-Shan; Kao, Chiu-Yen; Sen, Chandan K.; Friedman, Avner

2012-01-01

Cutaneous burn wounds represent a significant public health problem with 500,000 patients per year in the U.S. seeking medical attention. Immediately after skin burn injury, the volume of the wound burn expands due to a cascade of chemical reactions, including lipid peroxidation chain reactions. Based on these chemical reactions, the present paper develops for the first time a three-dimensional mathematical model to quantify the propagation of tissue damage within 12 hours post initial burn. We use the model to investigate the effect of supplemental antioxidant vitamin E for stopping the propagation. We show, for example, that if the production rate of vitamin E is increased, post burn, by five times the natural production in a healthy tissue, then this would slow down the lipid peroxide propagation by at least 50%. Our model is formulated in terms of differential equations, and sensitivity analysis is performed on the parameters to ensure the robustness of the results. PMID:22211391

Study on dynamic performance of SOFC

NASA Astrophysics Data System (ADS)

Zhan, Haiyang; Liang, Qianchao; Wen, Qiang; Zhu, Runkai

2017-05-01

In order to solve the problem of real-time matching of load and fuel cell power, it is urgent to study the dynamic response process of SOFC in the case of load mutation. The mathematical model of SOFC is constructed, and its performance is simulated. The model consider the influence factors such as polarization effect, ohmic loss. It also takes the diffusion effect, thermal effect, energy exchange, mass conservation, momentum conservation. One dimensional dynamic mathematical model of SOFC is constructed by using distributed lumped parameter method. The simulation results show that the I-V characteristic curves are in good agreement with the experimental data, and the accuracy of the model is verified. The voltage response curve, power response curve and the efficiency curve are obtained by this way. It lays a solid foundation for the research of dynamic performance and optimal control in power generation system of high power fuel cell stack.

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

Development of a Three-Dimensional, Unstructured Material Response Design Tool

NASA Technical Reports Server (NTRS)

Schulz, Joseph C.; Stern, Eric C.; Muppidi, Suman; Palmer, Grant E.; Schroeder, Olivia

2017-01-01

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. This extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

Thermal Pollution Mathematical Model. Volume 3: User's Manual for One-Dimensional Numerical Model for the Seasonal Thermocline. [environment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A user's manual for a one dimensional thermal model to predict the temperature profiles of a deep body of water for any number of annual cycles is presented. The model is essentially a set of partial differential equations which are solved by finite difference methods using a high speed digital computer. The model features the effects of area change with depth, nonlinear interaction of wind generated turbulence and buoyancy, adsorption of radiative heat flux below the surface, thermal discharges, and the effects of vertical convection caused by discharge. The main assumption in the formulation is horizontal homogeneity. The environmental impact of thermal discharges from power plants is emphasized. Although the model is applicable to most lakes, a specific site (Lake Keowee, S.C.) application is described in detail. The programs are written in FORTRAN 5.

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Common radiation analysis model for 75,000 pound thrust NERVA engine (1137400E)

NASA Technical Reports Server (NTRS)

Warman, E. A.; Lindsey, B. A.

1972-01-01

The mathematical model and sources of radiation used for the radiation analysis and shielding activities in support of the design of the 1137400E version of the 75,000 lbs thrust NERVA engine are presented. The nuclear subsystem (NSS) and non-nuclear components are discussed. The geometrical model for the NSS is two dimensional as required for the DOT discrete ordinates computer code or for an azimuthally symetrical three dimensional Point Kernel or Monte Carlo code. The geometrical model for the non-nuclear components is three dimensional in the FASTER geometry format. This geometry routine is inherent in the ANSC versions of the QAD and GGG Point Kernal programs and the COHORT Monte Carlo program. Data are included pertaining to a pressure vessel surface radiation source data tape which has been used as the basis for starting ANSC analyses with the DASH code to bridge into the COHORT Monte Carlo code using the WANL supplied DOT angular flux leakage data. In addition to the model descriptions and sources of radiation, the methods of analyses are briefly described.

Generation Algorithm of Discrete Line in Multi-Dimensional Grids

NASA Astrophysics Data System (ADS)

Du, L.; Ben, J.; Li, Y.; Wang, R.

2017-09-01

Discrete Global Grids System (DGGS) is a kind of digital multi-resolution earth reference model, in terms of structure, it is conducive to the geographical spatial big data integration and mining. Vector is one of the important types of spatial data, only by discretization, can it be applied in grids system to make process and analysis. Based on the some constraint conditions, this paper put forward a strict definition of discrete lines, building a mathematic model of the discrete lines by base vectors combination method. Transforming mesh discrete lines issue in n-dimensional grids into the issue of optimal deviated path in n-minus-one dimension using hyperplane, which, therefore realizing dimension reduction process in the expression of mesh discrete lines. On this basis, we designed a simple and efficient algorithm for dimension reduction and generation of the discrete lines. The experimental results show that our algorithm not only can be applied in the two-dimensional rectangular grid, also can be applied in the two-dimensional hexagonal grid and the three-dimensional cubic grid. Meanwhile, when our algorithm is applied in two-dimensional rectangular grid, it can get a discrete line which is more similar to the line in the Euclidean space.

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

NASA Astrophysics Data System (ADS)

La Rocca, Michele; Adduce, Claudia; Sciortino, Giampiero; Pinzon, Allen Bateman

2008-10-01

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

Recent Survey and Application of the simSUNDT Software

NASA Astrophysics Data System (ADS)

Persson, G.; Wirdelius, H.

2010-02-01

The simSUNDT software is based on a previous developed program (SUNDT). The latest version has been customized in order to generate realistic synthetic data (including a grain noise model), compatible with a number of off-line analysis software. The software consists of a Windows®-based preprocessor and postprocessor together with a mathematical kernel (UTDefect), dealing with the actual mathematical modeling. The model employs various integral transforms and integral equation and enables simulations of the entire ultrasonic testing situation. The model is completely three-dimensional though the simulated component is two-dimensional, bounded by the scanning surface and a planar back surface as an option. It is of great importance that inspection methods that are applied are proper validated and that their capability of detection of cracks and defects are quantified. In order to achieve this, statistical methods such as Probability of Detection (POD) often are applied, with the ambition to estimate the detectability as a function of defect size. Despite the fact that the proposed procedure with the utilization of test pieces is very expensive, it also tends to introduce a number of possible misalignments between the actual NDT situation that is to be performed and the proposed experimental simulation. The presentation will describe the developed model that will enable simulation of a phased array NDT inspection and the ambition to use this simulation software to generate POD information. The paper also includes the most recent developments of the model including some initial experimental validation of the phased array probe model.

Experimental and Numerical Investigation of Two Dimensional CO2 Adsorption/Desorption in Packed Sorption Beds under Non-Ideal Flows

NASA Technical Reports Server (NTRS)

Mohamadinejad, H.; Knox, J. C.; Smith, J. E.; Croomes, Scott (Technical Monitor)

2001-01-01

The experimental results of CO2 adsorption and desorption in a packed column indicated that the concentration wave front at the center of the packed column differs from those which are close to the wall of column filled with adsorbent material even though the ratio of column diameter to the particle size is greater than 20. The comparison of the experimental results with one dimensional model of packed column shows that in order to simulate the average breakthrough in a packed column a two dimensional (radial and axial) model of packed column is needed. In this paper the mathematical model of a non-slip flow through a packed column with 2 inches in diameter and 18 inches in length filled with 5A zeolite pellets is presented. The comparison of experimental results of CO2 absorption and desorption for the mixed and central breakthrough of the packed column with numerical results is also presented.

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

ERIC Educational Resources Information Center

Safi, Farshid; Desai, Siddhi

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

Experimental Mathematics and Mathematical Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

Three-dimensional ray-tracing model for the study of advanced refractive errors in keratoconus.

PubMed

Schedin, Staffan; Hallberg, Per; Behndig, Anders

2016-01-20

We propose a numerical three-dimensional (3D) ray-tracing model for the analysis of advanced corneal refractive errors. The 3D modeling was based on measured corneal elevation data by means of Scheimpflug photography. A mathematical description of the measured corneal surfaces from a keratoconus (KC) patient was used for the 3D ray tracing, based on Snell's law of refraction. A model of a commercial intraocular lens (IOL) was included in the analysis. By modifying the posterior IOL surface, it was shown that the imaging quality could be significantly improved. The RMS values were reduced by approximately 50% close to the retina, both for on- and off-axis geometries. The 3D ray-tracing model can constitute a basis for simulation of customized IOLs that are able to correct the advanced, irregular refractive errors in KC.

Some Applications of the Model of the Partion Points on a One Dimensional Lattice

NASA Astrophysics Data System (ADS)

Mejdani, R.; Huseini, H.

1996-02-01

We have shown that by using a model of gas of partition points on a one-dimensional lattice, we can find some results about the saturation curves for enzyme kinetics or the average domain-size, which we have obtained before by using a correlated walks' theory or a probabilistic (combinatoric) way. We have studied, using the same model and the same technique, the denaturation process, i.e., the breaking of the hydrogen bonds connecting the two strands, under treatment by heat. Also, we have discussed, without entering in details, the problem related to the spread of an infections disease and the stochastic model of partition points. We think that this model, being simple and mathematically transparent, can be advantageous for the other theoratical investigations in chemistry or modern biology. PACS NOS.: 05.50. + q; 05.70.Ce; 64.10.+h; 87.10. +e; 87.15.Rn

On numerical model of one-dimensional time-dependent gas flows through bed of encapsulated phase change material

NASA Astrophysics Data System (ADS)

Lutsenko, N. A.; Fetsov, S. S.

2017-10-01

Mathematical model and numerical method are proposed for investigating the one-dimensional time-dependent gas flows through a packed bed of encapsulated Phase Change Material (PCM). The model is based on the assumption of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for PCM and gas. The advantage of the method is that it does not require predicting the location of phase transition zone and can define it automatically as in a usual shock-capturing method. One of the applications of the developed numerical model is the simulation of novel Adiabatic Compressed Air Energy Storage system (A-CAES) with Thermal Energy Storage subsystem (TES) based on using the encapsulated PCM in packed bed. Preliminary test calculations give hope that the method can be effectively applied in the future for modelling the charge and discharge processes in such TES with PCM.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Mathematical geophysics: A survey of recent developments in seismology and geodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlaar, N.J.

1988-01-01

This survey deals with modern methods for the determination of the structure of the Earth and for the analysis and modeling of the dynamic processes in the Earth's interior. Seismology and the three-dimensional structure of the Earth are covered in chapters devoted to waves in the three-dimensional Earth and large-scale inversion, while the discussion of convection and lithospheric processes focuses on geomagnetism, mantle convection, post-glacial rebound, and thermomechanical processes in the lithosphere. The emphasis of the work is theoretical, but the reader will find a discussion of the pertinent observational evidence.

Inverse modeling approach for evaluation of kinetic parameters of a biofilm reactor using tabu search.

PubMed

Kumar, B Shiva; Venkateswarlu, Ch

2014-08-01

The complex nature of biological reactions in biofilm reactors often poses difficulties in analyzing such reactors experimentally. Mathematical models could be very useful for their design and analysis. However, application of biofilm reactor models to practical problems proves somewhat ineffective due to the lack of knowledge of accurate kinetic models and uncertainty in model parameters. In this work, we propose an inverse modeling approach based on tabu search (TS) to estimate the parameters of kinetic and film thickness models. TS is used to estimate these parameters as a consequence of the validation of the mathematical models of the process with the aid of measured data obtained from an experimental fixed-bed anaerobic biofilm reactor involving the treatment of pharmaceutical industry wastewater. The results evaluated for different modeling configurations of varying degrees of complexity illustrate the effectiveness of TS for accurate estimation of kinetic and film thickness model parameters of the biofilm process. The results show that the two-dimensional mathematical model with Edward kinetics (with its optimum parameters as mu(max)rho(s)/Y = 24.57, Ks = 1.352 and Ki = 102.36) and three-parameter film thickness expression (with its estimated parameters as a = 0.289 x 10(-5), b = 1.55 x 10(-4) and c = 15.2 x 10(-6)) better describes the biofilm reactor treating the industry wastewater.

Incorporating convection into one-dimensional solute redistribution during crystal growth from the melt I. The steady-state solution

NASA Astrophysics Data System (ADS)

Yen, C. T.; Tiller, W. A.

1992-03-01

A one-dimensional mathematical analysis is made of the redistribution of solute which occurs during crystal growth from a convected melt. In this analysis, the important contribution from lateral melt convection to one-dimensional solute redistribution analysis is taken into consideration via an annihilation/creation term in the one-dimensional solute transport equation. Calculations of solute redistribution under steady-state conditions have been carried out analytically. It is found that this new solute redistribution model overcomes several weaknesses that occur when applying the Burton, Prim and Slichter solute segregation equation (1953) in real melt growth situations. It is also found that, with this correction, the diffusion coefficients for solute's in liquid silicon are now found to be in the same range as other liquid metal diffusion coefficients.

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

Modeling of methanol decomposition on Pt/CeO2/ZrO2 catalyst in a packed bed microreactor

NASA Astrophysics Data System (ADS)

Pohar, Andrej; Belavič, Darko; Dolanc, Gregor; Hočevar, Stanko

2014-06-01

Methanol decomposition on Pt/CeO2/ZrO2 catalyst is studied inside a packed bed microreactor in the temperature range of 300-380 °C. The microreactor is fabricated using low-temperature co-fired ceramic (LTCC) technology, which is well suited for the production of relatively complex three-dimensional structures. It is packed with 2 wt% Pt-CeO2 catalyst, which is deposited onto ZrO2 spherical particles. A 1D mathematical model, which incorporates diffusion, convection and mass transfer through the boundary layer to the catalyst particles, as well as a 3D computational fluid dynamics model, are developed to describe the methanol decomposition process inside the packed bed. The microreactor exhibits reliable operation and no catalyst deactivation was observed during three months of experimentation. A comparison between the 1D mathematical model and the 3D model, considering the full 3D geometry of the microreactor is made and the differences between the models are identified and evaluated.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

NASA Technical Reports Server (NTRS)

Fischbach, Sean R.

2015-01-01

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Objective estimation of tropical cyclone innercore surface wind structure using infrared satellite images

NASA Astrophysics Data System (ADS)

Zhang, Changjiang; Dai, Lijie; Ma, Leiming; Qian, Jinfang; Yang, Bo

2017-10-01

An objective technique is presented for estimating tropical cyclone (TC) innercore two-dimensional (2-D) surface wind field structure using infrared satellite imagery and machine learning. For a TC with eye, the eye contour is first segmented by a geodesic active contour model, based on which the eye circumference is obtained as the TC eye size. A mathematical model is then established between the eye size and the radius of maximum wind obtained from the past official TC report to derive the 2-D surface wind field within the TC eye. Meanwhile, the composite information about the latitude of TC center, surface maximum wind speed, TC age, and critical wind radii of 34- and 50-kt winds can be combined to build another mathematical model for deriving the innercore wind structure. After that, least squares support vector machine (LSSVM), radial basis function neural network (RBFNN), and linear regression are introduced, respectively, in the two mathematical models, which are then tested with sensitivity experiments on real TC cases. Verification shows that the innercore 2-D surface wind field structure estimated by LSSVM is better than that of RBFNN and linear regression.

On a model of three-dimensional bursting and its parallel implementation

NASA Astrophysics Data System (ADS)

Tabik, S.; Romero, L. F.; Garzón, E. M.; Ramos, J. I.

2008-04-01

A mathematical model for the simulation of three-dimensional bursting phenomena and its parallel implementation are presented. The model consists of four nonlinearly coupled partial differential equations that include fast and slow variables, and exhibits bursting in the absence of diffusion. The differential equations have been discretized by means of a second-order accurate in both space and time, linearly-implicit finite difference method in equally-spaced grids. The resulting system of linear algebraic equations at each time level has been solved by means of the Preconditioned Conjugate Gradient (PCG) method. Three different parallel implementations of the proposed mathematical model have been developed; two of these implementations, i.e., the MPI and the PETSc codes, are based on a message passing paradigm, while the third one, i.e., the OpenMP code, is based on a shared space address paradigm. These three implementations are evaluated on two current high performance parallel architectures, i.e., a dual-processor cluster and a Shared Distributed Memory (SDM) system. A novel representation of the results that emphasizes the most relevant factors that affect the performance of the paralled implementations, is proposed. The comparative analysis of the computational results shows that the MPI and the OpenMP implementations are about twice more efficient than the PETSc code on the SDM system. It is also shown that, for the conditions reported here, the nonlinear dynamics of the three-dimensional bursting phenomena exhibits three stages characterized by asynchronous, synchronous and then asynchronous oscillations, before a quiescent state is reached. It is also shown that the fast system reaches steady state in much less time than the slow variables.

A tool for simulating collision probabilities of animals with marine renewable energy devices.

PubMed

Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

2017-01-01

The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.

Dynamical decoupling of unbounded Hamiltonians

NASA Astrophysics Data System (ADS)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Estimating the Uncertain Mathematical Structure of Hydrological Model via Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Bulygina, N.; Gupta, H.; O'Donell, G.; Wheater, H.

2008-12-01

The structure of hydrological model at macro scale (e.g. watershed) is inherently uncertain due to many factors, including the lack of a robust hydrological theory at the macro scale. In this work, we assume that a suitable conceptual model for the hydrologic system has already been determined - i.e., the system boundaries have been specified, the important state variables and input and output fluxes to be included have been selected, and the major hydrological processes and geometries of their interconnections have been identified. The structural identification problem then is to specify the mathematical form of the relationships between the inputs, state variables and outputs, so that a computational model can be constructed for making simulations and/or predictions of system input-state-output behaviour. We show how Bayesian data assimilation can be used to merge both prior beliefs in the form of pre-assumed model equations with information derived from the data to construct a posterior model. The approach, entitled Bayesian Estimation of Structure (BESt), is used to estimate a hydrological model for a small basin in England, at hourly time scales, conditioned on the assumption of 3-dimensional state - soil moisture storage, fast and slow flow stores - conceptual model structure. Inputs to the system are precipitation and potential evapotranspiration, and outputs are actual evapotranspiration and streamflow discharge. Results show the difference between prior and posterior mathematical structures, as well as provide prediction confidence intervals that reflect three types of uncertainty: due to initial conditions, due to input and due to mathematical structure.

Dimensionality of Motion and Binding Valency Govern Receptor-Ligand Kinetics As Revealed by Agent-Based Modeling.

PubMed

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor-ligand binding in the context of antibody-antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors-such as their dimensionality of motion, morphology, and binding valency-on the receptor-ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors.

Dimensionality of Motion and Binding Valency Govern Receptor–Ligand Kinetics As Revealed by Agent-Based Modeling

PubMed Central

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor–ligand binding in the context of antibody–antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors—such as their dimensionality of motion, morphology, and binding valency—on the receptor–ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors. PMID:29250071

Simulation and automation of thermal processes in oil well

NASA Astrophysics Data System (ADS)

Kostarev, N. A.; Trufanova, N. M.

2018-03-01

The paper presents a two-dimensional mathematical model and a numerical analysis of heat and mass transfer processes in an oil well. The proposed and implemented mathematical model of the process of heat and mass transfer in an oil well allows analyzing the temperature field in the whole space of an oil well and is suitable for any fields equipped with an electric centrifugal pump. Temperature and velocity fields were obtained, as well as the distribution of temperature on the wall of the pump tubing along the depth of the well. On the basis of the obtained temperature fields, the modes of periodic heating of the well by the heating cable were developed. Recommendations are given on the choice of power parameters and the time of warming up the well.

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo-Christov Heat Diffusion Theory

NASA Astrophysics Data System (ADS)

Ramesh, G. K.; Gireesha, B. J.; Shehzad, S. A.; Abbasi, F. M.

2017-07-01

Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Further, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier’s theory of heat flux.

Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor.

PubMed

Masić, Alma; Bengtsson, Jessica; Christensson, Magnus

2010-09-01

In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChip P was developed to allow good conditions for transport of substrates into the biofilm. The oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and it was simulated with a one-dimensional mathematical model. We extended the model by adding a CSTR equation, to connect the reactor to the biofilm through the boundary conditions. We showed the dependence of the thickness of the mass transfer boundary layer on the bulk flow rate. Finally, we estimated the erosion parameter lambda to increase the concordance between the measured and simulated profiles. This lead to a simple empirical relationship between lambda and the flow rate. The data gathered by in situ microelectrode measurements can, together with the mathematical model, be used in predictive modeling and give more insight in the design of new carriers, with the ambition of making process operation more energy efficient. Copyright 2010 Elsevier Inc. All rights reserved.

Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

NASA Astrophysics Data System (ADS)

Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

2018-05-01

Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

Recent statistical methods for orientation data

NASA Technical Reports Server (NTRS)

Batschelet, E.

1972-01-01

The application of statistical methods for determining the areas of animal orientation and navigation are discussed. The method employed is limited to the two-dimensional case. Various tests for determining the validity of the statistical analysis are presented. Mathematical models are included to support the theoretical considerations and tables of data are developed to show the value of information obtained by statistical analysis.

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

Architecture of a platform for hardware-in-the-loop simulation of flying vehicle control systems

NASA Astrophysics Data System (ADS)

Belokon', S. A.; Zolotukhin, Yu. N.; Filippov, M. N.

2017-07-01

A hardware-software platform is presented, which is designed for the development and hardware-in-the-loop simulation of flying vehicle control systems. This platform ensures the construction of the mathematical model of the plant, development of algorithms and software for onboard radioelectronic equipment and ground control station, and visualization of the three-dimensional model of the vehicle and external environment of the cockpit in the simulator training mode.

The estimation of the thyroid volume before surgery--an important prerequisite for minimally invasive thyroidectomy.

PubMed

Ruggieri, M; Fumarola, A; Straniero, A; Maiuolo, A; Coletta, I; Veltri, A; Di Fiore, A; Trimboli, P; Gargiulo, P; Genderini, M; D'Armiento, M

2008-09-01

Actually, thyroid volume >25 ml, obtained by preoperative ultrasound evaluation, is a very important exclusion criteria for minimally invasive thyroidectomy. So far, among different imaging techniques, two-dimensional ultrasonography has become the more accepted method for the assessment of thyroid volume (US-TV). The aims of this study were: (1) to estimate the preoperative thyroid volume in patients undergoing minimally invasive total thyroidectomy using a mathematical formula and (2) to verify its validity by comparing it with the postsurgical TV (PS-TV). In 53 patients who underwent minimally invasive total thyroidectomy (from January 2003 to December 2007), US-TV, obtained by ellipsoid volume formula, was compared to PS-TV determined by the Archimedes' principle. A mathematical formula able to predict the TV from the US-TV was applied in 34 cases in the last 2 years. Mean US-TV (14.4 +/- 5.9 ml) was significantly lower than mean PS-TV (21.7 +/- 10.3 ml). This underestimation was related to gland multinodularity and/or nodular involvement of the isthmus. A mathematical formula to reduce US-TV underestimation and predict the real TV was developed using a linear model. Mean predicted TV (16.8 +/- 3.7 ml) perfectly matched mean PS-TV, underestimating PS-TV in 19% of cases. We verified the accuracy of this mathematical model in patients' eligibility for minimally invasive total thyroidectomy, and we demonstrated that a predicted TV <25 ml was confirmed post-surgery in 94% of cases. We demonstrated that using a linear model, it is possible to predict from US the PS-TV with high accuracy. In fact, the mean predicted TV perfectly matched the mean PS-TV in all cases. In particular, the percentage of cases in which the predicted TV perfectly matched the PS-TV increases from 23%, estimated by US, to 43%. Moreover, the percentage of TV underestimation was reduced from 77% to 19%, as well as the range of the disagreement from up to 200% to 80%. This study shows that two-dimensional US can provide the accurate estimation of thyroid volume but that it can be improved by a mathematical model. This may contribute to a more appropriate surgical management of thyroid diseases.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Gravitational effects on global hemodynamics in different postures: A closed-loop multiscale mathematical analysis

NASA Astrophysics Data System (ADS)

Zhang, Xiancheng; Noda, Shigeho; Himeno, Ryutaro; Liu, Hao

2017-06-01

We present a novel methodology and strategy to predict pressures and flow rates in the global cardiovascular network in different postures varying from supine to upright. A closed-loop, multiscale mathematical model of the entire cardiovascular system (CVS) is developed through an integration of one-dimensional (1D) modeling of the large systemic arteries and veins, and zero-dimensional (0D) lumped-parameter modeling of the heart, the cardiac-pulmonary circulation, the cardiac and venous valves, as well as the microcirculation. A versatile junction model is proposed and incorporated into the 1D model to cope with splitting and/or merging flows across a multibranched junction, which is validated to be capable of estimating both subcritical and supercritical flows while ensuring the mass conservation and total pressure continuity. To model gravitational effects on global hemodynamics during postural change, a robust venous valve model is further established for the 1D venous flows and distributed throughout the entire venous network with consideration of its anatomically realistic numbers and locations. The present integrated model is proven to enable reasonable prediction of pressure and flow rate waveforms associated with cardiopulmonary circulation, systemic circulation in arteries and veins, as well as microcirculation within normal physiological ranges, particularly in mean venous pressures, which well match the in vivo measurements. Applications of the cardiovascular model at different postures demonstrate that gravity exerts remarkable influence on arterial and venous pressures, venous returns and cardiac outputs whereas venous pressures below the heart level show a specific correlation between central venous and hydrostatic pressures in right atrium and veins.

Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanakoglou, K.; School of Physics, Nuclear and Elementary Particle Physics Department, Aristotle University of Thessaloniki; Daskaloyannis, C.

The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, whilemore » the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.« less

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Students' Conceptions of Mathematics Bridging Courses

ERIC Educational Resources Information Center

Gordon, Sue; Nicholas, Jackie

2013-01-01

In this study we investigate the conceptions of mathematics bridging courses held by students enrolled in these courses at a major Australian university. We report on the participants' responses to email-interview questions about the mathematics bridging courses to describe a two-dimensional outcome space of variations in awareness about the…

Mathematical simulation of forced expiration.

PubMed

Elad, D; Kamm, R D; Shapiro, A H

1988-07-01

Flow limitation during forced expiration is simulated by a mathematical model. This model draws on the pressure-area law obtained in the accompanying paper, and the methods of analysis for one-dimensional flow in collapsible tubes developed by Shapiro (Trans. ASME J. Biomech. Eng. 99: 126-147, 1977). These methods represent an improvement over previous models in that 1) the effects of changing lung volume and of parenchymal-bronchial interdependence are simulated; 2) a more realistic representation of collapsed airways is employed; 3) a solution is obtained mouthward of the flow-limiting site by allowing for a smooth transition from sub- to supercritical flow speeds, then matching mouth pressure by imposing an elastic jump (an abrupt transition from super- to subcritical flow speeds) at the appropriate location; and 4) the effects of levels of effort (or vacuum pressure) in excess of those required to produce incipient flow limitation are examined, including the effects of potential physiological limitation.

Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

PubMed Central

Safaei, Soroush; Blanco, Pablo J.; Müller, Lucas O.; Hellevik, Leif R.; Hunter, Peter J.

2018-01-01

We propose a detailed CellML model of the human cerebral circulation that runs faster than real time on a desktop computer and is designed for use in clinical settings when the speed of response is important. A lumped parameter mathematical model, which is based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, is constructed using a bond graph formulation to ensure mass conservation and energy conservation. The model includes arterial vessels with geometric and anatomical data based on the ADAN circulation model. The peripheral beds are represented by lumped parameter compartments. We compare the hemodynamics predicted by the bond graph formulation of the cerebral circulation with that given by a classical one-dimensional Navier-Stokes model working on top of the whole-body ADAN model. Outputs from the bond graph model, including the pressure and flow signatures and blood volumes, are compared with physiological data. PMID:29551979

Basin-scale hydrogeologic modeling

NASA Astrophysics Data System (ADS)

Person, Mark; Raffensperger, Jeff P.; Ge, Shemin; Garven, Grant

1996-02-01

Mathematical modeling of coupled groundwater flow, heat transfer, and chemical mass transport at the sedimentary basin scale has been increasingly used by Earth scientists studying a wide range of geologic processes including the formation of excess pore pressures, infiltration-driven metamorphism, heat flow anomalies, nuclear waste isolation, hydrothermal ore genesis, sediment diagenesis, basin tectonics, and petroleum generation and migration. These models have provided important insights into the rates and pathways of groundwater migration through basins, the relative importance of different driving mechanisms for fluid flow, and the nature of coupling between the hydraulic, thermal, chemical, and stress regimes. The mathematical descriptions of basin transport processes, the analytical and numerical solution methods employed, and the application of modeling to sedimentary basins around the world are the subject of this review paper. The special considerations made to represent coupled transport processes at the basin scale are emphasized. Future modeling efforts will probably utilize three-dimensional descriptions of transport processes, incorporate greater information regarding natural geological heterogeneity, further explore coupled processes, and involve greater field applications.

Mathematics Competency for Beginning Chemistry Students Through Dimensional Analysis.

PubMed

Pursell, David P; Forlemu, Neville Y; Anagho, Leonard E

2017-01-01

Mathematics competency in nursing education and practice may be addressed by an instructional variation of the traditional dimensional analysis technique typically presented in beginning chemistry courses. The authors studied 73 beginning chemistry students using the typical dimensional analysis technique and the variation technique. Student quantitative problem-solving performance was evaluated. Students using the variation technique scored significantly better (18.3 of 20 points, p < .0001) on the final examination quantitative titration problem than those who used the typical technique (10.9 of 20 points). American Chemical Society examination scores and in-house assessment indicate that better performing beginning chemistry students were more likely to use the variation technique rather than the typical technique. The variation technique may be useful as an alternative instructional approach to enhance beginning chemistry students' mathematics competency and problem-solving ability in both education and practice. [J Nurs Educ. 2017;56(1):22-26.]. Copyright 2017, SLACK Incorporated.

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Generalized Lorenz equations on a three-sphere

NASA Astrophysics Data System (ADS)

Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A.

2017-06-01

Edward Lorenz is best known for one specific three-dimensional differential equation, but he actually created a variety of related N-dimensional models. In this paper, we discuss a unifying principle for these models and put them into an overall mathematical framework. Because this family of models is so large, we are forced to choose. We sample the variety of dynamics seen in these models, by concentrating on a four-dimensional version of the Lorenz models for which there are three parameters and the norm of the solution vector is preserved. We can therefore restrict our focus to trajectories on the unit sphere S 3 in ℝ4. Furthermore, we create a type of Poincaré return map. We choose the Poincaré surface to be the set where one of the variables is 0, i.e., the Poincaré surface is a two-sphere S 2 in ℝ3. Examining different choices of our three parameters, we illustrate the wide variety of dynamical behaviors, including chaotic attractors, period doubling cascades, Standard-Map-like structures, and quasiperiodic trajectories. Note that neither Standard-Map-like structure nor quasiperiodicity has previously been reported for Lorenz models.

How cells engulf: a review of theoretical approaches to phagocytosis

NASA Astrophysics Data System (ADS)

Richards, David M.; Endres, Robert G.

2017-12-01

Phagocytosis is a fascinating process whereby a cell surrounds and engulfs particles such as bacteria and dead cells. This is crucial both for single-cell organisms (as a way of acquiring nutrients) and as part of the immune system (to destroy foreign invaders). This whole process is hugely complex and involves multiple coordinated events such as membrane remodelling, receptor motion, cytoskeleton reorganisation and intracellular signalling. Because of this, phagocytosis is an excellent system for theoretical study, benefiting from biophysical approaches combined with mathematical modelling. Here, we review these theoretical approaches and discuss the recent mathematical and computational models, including models based on receptors, models focusing on the forces involved, and models employing energetic considerations. Along the way, we highlight a beautiful connection to the physics of phase transitions, consider the role of stochasticity, and examine links between phagocytosis and other types of endocytosis. We cover the recently discovered multistage nature of phagocytosis, showing that the size of the phagocytic cup grows in distinct stages, with an initial slow stage followed by a much quicker second stage starting around half engulfment. We also address the issue of target shape dependence, which is relevant to both pathogen infection and drug delivery, covering both one-dimensional and two-dimensional results. Throughout, we pay particular attention to recent experimental techniques that continue to inform the theoretical studies and provide a means to test model predictions. Finally, we discuss population models, connections to other biological processes, and how physics and modelling will continue to play a key role in future work in this area.

Investigation on the Yarn Squeezing Effect of Three Dimensional Full Five Directional Braided Composites

NASA Astrophysics Data System (ADS)

Hu, Long; Tao, Guoquan; Liu, Zhenguo; Wang, Yibo; Ya, Jixuan

2018-04-01

The influence of yarn squeezing effect on the geometric morphology and mechanical property of the three dimensional full five directional (3DF5D) braided composites is explored. Spatial path and cross-section shape of the yarns in the braided structure are characterized based on the micro computed tomography (micro CT) scanning images. The yarn distortion due to the squeezing effect is discussed and mathematical morphology of the yarn geometry is established. A new repeated unit cell (RUC) model of 3DF5D braided composites considering yarn squeezing effect is developed. Based on this model, mechanical properties of 3DF5D braided composites are analyzed. Good agreement is obtained between the predicted and experiment results. Moreover, the stress distribution of the new RUC model are compared with original RUC model, showing that the squeezing effect significantly increases the stress concentration level of the axial yarns.

An Incidence Loss Model for Wave Rotors with Axially Aligned Passages

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

1998-01-01

A simple mathematical model is described to account for the losses incurred when the flow in the duct (port) of a wave rotor is not aligned with the passages. The model, specifically for wave rotors with axially aligned passages, describes a loss mechanism which is sensitive to incident flow angle and Mach number. Implementation of the model in a one-dimensional CFD based wave rotor simulation is presented. Comparisons with limited experimental results are consistent with the model. Sensitivity studies are presented which highlight the significance of the incidence loss relative to other loss mechanisms in the wave rotor.

Updated Panel-Method Computer Program

NASA Technical Reports Server (NTRS)

Ashby, Dale L.

1995-01-01

Panel code PMARC_12 (Panel Method Ames Research Center, version 12) computes potential-flow fields around complex three-dimensional bodies such as complete aircraft models. Contains several advanced features, including internal mathematical modeling of flow, time-stepping wake model for simulating either steady or unsteady motions, capability for Trefftz computation of drag induced by plane, and capability for computation of off-body and on-body streamlines, and capability of computation of boundary-layer parameters by use of two-dimensional integral boundary-layer method along surface streamlines. Investigators interested in visual representations of phenomena, may want to consider obtaining program GVS (ARC-13361), General visualization System. GVS is Silicon Graphics IRIS program created to support scientific-visualization needs of PMARC_12. GVS available separately from COSMIC. PMARC_12 written in standard FORTRAN 77, with exception of NAMELIST extension used for input.

Interactive computer aided technology, evolution in the design/manufacturing process

NASA Technical Reports Server (NTRS)

English, C. H.

1975-01-01

A powerful computer-operated three dimensional graphic system and associated auxiliary computer equipment used in advanced design, production design, and manufacturing was described. This system has made these activities more productive than when using older and more conventional methods to design and build aerospace vehicles. With the use of this graphic system, designers are now able to define parts using a wide variety of geometric entities, define parts as fully surface 3-dimensional models as well as "wire-frame" models. Once geometrically defined, the designer is able to take section cuts of the surfaced model and automatically determine all of the section properties of the planar cut, lightpen detect all of the surface patches and automatically determine the volume and weight of the part. Further, his designs are defined mathematically at a degree of accuracy never before achievable.

A mathematical formula to estimate in vivo thyroid volume from two-dimensional ultrasonography.

PubMed

Trimboli, Pierpaolo; Ruggieri, Massimo; Fumarola, Angela; D'Alò, Michele; Straniero, Andrea; Maiuolo, Amelia; Ulisse, Salvatore; D'Armiento, Massimino

2008-08-01

The determination of thyroid volume (TV) is required for the management of thyroid diseases. Since two-dimensional ultrasonography (2D-US) has become the accepted method for the assessment of TV (2D-US-TV), we verified whether it accurately assesses postsurgical measured TV (PS-TV). In 92 patients who underwent total thyroidectomy by conventional cervicotomy, 2D-US-TV obtained by the ellipsoid volume formula was compared to PS-TV, determined by the Archimedes' principle. Mean 2D-US-TV (23.9 +/- 14.8 mL) was significantly lower than mean PS-TV (33.4 +/- 20.1 mL). Underestimation was observed in 77% of cases, and it was related to gland multinodularity and/or nodular involvement of the isthmus, while 2D-US-TV matched the PS-TV in the remaining 21 cases (23%). A mathematical formula, to estimate PS-TV from US-TV, was derived using a linear model (Calculated-TV = [1.24 x 2D-US-TV]+ 3.66). Calculated-TV (mean value 33.4 +/- 18.3 mL) significantly (p < 0.01) increased from 21 (23%) to 31 (34%) of the cases that matched PS-TV. In addition, it significantly (p < 0.01) decreased from 77% to 27% the percentage of cases where PS-TV was underestimated as well as the range of the disagreement from 245% to 92%. This study shows that 2D-US does not provide an accurate estimation of TV and suggests that it can be improved by a mathematical model different from the ellipsoid model. If confirmed in prospective studies, this may contribute to a more appropriate management of thyroid diseases.

Three-dimensional measurement of femur based on structured light scanning

NASA Astrophysics Data System (ADS)

Li, Jie; Ouyang, Jianfei; Qu, Xinghua

2009-12-01

Osteometry is fundamental to study the human skeleton. It has been widely used in palaeoanthropology, bionics, and criminal investigation for more than 200 years. The traditional osteometry is a simple 1-dimensional measurement that can only get 1D size of the bones in manual step-by-step way, even though there are more than 400 parameters to be measured. For today's research and application it is significant and necessary to develop an advanced 3-dimensional osteometry technique. In this paper a new 3D osteometry is presented, which focuses on measurement of the femur, the largest tubular bone in human body. 3D measurement based on the structured light scanning is developed to create fast and precise measurement of the entire body of the femur. The cloud data and geometry model of the sample femur is established in mathematic, accurate and fast way. More than 30 parameters are measured and compared with each other. The experiment shows that the proposed method can meet traditional osteometry and obtain all 1D geometric parameters of the bone at the same time by the mathematics model, such as trochanter-lateral condyle length, superior breadth of shaft, and collo-diaphyseal angle, etc. In the best way, many important geometric parameters that are very difficult to measure by existing osteometry, such as volume, surface area, and curvature of the bone, can be obtained very easily. The overall measuring error is less than 0.1mm.

Three-dimensional measurement of femur based on structured light scanning

NASA Astrophysics Data System (ADS)

Li, Jie; Ouyang, Jianfei; Qu, Xinghua

2010-03-01

Osteometry is fundamental to study the human skeleton. It has been widely used in palaeoanthropology, bionics, and criminal investigation for more than 200 years. The traditional osteometry is a simple 1-dimensional measurement that can only get 1D size of the bones in manual step-by-step way, even though there are more than 400 parameters to be measured. For today's research and application it is significant and necessary to develop an advanced 3-dimensional osteometry technique. In this paper a new 3D osteometry is presented, which focuses on measurement of the femur, the largest tubular bone in human body. 3D measurement based on the structured light scanning is developed to create fast and precise measurement of the entire body of the femur. The cloud data and geometry model of the sample femur is established in mathematic, accurate and fast way. More than 30 parameters are measured and compared with each other. The experiment shows that the proposed method can meet traditional osteometry and obtain all 1D geometric parameters of the bone at the same time by the mathematics model, such as trochanter-lateral condyle length, superior breadth of shaft, and collo-diaphyseal angle, etc. In the best way, many important geometric parameters that are very difficult to measure by existing osteometry, such as volume, surface area, and curvature of the bone, can be obtained very easily. The overall measuring error is less than 0.1mm.

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Mathematical modeling of the in-mold coating process for injection-molded thermoplastic parts

NASA Astrophysics Data System (ADS)

Chen, Xu

In-Mold Coating (IMC) has been successfully used for many years for exterior body panels made from compression molded Sheet Molding Compound (SMC). The coating material is a single component reactive fluid, designed to improve the surface quality of SMC moldings in terms of functional and cosmetic properties. When injected onto a cured SMC part, IMC cures and bonds to provide a pain-like surface. Because of its distinct advantages, IMC is being considered for application to injection molded thermoplastic parts. For a successful in mold coating operation, there are two key issues related to the flow of the coating. First, the injection nozzle should be located such that the thermoplastic substrate is totally covered and the potential for air trapping is minimized. The selected location should be cosmetically acceptable since it most likely will leave a mark on the coated surface. The nozzle location also needs to be accessible for easy of maintenance. Secondly, the hydraulic force generated by the coating injection pressure should not exceed the available clamping tonnage. If the clamping force is exceeded, coating leakage will occur. In this study, mathematical models for IMC flow on the compressible thermoplastic substrate have been developed. Finite Difference Method (FDM) is first used to solve the 1 dimensional (1D) IMC flow problem. In order to investigate the application of Control Volume based Finite Element Method (CV/FEM) to more complicated two dimensional IMC flow, that method is first evaluated by solving the 1D IMC flow problem. An analytical solution, which can be obtained when a linear relationship between the coating thickness and coating injection pressure is assumed, is used to verify the numerical results. The mathematical models for the 2 dimensional (2D) IMC flow are based on the generalized Hele-Shaw approximation. It has been found experimentally that the power law viscosity model adequately predicts the rheological behavior of the coating. The compressibility of the substrate is modeled by the 2-domain Tait PVT equation. CV/FEM is used to solve the discretized governing equations. A computer code has been developed to predict the fill pattern of the coating and the injection pressure. A number of experiments have been conducted to verify the numerical predictions of the computer code. It has been found both numerically and experimentally that the substrate thickness plays a significant role on the IMC fill pattern.

3-Dimensional stereo implementation of photoacoustic imaging based on a new image reconstruction algorithm without using discrete Fourier transform

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu

2017-05-01

In this paper, we propose a new three-dimensional stereo image reconstruction algorithm for a photoacoustic medical imaging system. We also introduce and discuss a new theoretical algorithm by using the physical concept of Radon transform. The main key concept of proposed theoretical algorithm is to evaluate the existence possibility of the acoustic source within a searching region by using the geometric distance between each sensor element of acoustic detector and the corresponding searching region denoted by grid. We derive the mathematical equation for the magnitude of the existence possibility which can be used for implementing a new proposed algorithm. We handle and derive mathematical equations of proposed algorithm for the one-dimensional sensing array case as well as two dimensional sensing array case too. A mathematical k-wave simulation data are used for comparing the image quality of the proposed algorithm with that of general conventional algorithm in which the FFT should be necessarily used. From the k-wave Matlab simulation results, we can prove the effectiveness of the proposed reconstruction algorithm.

Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm.

PubMed

Nittala, Aparna; Ghosh, Soumitra; Stefanovski, Darko; Bergman, Richard; Wang, Xujing

2006-07-14

Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available. A formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data. The degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5-5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation. Dimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms.

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

PubMed Central

Mollard, Séverine; Fanciullino, Raphaelle; Giacometti, Sarah; Serdjebi, Cindy; Benzekry, Sebastien; Ciccolini, Joseph

2016-01-01

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology. PMID:27812027

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1987-01-01

The research goal was a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. This presents a formidable mathematical problem. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity are defined. Each model is summarized.

Energy transfer simulation for radiantly heated and cooled enclosures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chapman, K.S.; Zhang, P.

1996-11-01

This paper presents the development of a three-dimensional mathematical model to compute heat transfer within a radiantly heated or cooled room, which then calculates the mass-averaged room air temperature and the wall surface temperature distributions. The radiation formulation used in the model accommodates arbitrary placement of walls and objects within the room. The convection model utilizes Nusselt number correlations published in the open literature. The complete energy transfer model is validated by comparing calculated room temperatures to temperatures measured in a radiantly heated room. This three-dimensional model may be applied to a building to assist the heating/cooling system design engineermore » in sizing a radiant heating/cooling system. By coupling this model with a thermal comfort model, the comfort levels throughout the room can be easily and efficiently mapped for a given radiant heater/cooler location. In addition, obstacles such as airplanes, trucks, furniture, and partitions can be easily incorporated to determine their effect on the radiant heating system performance.« less

Thermal Pollution Mathematical Model. Volume 2; Verification of One-Dimensional Numerical Model at Lake Keowee

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Exploring extra dimensions with scalar fields

NASA Astrophysics Data System (ADS)

Brown, Katherine; Mathur, Harsh; Verostek, Mike

2018-05-01

This paper provides a pedagogical introduction to the physics of extra dimensions by examining the behavior of scalar fields in three landmark models: the ADD, Randall-Sundrum, and DGP spacetimes. Results of this analysis provide qualitative insights into the corresponding behavior of gravitational fields and elementary particles in each of these models. In these "brane world" models, the familiar four dimensional spacetime of everyday experience is called the brane and is a slice through a higher dimensional spacetime called the bulk. The particles and fields of the standard model are assumed to be confined to the brane, while gravitational fields are assumed to propagate in the bulk. For all three spacetimes, we calculate the spectrum of propagating scalar wave modes and the scalar field produced by a static point source located on the brane. For the ADD and Randall-Sundrum models, at large distances, the field looks like that of a point source in four spacetime dimensions, but at short distances, it crosses over to a form appropriate to the higher dimensional spacetime. For the DGP model, the field has the higher dimensional form at long distances rather than short. The behavior of these scalar fields, derived using only undergraduate level mathematics, closely mirror the results that one would obtain by performing the far more difficult task of analyzing the behavior of gravitational fields in these spacetimes.

CE-QUAL-W2: A Numerical Two-Dimensional, Laterally Averaged Model of Hydrodynamics and Water Quality; User’s Manual.

DTIC Science & Technology

1986-08-01

publication by Ms. Jessica S. Ruff, Information Products Division, WES. This manual is published in loose-leaf format for convenience in ." ._ periodic...transfer computations. m. Variety of output options. Background 8. This manual is a product of a program of evaluation and refinement of mathematical water...zooplankton and higher order herbivores. However, these groups are presently not included in the model. Macrophyte production may also have an impact upon

Computing Mass Properties From AutoCAD

NASA Technical Reports Server (NTRS)

Jones, A.

1990-01-01

Mass properties of structures computed from data in drawings. AutoCAD to Mass Properties (ACTOMP) computer program developed to facilitate quick calculations of mass properties of structures containing many simple elements in such complex configurations as trusses or sheet-metal containers. Mathematically modeled in AutoCAD or compatible computer-aided design (CAD) system in minutes by use of three-dimensional elements. Written in Microsoft Quick-Basic (Version 2.0).

An exactly solvable, spatial model of mutation accumulation in cancer

NASA Astrophysics Data System (ADS)

Paterson, Chay; Nowak, Martin A.; Waclaw, Bartlomiej

2016-12-01

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

Mathematical Skills in Ninth-graders: Relationship with Visuo-spatial Abilities and Working Memory.

ERIC Educational Resources Information Center

Reuhkala, Minna

2001-01-01

Investigates the relationship between working memory (WM) capacity (particularly visuo-spatial working memory (VSWM)), the ability to mentally rotate three-dimensional objects, and mathematical skills. Explains that in experiment 1, VSWM was examined; and in experiment 2, contributions of other WM components to mathematical skills was examined.…

Developing a Multi-Dimensional Early Elementary Mathematics Screener and Diagnostic Tool: The Primary Mathematics Assessment

ERIC Educational Resources Information Center

Brendefur, Jonathan L.; Johnson, Evelyn S.; Thiede, Keith W.; Strother, Sam; Severson, Herb H.

2018-01-01

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention…

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Large-scale Instability during Gravitational Collapse with Neutrino Transport and a Core-Collapse Supernova

NASA Astrophysics Data System (ADS)

Aksenov, A. G.; Chechetkin, V. M.

2018-04-01

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (≳10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented.

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

Study of ecological compensation in complex river networks based on a mathematical model.

PubMed

Wang, Xiao; Shen, Chunqi; Wei, Jun; Niu, Yong

2018-05-31

Transboundary water pollution has resulted in increasing conflicts between upstream and downstream administrative districts. Ecological compensation is an efficient means of restricting pollutant discharge and achieving sustainable utilization of water resources. The tri-provincial region of Taihu Basin is a typical river networks area. Pollutant flux across provincial boundaries in the Taihu Basin is hard to determine due to complex hydrologic and hydrodynamic conditions. In this study, ecological compensation estimation for the tri-provincial area based on a mathematical model is investigated for better environmental management. River discharge and water quality are predicted with the one-dimensional mathematical model and validated with field measurements. Different ecological compensation criteria are identified considering the notable regional discrepancy in sewage treatment costs. Finally, the total compensation payment is estimated. Our study indicates that Shanghai should be the receiver of payment from both Jiangsu and Zhenjiang in 2013, with 305 million and 300 million CNY, respectively. Zhejiang also contributes more pollutants to Jiangsu, and the compensation to Jiangsu is estimated as 9.3 million CNY. The proposed ecological compensation method provides an efficient way for solving the transboundary conflicts in a complex river networks area and is instructive for future policy-making.

Thermal mathematical modeling of a multicell common pressure vessel nickel-hydrogen battery

NASA Technical Reports Server (NTRS)

Kim, Junbom; Nguyen, T. V.; White, R. E.

1992-01-01

A two-dimensional and time-dependent thermal model of a multicell common pressure vessel (CPV) nickel-hydrogen battery was developed. A finite element solver called PDE/Protran was used to solve this model. The model was used to investigate the effects of various design parameters on the temperature profile within the cell. The results were used to help find a design that will yield an acceptable temperature gradient inside a multicell CPV nickel-hydrogen battery. Steady-state and unsteady-state cases with a constant heat generation rate and a time-dependent heat generation rate were solved.

Effect of operational cycle time length on nitrogen removal in an alternating oxidation ditch system.

PubMed

Mantziaras, I D; Stamou, A; Katsiri, A

2011-06-01

This paper refers to nitrogen removal optimization of an alternating oxidation ditch system through the use of a mathematical model and pilot testing. The pilot system where measurements have been made has a total volume of 120 m(3) and consists of two ditches operating in four phases during one cycle and performs carbon oxidation, nitrification, denitrification and settling. The mathematical model consists of one-dimensional mass balance (convection-dispersion) equations based on the IAWPRC ASM 1 model. After the calibration and verification of the model, simulation system performance was made. Optimization is achieved by testing operational cycles and phases with different time lengths. The limits of EU directive 91/271 for nitrogen removal have been used for comparison. The findings show that operational cycles with smaller time lengths can achieve higher nitrogen removals and that an "equilibrium" between phase time percentages in the whole cycle, for a given inflow, must be achieved.

Modelling microtubules in the brain as n-qudit quantum Hopfield network and beyond

NASA Astrophysics Data System (ADS)

Pyari Srivastava, Dayal; Sahni, Vishal; Saran Satsangi, Prem

2016-01-01

The scientific approach to understand the nature of consciousness revolves around the study of the human brain. Neurobiological studies that compare the nervous system of different species have accorded the highest place to humans on account of various factors that include a highly developed cortical area comprising of approximately 100 billion neurons, that are intrinsically connected to form a highly complex network. Quantum theories of consciousness are based on mathematical abstraction and the Penrose-Hameroff Orch-OR theory is one of the most promising ones. Inspired by the Penrose-Hameroff Orch-OR theory, Behrman et al. have simulated a quantum Hopfield neural network with the structure of a microtubule. They have used an extremely simplified model of the tubulin dimers with each dimer represented simply as a qubit, a single quantum two-state system. The extension of this model to n-dimensional quantum states or n-qudits presented in this work holds considerable promise for even higher mathematical abstraction in modelling consciousness systems.

Fitting a Structured Juvenile-Adult Model for Green Tree Frogs to Population Estimates from Capture-Mark-Recapture Field Data

USGS Publications Warehouse

Ackleh, A.S.; Carter, J.; Deng, K.; Huang, Q.; Pal, N.; Yang, X.

2012-01-01

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation. ?? 2011 Society for Mathematical Biology.

Longitudinal dispersion modeling in small streams

NASA Astrophysics Data System (ADS)

Pekarova, Pavla; Pekar, Jan; Miklanek, Pavol

2014-05-01

The environmental problems caused by the increasing of pollutant loads discharged into natural water bodies are very complex. For that reason the cognition of transport mechanism and mixing characteristics in natural streams is very important. The mathematical and numerical models have become very useful tools for solving the water management problems. The mathematical simulations based on numerical models of pollution mixing in streams can be used (for example) for prediction of spreading of accidental contaminant waves in rivers. The paper deals with the estimation of the longitudinal dispersion coefficients and with the numerical simulation of transport and transformation of accidental pollution in the small natural streams. There are different ways of solving problems of pollution spreading in open channels, in natural rivers. One of them is the hydrodynamic approach, which endeavours to understand and quantify the spreading phenomenon in a stream. The hydrodynamic models are based on advection-diffusion equation and the majority of them are one-dimensional models. Their disadvantage is inability to simulate the spread of pollution until complete dispersion of pollutant across the stream section is finished. Two-dimensional mixing models do not suffer from these limitations. On the other hand, the one-dimensional models are simpler than two-dimensional ones, they need not so much input data and they are often swifter. Three-dimensional models under conditions of natural streams are applicable with difficulties (or inapplicable) for their complexity and demands on accuracy and amount of input data. As there was mentioned above the two-dimensional models can be used also until complete dispersion of pollutant across the stream section is not finished, so we decided to apply the two-dimensional model SIRENIE. Experimental microbasin Rybarik is the part of the experimental Mostenik brook basin of IH SAS Bratislava. It was established as a Field Hydrological Laboratory in 1958. Since 1986 started a chemical program in the basin. The total area of the Rybarik basin is 0.119 km2. The length of the stream from spring to closing profile is 256 m, the mean slope of the stream is 9.1%, and the mean slope of the basin is 14.9%. The elevation is from 369 to 434 m above the sea level. The geological conditions in the Rybarik basin are characterized by flysh substrates (altering layers of clay and sandstones). The basin is from 2/3 cultivated by the state farm, private farmer covers the rest of the area. The forest coverage during the period 1986-2004 was approximately 10%, rest of the land is arable. NaCl (10-30 g) was injected to the Rybárik brook at different water levels and in different seasons. The electric conductivity was measured 100 and 250 m downstream the injection point. The samples were taken for Cl- concentration analyses during the first cases. The Cl and EC waves were identical. Coefficients of the longitudinal dispersion were estimated by trial-error method in the Rybárik brook using model SIRENIE. Coefficients were in range of 0.2 - 0.7 m2.s-1. Acknowledgement: This work was supported by project VEGA 0010/11.

Qualitative methods in quantum theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Migdal, A.B.

The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

Modeling physiological resistance in bacterial biofilms.

PubMed

Cogan, N G; Cortez, Ricardo; Fauci, Lisa

2005-07-01

A mathematical model of the action of antimicrobial agents on bacterial biofilms is presented. The model includes the fluid dynamics in and around the biofilm, advective and diffusive transport of two chemical constituents and the mechanism of physiological resistance. Although the mathematical model applies in three dimensions, we present two-dimensional simulations for arbitrary biofilm domains and various dosing strategies. The model allows the prediction of the spatial evolution of bacterial population and chemical constituents as well as different dosing strategies based on the fluid motion. We find that the interaction between the nutrient and the antimicrobial agent can reproduce survival curves which are comparable to other model predictions as well as experimental results. The model predicts that exposing the biofilm to low concentration doses of antimicrobial agent for longer time is more effective than short time dosing with high antimicrobial agent concentration. The effects of flow reversal and the roughness of the fluid/biofilm are also investigated. We find that reversing the flow increases the effectiveness of dosing. In addition, we show that overall survival decreases with increasing surface roughness.

Visualization of nuclear particle trajectories in nuclear oil-well logging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Case, C.R.; Chiaramonte, J.M.

Nuclear oil-well logging measures specific properties of subsurface geological formations as a function of depth in the well. The knowledge gained is used to evaluate the hydrocarbon potential of the surrounding oil field. The measurements are made by lowering an instrument package into an oil well and slowly extracting it at a constant speed. During the extraction phase, neutrons or gamma rays are emitted from the tool, interact with the formation, and scatter back to the detectors located within the tool. Even though only a small percentage of the emitted particles ever reach the detectors, mathematical modeling has been verymore » successful in the accurate prediction of these detector responses. The two dominant methods used to model these devices have been the two-dimensional discrete ordinates method and the three-dimensional Monte Carlo method has routinely been used to investigate the response characteristics of nuclear tools. A special Los Alamos National Laboratory version of their standard MCNP Monte carlo code retains the details of each particle history of later viewing within SABRINA, a companion three-dimensional geometry modeling and debugging code.« less

PREFACE: Physics-Based Mathematical Models for Nanotechnology

NASA Astrophysics Data System (ADS)

Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

2008-03-01

In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop. Nanotechnology is the study and application of phenomena at or below the dimensions of 100 nm and has received a lot of public attention following popular accounts such as in the bestselling book by Michael Crichton, Prey. It is an area where fundamental questions of applied mathematics and mathematical physics, design of computational methodologies, physical insight, engineering and experimental techniques are meeting together in a quest for an adequate description of nanomaterials and nanostructures for applications in optoelectronics, medicine, energy-saving, bio- and other key technologies which will profoundly influence our life in the 21st century and beyond. There are already hundreds of applications in daily life such as in cosmetics and the hard drives in MP3 players (the 2007 Nobel prize in physics was recently awarded for the science that allowed the miniaturization of the drives), delivering drugs, high-definition DVD players and stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a task of enormous computational complexity in solving a large-scale many-body problem. On the other hand, taking each quantum dot in isolation would lead to a manageable task for modern supercomputers, but accounting for the wetting layer even in the individual quantum dot model would increase the computational complexity of the problem in several times. As a result, the entire problem in its generality would be hardly feasible from a practical, routine-based simulation, point of view. Moreover, in calculating atomic positions the definitions of atomic forces that enter the Hamiltonian in such large scale atomic simulations are approximate by nature and a number of important coupled effects, such as piezoelectric, remain frequently outside the scope of the analysis. To attack the problem in hand, one needs to resort to some clever averaging over atomic scales. Such averaging can be achieved by empirical tight-binding, pseudopotential, and k.p approximations. These approximations are very important in further development of mathematical models for LDSNs due to the fact they are well suited for incorporating additional effects into the model, including strain, piezoelectric effects, spontaneous polarization, geometric and materials nonlinearities. These effects, despite their importance, have not been studied with vigor they deserve, in particular in the context of mathematical models for bandstructure calculations. There is a growing interest to such models as they should provide a key to better predicting optoelectromechanical properties of LDSNs. With anticipated new discoveries in theoretical and experimental analysis of LDSNs in the coming years, one of the main emphases of the workshop was on the models that would allow incorporating these effects consistently into the state-of-the-art models for LDSNs. From a mathematical point of view, many such models can be reduced to a large eigenvalue PDE problem (e.g., with the Hamiltonian accounting for the Burt-Foreman correction) coupled to strain and piezoelectric potential calculation. In its turn, in its general setting the problem of strain and piezoelectric potential calculation requires the solution of a nonlinear system of partial differential equation. A large experience in solving these two parts of the problem separately, independently of each other, has been already accumulated in the distinct communities of the researchers. This BIRS workshop effectively combined expertise of these research communities, summarized the state-of-the-art for modeling LDSNs and key challenges facing these communities, and explored ways to address those challenges in interdisciplinary team settings. The workshop brought together researchers working on different aspects of the analysis and modeling of LDSNs which require a concerted efforts of teams of researchers with close interactions between applied and pure mathematicians, physicists (theoreticians and experimentalists), computational scientists, and engineers. These scientific and engineering communities were represented in Banff by the researchers from Japan, Canada, the USA, Russia, France, Denmark, Germany, and the UK (further details can be found at http://www.m2netlab.wlu.ca/ldsn-banff/). We had four main plenary talks of one hour duration that gave state-of-the-art overviews of the subject from perspectives of applied mathematics (Professor Russel Caflisch of the University of California at Los Angeles), physics (Professor Antti-Pekka Jauho of the Danish Technical University), and computational science and engineering communities (Professor Gerhard Klimeck of Purdue University), as well as from a point of view of experimentalists (Dr Gail Brown of the Materials Lab/Air Force Research Lab at Wright-Patterson AFB). These talks helped identify the areas where joint efforts needed to be directed to, and they set up the scene for further work during the workshop, including discussions at the workshop open problem sessions. All participants had time to present their research and a specific time was allocated for on-site demonstrations of software and explanations of tools applied in the LDSN analysis. This special issue provides a flavor of the problems discussed at the workshop. It contains 12 refereed papers. Additional information, including the abstracts of all presented talks, can be found at http://www.m2netlab.wlu.ca/ldsn-banff/. Using this opportunity, we would like to thank the referees of this volume for their time and efforts. Without their timely professional comments this volume would not have been made possible. In conclusion, we note that advances in mathematics, physics and computation of LDSNs, impact such seemingly distant applications as biotechnology and medicine, quantum information processing and optoelectronics. The research into LDSNs offered exciting new challenges that are intrinsically interdisciplinary in nature and should be addressed by a multidisciplinary team of applied mathematicians, theoretical and experimental physicists, engineers and computational scientists. We hope that we are able to pass this idea to the reader. Lok C Lew Yan Voon(Wright State University, OH, USA) Roderick Melnik(M2NeT Lab, Wilfrid Laurier University, ON, Canada) Morten Willatzen(MCI, University of Southern Denmark, Denmark)

Efficient simulation and model reformulation of two-dimensional electrochemical thermal behavior of lithium-ion batteries

DOE PAGES

Northrop, Paul W. C.; Pathak, Manan; Rife, Derek; ...

2015-03-09

Lithium-ion batteries are an important technology to facilitate efficient energy storage and enable a shift from petroleum based energy to more environmentally benign sources. Such systems can be utilized most efficiently if good understanding of performance can be achieved for a range of operating conditions. Mathematical models can be useful to predict battery behavior to allow for optimization of design and control. An analytical solution is ideally preferred to solve the equations of a mathematical model, as it eliminates the error that arises when using numerical techniques and is usually computationally cheap. An analytical solution provides insight into the behaviormore » of the system and also explicitly shows the effects of different parameters on the behavior. However, most engineering models, including the majority of battery models, cannot be solved analytically due to non-linearities in the equations and state dependent transport and kinetic parameters. The numerical method used to solve the system of equations describing a battery operation can have a significant impact on the computational cost of the simulation. In this paper, a model reformulation of the porous electrode pseudo three dimensional (P3D) which significantly reduces the computational cost of lithium ion battery simulation, while maintaining high accuracy, is discussed. This reformulation enables the use of the P3D model into applications that would otherwise be too computationally expensive to justify its use, such as online control, optimization, and parameter estimation. Furthermore, the P3D model has proven to be robust enough to allow for the inclusion of additional physical phenomena as understanding improves. In this study, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects.« less

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

Three-dimensional couette flow of dusty fluid with heat transfer in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Gayathri, R.; Govindarajan, A.; Sasikala, R.

2018-04-01

This paper is focused on the mathematical modelling of three-dimensional couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates in the presence of an induced magnetic field. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phase are obtained by solving the governing partial differentiation equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem. It is found that the velocity profiles of both fluid and dust particles decrease due to the increase of (magnetic parameter) Hartmann number.

Swarming in viscous fluids: three-dimensional patterns in swimmer- and force-induced flows

NASA Astrophysics Data System (ADS)

Chuang, Yao-Li; D'Orsogna, Maria R.; Chou, Tom

Mathematical models of self-propelled interacting particles have reproduced various fascinating ``swarming'' patterns observed in natural and artificial systems. The formulation of such models usually ignores the influence of the surrounding medium in which the particles swarm. Here we develop from first principles a three-dimensional theory of swarming particles in a viscous fluid environment and investigate how the hydrodynamic coupling among the particles may affect their collective behavior. Specifically, we examine the hydrodynamic coupling among self-propelled particles interacting through ``social'' or ``mechanical'' forces. We discover that new patterns arise as a consequence of different interactions and self-propulsion mechanisms. Examples include flocks with prolate or oblate shapes, intermittent mills, recirculating peloton-like structures, and jet-like fluid flows that kinetically destabilize mill-like structures. Our results reveal possible mechanisms for three-dimensional swarms to kinetically control their collective behaviors in fluids. Supported by NSF DMS 1021818 & 1021850, ARO W1911NF-14-1-0472, ARO MURI W1911NF-11-10332.

The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2016-01-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…

Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

The operating diagram of a model of two competitors in a chemostat with an external inhibitor.

PubMed

Dellal, Mohamed; Lakrib, Mustapha; Sari, Tewfik

2018-05-24

Understanding and exploiting the inhibition phenomenon, which promotes the stable coexistence of species, is a major challenge in the mathematical theory of the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor. The model is a four-dimensional system of ordinary differential equations. Using general monotonic growth rate functions of the species and absorption rate of the inhibitor, we give a complete analysis for the existence and local stability of all steady states. We focus on the behavior of the system with respect of the three operating parameters represented by the dilution rate and the input concentrations of the substrate and the inhibitor. The operating diagram has the operating parameters as its coordinates and the various regions defined in it correspond to qualitatively different asymptotic behavior: washout, competitive exclusion of one species, coexistence of the species around a stable steady state and coexistence around a stable cycle. This bifurcation diagram which determines the effect of the operating parameters, is very useful to understand the model from both the mathematical and biological points of view, and is often constructed in the mathematical and biological literature. Copyright © 2018 Elsevier Inc. All rights reserved.

Numerical simulation on hydromechanical coupling in porous media adopting three-dimensional pore-scale model.

PubMed

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view.

Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

PubMed Central

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view. PMID:24955384

Modeling and visual simulation of Microalgae photobioreactor

NASA Astrophysics Data System (ADS)

Zhao, Ming; Hou, Dapeng; Hu, Dawei

Microalgae is a kind of nutritious and high photosynthetic efficiency autotrophic plant, which is widely distributed in the land and the sea. It can be extensively used in medicine, food, aerospace, biotechnology, environmental protection and other fields. Photobioreactor which is important equipment is mainly used to cultivate massive and high-density microalgae. In this paper, based on the mathematical model of microalgae which grew under different light intensity, three-dimensional visualization model was built and implemented in 3ds max, Virtools and some other three dimensional software. Microalgae is photosynthetic organism, it can efficiently produce oxygen and absorb carbon dioxide. The goal of the visual simulation is to display its change and impacting on oxygen and carbon dioxide intuitively. In this paper, different temperatures and light intensities were selected to control the photobioreactor, and dynamic change of microalgal biomass, Oxygen and carbon dioxide was observed with the aim of providing visualization support for microalgal and photobioreactor research.

Canards and black swans in a model of a 3-D autocatalator

NASA Astrophysics Data System (ADS)

Shchepakina, E.

2005-01-01

The mathematical model of a 3-D autocatalator is studied using the geometric theory of singular perturbations, namely, the black swan and canard techniques. Critical regimes are modeled by canards (one-dimensional stable-unstable slow integral manifolds). The meaning of criticality here is as follows. The critical regime corresponds to a chemical reaction which separates the domain of self-accelerating reactions from the domain of slow reactions. A two-dimensional stable-unstable slow integral manifold (black swan) consisting entirely of canards, which simulate the critical phenomena for different initial data of the dynamical system, is constructed. It is shown that this procedure leads to the phenomenon of auto-oscillations in the chemical system. The geometric approach combined with asymptotic and numerical methods permits us to explain the strong parametric sensitivity and to obtain asymptotic representations of the critical behavior of the chemical system.

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1997-01-01

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bubbly vertex dynamics: A dynamical and geometrical model for epithelial tissues with curved cell shapes

NASA Astrophysics Data System (ADS)

Ishimoto, Yukitaka; Morishita, Yoshihiro

2014-11-01

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

Prediction of Crack Growth Aqueous Environments.

DTIC Science & Technology

1983-06-01

one- dimensional one. The mathematical model for the electrical representation shown in Figure 1 requires solutions to a set of differential equations ... equation (5) is equivalent to that at a plane-parallel electrode. That is, it contains the info~rmation that would be available if it were possible to...concentration, and A" expresses the electrode electrolyte area per unit length that is actively engaged in reaction. The other parameters in equation (7

Three-dimensional FLASH Laser Radar Range Estimation via Blind Deconvolution

DTIC Science & Technology

2009-10-01

scene can result in errors due to several factors including the optical spatial impulse response, detector blurring, photon noise , timing jitter, and...estimation error include spatial blur, detector blurring, noise , timing jitter, and inter-sample targets. Unlike previous research, this paper ac- counts...for pixel coupling by defining the range image mathematical model as a 2D convolution between the system spatial impulse response and the object (target

A natural way to do spatial linear geometry in MACSYMA

NASA Technical Reports Server (NTRS)

Bulnes, J.

1977-01-01

A set of routines appropriate for use as an interactive aid in 3-dimensional calculations with planes, lines and points is presented. The mathematical language used is vector calculus. The simplicity with which these routines can be written in MACSYMA is demonstrated. Because of the natural way in which geometric intuition is mapped into them, they can serve as a model for an interactive computational aid for architects.

Heat Exchange with Air and Temperature Profile of a Moving Oversize Tire

NASA Astrophysics Data System (ADS)

Grinchuk, P. S.; Fisenko, S. P.

2016-11-01

A one-dimensional mathematical model of heat transfer in a tire with account for the deformation energy dissipation and heat exchange of a moving tire with air has been developed. The mean temperature profiles are calculated and transition to a stationary thermal regime is considered. The influence of the rate of energy dissipation and of effective thermal conductivity of rubber on the temperature field is investigated quantitatively.

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Numerical simulations of a reduced model for blood coagulation

NASA Astrophysics Data System (ADS)

Pavlova, Jevgenija; Fasano, Antonio; Sequeira, Adélia

2016-04-01

In this work, the three-dimensional numerical resolution of a complex mathematical model for the blood coagulation process is presented. The model was illustrated in Fasano et al. (Clin Hemorheol Microcirc 51:1-14, 2012), Pavlova et al. (Theor Biol 380:367-379, 2015). It incorporates the action of the biochemical and cellular components of blood as well as the effects of the flow. The model is characterized by a reduction in the biochemical network and considers the impact of the blood slip at the vessel wall. Numerical results showing the capacity of the model to predict different perturbations in the hemostatic system are discussed.

A finite area scheme for shallow granular flows on three-dimensional surfaces

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

Dynamic one-dimensional modeling of secondary settling tanks and design impacts of sizing decisions.

PubMed

Li, Ben; Stenstrom, Michael K

2014-03-01

As one of the most significant components in the activated sludge process (ASP), secondary settling tanks (SSTs) can be investigated with mathematical models to optimize design and operation. This paper takes a new look at the one-dimensional (1-D) SST model by analyzing and considering the impacts of numerical problems, especially the process robustness. An improved SST model with Yee-Roe-Davis technique as the PDE solver is proposed and compared with the widely used Takács model to show its improvement in numerical solution quality. The improved and Takács models are coupled with a bioreactor model to reevaluate ASP design basis and several popular control strategies for economic plausibility, contaminant removal efficiency and system robustness. The time-to-failure due to rising sludge blanket during overloading, as a key robustness indicator, is analyzed to demonstrate the differences caused by numerical issues in SST models. The calculated results indicate that the Takács model significantly underestimates time to failure, thus leading to a conservative design. Copyright © 2013 Elsevier Ltd. All rights reserved.

Three-Dimensional Geometric Modeling of Membrane-bound Organelles in Ventricular Myocytes: Bridging the Gap between Microscopic Imaging and Mathematical Simulation

PubMed Central

Yu, Zeyun; Holst, Michael J.; Hayashi, Takeharu; Bajaj, Chandrajit L.; Ellisman, Mark H.; McCammon, J. Andrew; Hoshijima, Masahiko

2009-01-01

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca2+-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation-contraction (E-C) coupling through dynamic Ca2+ mobilization in cardiomyocytes. PMID:18835449

Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: bridging the gap between microscopic imaging and mathematical simulation.

PubMed

Yu, Zeyun; Holst, Michael J; Hayashi, Takeharu; Bajaj, Chandrajit L; Ellisman, Mark H; McCammon, J Andrew; Hoshijima, Masahiko

2008-12-01

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca(2+)-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation-contraction (E-C) coupling through dynamic Ca(2+) mobilization in cardiomyocytes.

Three-Dimensional Modeling of Flow and Thermochemical Behavior in a Blast Furnace

NASA Astrophysics Data System (ADS)

Shen, Yansong; Guo, Baoyu; Chew, Sheng; Austin, Peter; Yu, Aibing

2015-02-01

An ironmaking blast furnace (BF) is a complex high-temperature moving bed reactor involving counter-, co- and cross-current flows of gas, liquid and solid, coupled with heat and mass exchange and chemical reactions. Two-dimensional (2D) models were widely used for understanding its internal state in the past. In this paper, a three-dimensional (3D) CFX-based mathematical model is developed for describing the internal state of a BF in terms of multiphase flow and the related thermochemical behavior, as well as process indicators. This model considers the intense interactions between gas, solid and liquid phases, and also their competition for the space. The model is applied to a BF covering from the burden surface at the top to the liquid surface in the hearth, where the raceway cavity is considered explicitly. The results show that the key in-furnace phenomena such as flow/temperature patterns and component distributions of solid, gas and liquid phases can be described and characterized in different regions inside the BF, including the gas and liquids flow circumferentially over the 3D raceway surface. The in-furnace distributions of key performance indicators such as reduction degree and gas utilization can also be predicted. This model offers a cost-effective tool to understand and control the complex BF flow and performance.

Similarity of the Multidimensional Space Defined by Parallel Forms of a Mathematics Test.

ERIC Educational Resources Information Center

Reckase, Mark D.; And Others

The purpose of the paper is to determine whether test forms of the Mathematics Usage Test (AAP Math) of the American College Testing Program are parallel in a multidimensional sense. The AAP Math is an achievement test of mathematics concepts acquired by high school students by the end of their third year. To determine the dimensionality of the…

The Effect of an Augmented Reality Enhanced Mathematics Lesson on Student Achievement and Motivation

ERIC Educational Resources Information Center

Estapa, Anne; Nadolny, Larysa

2015-01-01

The purpose of the study was to assess student achievement and motivation during a high school augmented reality mathematics activity focused on dimensional analysis. Included in this article is a review of the literature on the use of augmented reality in mathematics and the combination of print with augmented reality, also known as interactive…

The Effect of Using Dynamic Mathematics Software: Cross Section and Visualization

ERIC Educational Resources Information Center

Kösa, Temel

2016-01-01

The main purpose of this study is to determine the effects of using dynamic mathematics software on pre-service mathematics teachers' ability to infer the shape of a cross section of a three-dimensional solid, as well as on their spatial visualization skills. The study employed a quasi-experimental design with a control group; the Purdue Spatial…

Physical and mathematical cochlear models

NASA Astrophysics Data System (ADS)

Lim, Kian-Meng

2000-10-01

The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity, and non-linear effects such as compression of response with stimulus level, two-tone suppression and the generation of harmonic and distortion products.

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Chuang, H. Andrew

1999-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

Simulating Microbial Community Patterning Using Biocellion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Seung-Hwa; Kahan, Simon H.; Momeni, Babak

2014-04-17

Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis forma- tion. Momeni et al. [5] investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling and simulation to actual patterns observed in wet-lab experiments. However, simu- lations of millions of cells in a three-dimensional community are ex- tremely time-consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vastmore » space of parameter combinations and assumptions. Improving the speed, scale, and accu- racy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high performance software framework for ac- celerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accu- racy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion fur- ther accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chap- ter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.« less

High Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid must be solved simultaneously. In this paper, we present several partitioned procedures for time-integrating this focus coupled problem and discuss their merits in terms of accuracy, stability, heterogeneous computing, I/O transfers, subcycling, and parallel processing. All theoretical results are derived for a one-dimensional piston model problem with a compressible flow, because the complete three-dimensional aeroelastic problem is difficult to analyze mathematically. However, the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two-dimensional transient aeroelastic response of a flexible panel in a transonic nonlinear Euler flow regime.

Variance-based interaction index measuring heteroscedasticity

NASA Astrophysics Data System (ADS)

Ito, Keiichi; Couckuyt, Ivo; Poles, Silvia; Dhaene, Tom

2016-06-01

This work is motivated by the need to deal with models with high-dimensional input spaces of real variables. One way to tackle high-dimensional problems is to identify interaction or non-interaction among input parameters. We propose a new variance-based sensitivity interaction index that can detect and quantify interactions among the input variables of mathematical functions and computer simulations. The computation is very similar to first-order sensitivity indices by Sobol'. The proposed interaction index can quantify the relative importance of input variables in interaction. Furthermore, detection of non-interaction for screening can be done with as low as 4 n + 2 function evaluations, where n is the number of input variables. Using the interaction indices based on heteroscedasticity, the original function may be decomposed into a set of lower dimensional functions which may then be analyzed separately.

Vertically reciprocating auger

NASA Technical Reports Server (NTRS)

Etheridge, Mark; Morgan, Scott; Fain, Robert; Pearson, Jonathan; Weldi, Kevin; Woodrough, Stephen B., Jr.

1988-01-01

The mathematical model and test results developed for the Vertically Reciprocating Auger (VRA) are summarized. The VRA is a device capable of transporting cuttings that result from below surface drilling. It was developed chiefly for the lunar surface, where conventional fluid flushing while drilling would not be practical. The VRA uses only reciprocating motion and transports material through reflections with the surface above. Particles are reflected forward and land ahead of radially placed fences, which prevent the particles from rolling back down the auger. Three input wave forms are considered to drive the auger. A modified sawtooth wave form was chosen for testing, over a modified square wave or sine wave, due to its simplicity and effectiveness. The three-dimensional mathematical model predicted a sand throughput rate of 0.2667 pounds/stroke, while the actual test setup transported 0.075 pounds/stroke. Based on this result, a correction factor of 0.281 is suggested for a modified sawtooth input.

Theoretical analysis of ozone generation by pulsed dielectric barrier discharge in oxygen

NASA Astrophysics Data System (ADS)

Wei, L. S.; Zhou, J. H.; Wang, Z. H.; Cen, K. F.

2007-08-01

The use of very short high-voltage pulses combined with a dielectric layer results in high-energy electrons that dissociate oxygen molecules into atoms, which are a prerequisite for the subsequent production of ozone by collisions with oxygen molecules and third particles. The production of ozone depends on both the electrical and the physical parameters. For ozone generation by pulsed dielectric barrier discharge in oxygen, a mathematical model, which describes the relation between ozone concentration and these parameters that are of importance in its design, is developed according to dimensional analysis theory. A formula considering the ozone destruction factor is derived for predicting the characteristics of the ozone generation, within the range of the corona inception voltage to the gap breakdown voltage. The trend showing the dependence of the concentration of ozone in oxygen on these parameters generally agrees with the experimental results, thus confirming the validity of the mathematical model.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

The finite-dimensional Freeman thesis.

PubMed

Rudolph, Lee

2008-06-01

I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

National geodetic satellite program, part 2

NASA Technical Reports Server (NTRS)

Schmid, H.

1977-01-01

Satellite geodesy and the creation of worldwide geodetic reference systems is discussed. The geometric description of the surface and the analytical description of the gravity field of the earth by means of worldwide reference systems, with the aid of satellite geodesy, are presented. A triangulation method based on photogrammetric principles is described in detail. Results are derived in the form of three dimensional models. These mathematical models represent the frame of reference into which one can fit the existing geodetic results from the various local datums, as well as future measurements.

Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

NASA Astrophysics Data System (ADS)

Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

2018-01-01

This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

Continuous and Discontinuous Galerkin Methods for a Scalable Three-Dimensional Nonhydrostatic Atmospheric Model: Limited-Area Mode

DTIC Science & Technology

2012-01-01

atmosphere model, Int. J . High Perform. Comput. Appl. 26 (1) (2012) 74–89. [8] J.M. Dennis, M. Levy, R.D. Nair, H.M. Tufo, T . Voran. Towards and efficient...26] A. Klockner, T . Warburton, J . Bridge, J.S, Hesthaven, Nodal discontinuous galerkin methods on graphics processors, J . Comput. Phys. 228 (21) (2009...mode James F. Kelly, Francis X. Giraldo ⇑ Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, United States a r t i c l e i n

Local and global bifurcations in an economic growth model with endogenous labour supply and multiplicative external habits

NASA Astrophysics Data System (ADS)

Gori, Luca; Sodini, Mauro

2014-03-01

This paper analyses the mathematical properties of an economic growth model with overlapping generations, endogenous labour supply, and multiplicative external habits. The dynamics of the economy is characterised by a two-dimensional map describing the time evolution of capital and labour supply. We show that if the relative importance of external habits in the utility function is sufficiently high, multiple (determinate or indeterminate) fixed points and poverty traps can exist. In addition, periodic or quasiperiodic behaviour and/or coexistence of attractors may occur.

The local heat transfer mathematical model between vibrated fluidized beds and horizontal tubes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Xuejun; College of Biology and Chemical Engineering, Panzhihua University, Panzhihua 617000; Ye, Shichao

2008-05-15

A dimensionless mathematical model is proposed to predict the local heat transfer coefficients between vibrated fluidized beds and immersed horizontal tubes, and the effects of the thickness of gas film and the contact time of particle packets are well considered. Experiments using the glass beads (the average diameter bar d{sub p}=1.83mm) were conducted in a two-dimensional vibrated fluidized bed (240 mm x 80 mm). The local heat transfer law between vibrated fluidized bed and horizontal tube surface has been investigated. The results show that the values of theoretical prediction are in good agreement with experimental data, so the model ismore » able to predict the local heat transfer coefficients between vibrated fluidized beds and immersed horizontal tubes reasonably well, and the error is in range of {+-}15%. The results can provide references for future designing and researching on the vibrated fluidized beds with immersed horizontal tubes. (author)« less

A mathematical model for human brain cooling during cold-water near-drowning.

PubMed

Xu, X; Tikuisis, P; Giesbrecht, G

1999-01-01

A two-dimensional mathematical model was developed to estimate the contributions of different mechanisms of brain cooling during cold-water near-drowning. Mechanisms include 1) conductive heat loss through tissue to the water at the head surface and in the upper airway and 2) circulatory cooling to aspirated water via the lung and via venous return from the scalp. The model accounts for changes in boundary conditions, blood circulation, respiratory ventilation of water, and head size. Results indicate that conductive heat loss through the skull surface or the upper airways is minimal, although a small child-sized head will conductively cool faster than a large adult-sized head. However, ventilation of cold water may provide substantial brain cooling through circulatory cooling. Although it seems that water breathing is required for rapid "whole" brain cooling, it is possible that conductive cooling may provide some advantage by cooling the brain cortex peripherally and the brain stem centrally via the upper airway.

Stability and Control of Human Trunk Movement During Walking.

PubMed

Wu, Q.; Sepehri, N.; Thornton-Trump, A. B.; Alexander, M.

1998-01-01

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.

A two-dimensional composite grid numerical model based on the reduced system for oceanography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Y.F.; Browning, G.L.; Chesshire, G.

The proper mathematical limit of a hyperbolic system with multiple time scales, the reduced system, is a system that contains no high-frequency motions and is well posed if suitable boundary conditions are chosen for the initial-boundary value problem. The composite grid method, a robust and efficient grid-generation technique that smoothly and accurately treats general irregular boundaries, is used to approximate the two-dimensional version of the reduced system for oceanography on irregular ocean basins. A change-of-variable technique that substantially increases the accuracy of the model and a method for efficiently solving the elliptic equation for the geopotential are discussed. Numerical resultsmore » are presented for circular and kidney-shaped basins by using a set of analytic solutions constructed in this paper.« less

Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator

NASA Astrophysics Data System (ADS)

Yuan, X.-X.; He, L.; Wang, S.-T.; Deng, D.-L.; Wang, F.; Lian, W.-Q.; Wang, X.; Zhang, C.-H.; Zhang, H.-L.; Chang, X.-Y.; Duan, L.-M.

2017-06-01

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including fascinating topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.

Practical application of stereological methods in experimental kidney animal models.

PubMed

Fernández García, María Teresa; Núñez Martínez, Paula; García de la Fuente, Vanessa; Sánchez Pitiot, Marta; Muñiz Salgueiro, María Del Carmen; Perillán Méndez, Carmen; Argüelles Luis, Juan; Astudillo González, Aurora

The kidneys are vital organs responsible for excretion, fluid and electrolyte balance and hormone production. The nephrons are the kidney's functional and structural units. The number, size and distribution of the nephron components contain relevant information on renal function. Stereology is a branch of morphometry that applies mathematical principles to obtain three-dimensional information from serial, parallel and equidistant two-dimensional microscopic sections. Because of the complexity of stereological studies and the lack of scientific literature on the subject, the aim of this paper is to clearly explain, through animal models, the basic concepts of stereology and how to calculate the main kidney stereological parameters that can be applied in future experimental studies. Copyright © 2016 Sociedad Española de Nefrología. Published by Elsevier España, S.L.U. All rights reserved.

Estimating oxygen distribution from vasculature in three-dimensional tumour tissue

PubMed Central

Kannan, Pavitra; Warren, Daniel R.; Markelc, Bostjan; Bates, Russell; Muschel, Ruth; Partridge, Mike

2016-01-01

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution. PMID:26935806

Estimating oxygen distribution from vasculature in three-dimensional tumour tissue.

PubMed

Grimes, David Robert; Kannan, Pavitra; Warren, Daniel R; Markelc, Bostjan; Bates, Russell; Muschel, Ruth; Partridge, Mike

2016-03-01

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution. © 2016 The Authors.

The Interrelationships of Mathematical Precursors in Kindergarten

PubMed Central

Cirino, Paul T.

2011-01-01

This study evaluated the interrelations among cognitive precursors across quantitative, linguistic, and spatial attention domains that have been implicated for math achievement in young children. The dimensionality of the quantity precursors was evaluated in 286 Kindergarteners via latent variable techniques, and the contribution of precursors from each domain was established for small sums addition. Results showed a five factor structure for the quantity precursors with the major distinction between nonsymbolic and symbolic tasks. The overall model demonstrated good fit, and strong predictive power (R2 = 55%) for addition number combinations. Linguistic and spatial attention domains showed indirect relationships with outcomes, with their effects mediated by symbolic quantity measures. These results have implications for the measurement of mathematical precursors, and yield promise for predicting future math performance. PMID:21194711

Huygens' inspired multi-pendulum setups: Experiments and stability analysis

NASA Astrophysics Data System (ADS)

Hoogeboom, F. N.; Pogromsky, A. Y.; Nijmeijer, H.

2016-11-01

This paper examines synchronization of a set of metronomes placed on a lightweight foam platform. Two configurations of the set of metronomes are considered: a row setup containing one-dimensional coupling and a cross setup containing two-dimensional coupling. Depending on the configuration and coupling between the metronomes, i.e., the platform parameters, in- and/or anti-phase synchronized behavior is observed in the experiments. To explain this behavior, mathematical models of a metronome and experimental setups have been derived and used in a local stability analysis. It is numerically and experimentally demonstrated that varying the coupling parameters for both configurations has a significant influence on the stability of the synchronized solutions.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1990-01-01

It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.

Towards an M5-brane model I: A 6d superconformal field theory

NASA Astrophysics Data System (ADS)

Sämann, Christian; Schmidt, Lennart

2018-04-01

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang-Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.

Numerical simulation of vortex pyrolysis reactors for condensable tar production from biomass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, R.S.; Bellan, J.

1998-08-01

A numerical study is performed in order to evaluate the performance and optimal operating conditions of vortex pyrolysis reactors used for condensable tar production from biomass. A detailed mathematical model of porous biomass particle pyrolysis is coupled with a compressible Reynolds stress transport model for the turbulent reactor swirling flow. An initial evaluation of particle dimensionality effects is made through comparisons of single- (1D) and multi-dimensional particle simulations and reveals that the 1D particle model results in conservative estimates for total pyrolysis conversion times and tar collection. The observed deviations are due predominantly to geometry effects while directional effects frommore » thermal conductivity and permeability variations are relatively small. Rapid ablative particle heating rates are attributed to a mechanical fragmentation of the biomass particles that is modeled using a critical porosity for matrix breakup. Optimal thermal conditions for tar production are observed for 900 K. Effects of biomass identity, particle size distribution, and reactor geometry and scale are discussed.« less

Application Of Three-Dimensional Videography To Human Motion Studies: Constraints, Assumptions, And Mathematics

NASA Astrophysics Data System (ADS)

Rab, George T.

1988-02-01

Three-dimensional human motion analysis has been used for complex kinematic description of abnormal gait in children with neuromuscular disease. Multiple skin markers estimate skeletal segment position, and a sorting and smoothing routine provides marker trajectories. The position and orientation of the moving skeleton in space are derived mathematically from the marker positions, and joint motions are calculated from the Eulerian transformation matrix between linked proximal and distal skeletal segments. Reproduceability has been excellent, and the technique has proven to be a useful adjunct to surgical planning.

Evolvable mathematical models: A new artificial Intelligence paradigm

NASA Astrophysics Data System (ADS)

Grouchy, Paul

We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.

n-D shape/texture optimal synthetic description and modeling by GEOGINE

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco F.

2004-12-01

GEOGINE(GEOmetrical enGINE), a state-of-the-art OMG (Ontological Model Generator) based on n-D Tensor Invariants for multidimensional shape/texture optimal synthetic description and learning, is presented. Usually elementary geometric shape robust characterization, subjected to geometric transformation, on a rigorous mathematical level is a key problem in many computer applications in different interest areas. The past four decades have seen solutions almost based on the use of n-Dimensional Moment and Fourier descriptor invariants. The present paper introduces a new approach for automatic model generation based on n -Dimensional Tensor Invariants as formal dictionary. An ontological model is the kernel used for specifying ontologies so that how close an ontology can be from the real world depends on the possibilities offered by the ontological model. By this approach even chromatic information content can be easily and reliably decoupled from target geometric information and computed into robus colour shape parameter attributes. Main GEOGINEoperational advantages over previous approaches are: 1) Automated Model Generation, 2) Invariant Minimal Complete Set for computational efficiency, 3) Arbitrary Model Precision for robust object description.

AMOEBA clustering revisited. [cluster analysis, classification, and image display program

NASA Technical Reports Server (NTRS)

Bryant, Jack

1990-01-01

A description of the clustering, classification, and image display program AMOEBA is presented. Using a difficult high resolution aircraft-acquired MSS image, the steps the program takes in forming clusters are traced. A number of new features are described here for the first time. Usage of the program is discussed. The theoretical foundation (the underlying mathematical model) is briefly presented. The program can handle images of any size and dimensionality.

Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

DTIC Science & Technology

2007-03-01

mathematical frame- 1-6 work of linear algebra and functional analysis [122, 33], while Kalman-Bucy filtering [96, 32] is an especially important...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, March 2002. 85. Hoffman, Kenneth and Ray Kunze. Linear Algebra (Second Edition...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, December 1989. 189. Strang, Gilbert. Linear Algebra and Its Applications

Mathematical Modeling Of Life-Support Systems

NASA Technical Reports Server (NTRS)

Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.

1994-01-01

Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.

PubMed

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M

2016-10-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. Copyright © 2016. Published by Elsevier Ltd.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

PubMed Central

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M.

2017-01-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. PMID:27544910

String & Sticky Tape Experiments: Two-Dimensional Collisions Using Pendulums.

ERIC Educational Resources Information Center

Edge, R. D.

1989-01-01

Introduces a method for two-dimensional kinematics measurements by hanging marbles with long strings. Describes experimental procedures for conservation of momentum and obtaining the coefficient of restitution. Provides diagrams and mathematical expressions for the activities. (YP)

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

The Effect of 3D Virtual Learning Environment on Secondary School Third Grade Students' Attitudes toward Mathematics

ERIC Educational Resources Information Center

Simsek, Irfan

2016-01-01

With this research, in Second Life environment which is a three dimensional online virtual world, it is aimed to reveal the effects of student attitudes toward mathematics courses and design activities which will enable the third grade students of secondary school (primary education seventh grade) to see the 3D objects in mathematics courses in a…

Analysis of students’ spatial thinking in geometry: 3D object into 2D representation

NASA Astrophysics Data System (ADS)

Fiantika, F. R.; Maknun, C. L.; Budayasa, I. K.; Lukito, A.

2018-05-01

The aim of this study is to find out the spatial thinking process of students in transforming 3-dimensional (3D) object to 2-dimensional (2D) representation. Spatial thinking is helpful in using maps, planning routes, designing floor plans, and creating art. The student can engage geometric ideas by using concrete models and drawing. Spatial thinking in this study is identified through geometrical problems of transforming a 3-dimensional object into a 2-dimensional object image. The problem was resolved by the subject and analyzed by reference to predetermined spatial thinking indicators. Two representative subjects of elementary school were chosen based on mathematical ability and visual learning style. Explorative description through qualitative approach was used in this study. The result of this study are: 1) there are different representations of spatial thinking between a boy and a girl object, 2) the subjects has their own way to invent the fastest way to draw cube net.

A new digitized reverse correction method for hypoid gears based on a one-dimensional probe

NASA Astrophysics Data System (ADS)

Li, Tianxing; Li, Jubo; Deng, Xiaozhong; Yang, Jianjun; Li, Genggeng; Ma, Wensuo

2017-12-01

In order to improve the tooth surface geometric accuracy and transmission quality of hypoid gears, a new digitized reverse correction method is proposed based on the measurement data from a one-dimensional probe. The minimization of tooth surface geometrical deviations is realized from the perspective of mathematical analysis and reverse engineering. Combining the analysis of complex tooth surface generation principles and the measurement mechanism of one-dimensional probes, the mathematical relationship between the theoretical designed tooth surface, the actual machined tooth surface and the deviation tooth surface is established, the mapping relation between machine-tool settings and tooth surface deviations is derived, and the essential connection between the accurate calculation of tooth surface deviations and the reverse correction method of machine-tool settings is revealed. Furthermore, a reverse correction model of machine-tool settings is built, a reverse correction strategy is planned, and the minimization of tooth surface deviations is achieved by means of the method of numerical iterative reverse solution. On this basis, a digitized reverse correction system for hypoid gears is developed by the organic combination of numerical control generation, accurate measurement, computer numerical processing, and digitized correction. Finally, the correctness and practicability of the digitized reverse correction method are proved through a reverse correction experiment. The experimental results show that the tooth surface geometric deviations meet the engineering requirements after two trial cuts and one correction.

A multiphysics 3D model of tissue growth under interstitial perfusion in a tissue-engineering bioreactor.

PubMed

Nava, Michele M; Raimondi, Manuela T; Pietrabissa, Riccardo

2013-11-01

The main challenge in engineered cartilage consists in understanding and controlling the growth process towards a functional tissue. Mathematical and computational modelling can help in the optimal design of the bioreactor configuration and in a quantitative understanding of important culture parameters. In this work, we present a multiphysics computational model for the prediction of cartilage tissue growth in an interstitial perfusion bioreactor. The model consists of two separate sub-models, one two-dimensional (2D) sub-model and one three-dimensional (3D) sub-model, which are coupled between each other. These sub-models account both for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Navier-Stokes equation, the mass transport equation and the biomass growth. The biomass, assumed as a phase comprising cells and the synthesised extracellular matrix, has been modelled by using a moving boundary approach. In particular, the boundary at the fluid-biomass interface is moving with a velocity depending from the local oxygen concentration and viscous stress. In this work, we show that all parameters predicted, such as oxygen concentration and wall shear stress, by the 2D sub-model with respect to the ones predicted by the 3D sub-model are systematically overestimated and thus the tissue growth, which directly depends on these parameters. This implies that further predictive models for tissue growth should take into account of the three dimensionality of the problem for any scaffold microarchitecture.

Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories

NASA Astrophysics Data System (ADS)

Zemba, Guillermo Raul

A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

Computational models for the study of heart-lung interactions in mammals.

PubMed

Ben-Tal, Alona

2012-01-01

The operation and regulation of the lungs and the heart are closely related. This is evident when examining the anatomy within the thorax cavity, in the brainstem and in the aortic and carotid arteries where chemoreceptors and baroreceptors, which provide feedback affecting the regulation of both organs, are concentrated. This is also evident in phenomena such as respiratory sinus arrhythmia where the heart rate increases during inspiration and decreases during expiration, in other types of synchronization between the heart and the lungs known as cardioventilatory coupling and in the association between heart failure and sleep apnea where breathing is interrupted periodically by periods of no-breathing. The full implication and physiological significance of the cardiorespiratory coupling under normal, pathological, or extreme physiological conditions are still unknown and are subject to ongoing investigation both experimentally and theoretically using mathematical models. This article reviews mathematical models that take heart-lung interactions into account. The main ideas behind low dimensional, phenomenological models for the study of the heart-lung synchronization and sleep apnea are described first. Higher dimensions, physiology-based models are described next. These models can vary widely in detail and scope and are characterized by the way the heart-lung interaction is taken into account: via gas exchange, via the central nervous system, via the mechanical interactions, and via time delays. The article emphasizes the need for the integration of the different sources of heart-lung coupling as well as the different mathematical approaches. Copyright © 2011 Wiley Periodicals, Inc.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

PubMed

Duarte, Jorge; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2015-12-01

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

A 3-dimensional mathematical model of microbial proliferation that generates the characteristic cumulative relative abundance distributions in gut microbiomes

PubMed Central

Takayasu, Lena; Suda, Wataru; Watanabe, Eiichiro; Fukuda, Shinji; Takanashi, Kageyasu; Ohno, Hiroshi; Takayasu, Misako; Takayasu, Hideki; Hattori, Masahira

2017-01-01

The gut microbiome is highly variable among individuals, largely due to differences in host lifestyle and physiology. However, little is known about the underlying processes or rules that shape the complex microbial community. In this paper, we show that the cumulative relative abundance distribution (CRAD) of microbial species can be approximated by a power law function, and found that the power exponent of CRADs generated from 16S rRNA gene and metagenomic data for normal gut microbiomes of humans and mice was similar consistently with ∼0.9. A similarly robust power exponent was observed in CRADs of gut microbiomes during dietary interventions and several diseases. However, the power exponent was found to be ∼0.6 in CRADs from gut microbiomes characterized by lower species richness, such as those of human infants and the small intestine of mice. In addition, the CRAD of gut microbiomes of mice treated with antibiotics differed slightly from those of infants and the small intestines of mice. Based on these observations, in addition to data on the spatial distribution of microbes in the digestive tract, we developed a 3-dimensional mathematical model of microbial proliferation that reproduced the experimentally observed CRAD patterns. Our model indicated that the CRAD may be determined by the ratio of emerging to pre-existing species during non-uniform spatially competitive proliferation, independent of species composition. PMID:28792501

Estimate of temperature change due to ice and snow accretion in the boreal forest regions

NASA Astrophysics Data System (ADS)

Sugiura, K.; Nagai, S.; Suzuki, R.; Eicken, H.; Maximov, T. C.

2016-12-01

Previous research has demonstrated that there is a wide difference between the surface albedo in winter/spring in snow-covered forest regions in various global climate models. If the forest is covered with snow, the surface albedo would increase. In this study, we carried out field observations to monitor the frequency of ice and snow accretion in the boreal forest regions. The time-lapse digital camera was set up on each side of the observation towers at the site located to the north of Fairbanks (USA) and at the site located to the north of Yakutsk (Russia). It was confirmed that both forests were not necessarily covered with snow without a break from the start of continuous snow cover until the end. In addition, the boreal forest at the Yakutsk site is covered with snow in comparison with the boreal forest at the Fairbanks site for a long term such as for about five month. Using a one-dimensional mathematics model about the energy flow including atmospheric multiple scattering, we estimated temperature change due to ice and snow accretion in the boreal forest regions. The result show that the mean surface temperature rises approximately 0.5 [oC] when the boreal forest is not covered with snow. In this presentation, we discuss the snow albedo parameterization in the boreal forest regions and the one-dimensional mathematics model to provide a basis for a better understanding of the role of snow in the climate system.

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

PubMed

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Sub-grid scale models for discontinuous Galerkin methods based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric; Duraisamy, Karthk

2017-11-01

The optimal prediction framework of Chorin et al., which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived closure models. The M-Z formalism provides a methodology to reformulate a high-dimensional Markovian dynamical system as a lower-dimensional, non-Markovian (non-local) system. In this lower-dimensional system, the effects of the unresolved scales on the resolved scales are non-local and appear as a convolution integral. The non-Markovian system is an exact statement of the original dynamics and is used as a starting point for model development. In this work, we investigate the development of M-Z-based closures model within the context of the Variational Multiscale Method (VMS). The method relies on a decomposition of the solution space into two orthogonal subspaces. The impact of the unresolved subspace on the resolved subspace is shown to be non-local in time and is modeled through the M-Z-formalism. The models are applied to hierarchical discontinuous Galerkin discretizations. Commonalities between the M-Z closures and conventional flux schemes are explored. This work was supported in part by AFOSR under the project ''LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Exploring individual differences in children's mathematical skills: a correlational and dimensional approach.

PubMed

Sigmundsson, H; Polman, R C J; Lorås, H

2013-08-01

Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning.

A three-dimensional thermal and electromagnetic model of whole limb heating with a MAPA.

PubMed

Charny, C K; Levin, R L

1991-10-01

Previous studies by the authors have shown that if properly implemented, the Pennes assumptions can be applied to quantify bioheat transfer during extremity heating. Given its relative numerical simplicity and its ability to predict temperatures in thermoregulated tissue, the Pennes model of bioheat transfer was utilized in a three-dimensional thermal model of limb heating. While the arterial blood temperature was assumed to be radially uniform within a cross section of the limb, axial gradients in the arterial and venous blood temperatures were computed with this three-dimensional model. A realistically shaped, three-dimensional finite element model of a tumor-bearing human lower leg was constructed and was "attached" mathematically to the whole body thermal model of man described in previous studies by the authors. The central as well as local thermoregulatory feedback control mechanisms which determine blood perfusion to the various tissues and rate of evaporation by sweating were input into the limb model. In addition, the temperature of the arterial blood which feeds into the most proximal section of the lower leg was computed by the whole body thermal model. The variations in the shape of the tissues which comprise the limb were obtained from computerized tomography scans. Axial variations in the energy deposition patterns along the length of the limb exposed to a miniannular phased array (MAPA) applicator were also input into this model of limb heating. Results indicate that proper positioning of the limb relative to the MAPA is a significant factor in determining the effectiveness of the treatment. A patient-specific hyperthermia protocol can be designed using this coupled electromagnetic and thermal model.

The influence of a wind tunnel on helicopter rotational noise: Formulation of analysis

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

An analytical model is discussed that can be used to examine the effects of wind tunnel walls on helicopter rotational noise. A complete physical model of an acoustic source in a wind tunnel is described and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. The simplified physical model is then modeled as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. Details of generating a suitable Green's function and integral equation are included and the equation is discussed and also given for a two-dimensional case.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

Point-Mass Aircraft Trajectory Prediction Using a Hierarchical, Highly-Adaptable Software Design

NASA Technical Reports Server (NTRS)

Karr, David A.; Vivona, Robert A.; Woods, Sharon E.; Wing, David J.

2017-01-01

A highly adaptable and extensible method for predicting four-dimensional trajectories of civil aircraft has been developed. This method, Behavior-Based Trajectory Prediction, is based on taxonomic concepts developed for the description and comparison of trajectory prediction software. A hierarchical approach to the "behavioral" layer of a point-mass model of aircraft flight, a clear separation between the "behavioral" and "mathematical" layers of the model, and an abstraction of the methods of integrating differential equations in the "mathematical" layer have been demonstrated to support aircraft models of different types (in particular, turbojet vs. turboprop aircraft) using performance models at different levels of detail and in different formats, and promise to be easily extensible to other aircraft types and sources of data. The resulting trajectories predict location, altitude, lateral and vertical speeds, and fuel consumption along the flight path of the subject aircraft accurately and quickly, accounting for local conditions of wind and outside air temperature. The Behavior-Based Trajectory Prediction concept was implemented in NASA's Traffic Aware Planner (TAP) flight-optimizing cockpit software application.

A 3D mathematical model for the horizontal anode baking furnace

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kocaefe, Y.S.; Dernedde, E.; Kocaefe, D.

In the aluminum industry, carbon anodes are baked in large horizontal or vertical ring-type furnaces. The anode quality depends strongly on the baking conditions (heating rate, soaking time and final anode temperature). A three-dimensional mathematical model has been developed for a horizontal anode baking furnace to assess the effects of different parameters on the baking process and to improve the furnace operation and design at Noranda Aluminum Smelter in New Madrid, Missouri. The commercial CFD code CFDS-FLOW3D is used to solve the governing differential equations. The model gives the temperature, velocity and concentration distributions in the flue, and the variationmore » of the temperature distribution with time in the pit. In this paper, a description of the 3D model for the horizontal anode baking furnace will be given. Some of the results from a case study will also be presented. The results show clearly the importance of flue geometry on the gas flow distribution in the flue and the heat transfer to the anodes.« less

On the effects of mass and momentum transfer from droplets impacting on steady two-dimensional rimming flow in a horizontal cylinder

NASA Astrophysics Data System (ADS)

Williams, J.; Hibberd, S.; Power, H.; Riley, D. S.

2012-05-01

Motivated by applications in aero-engines, steady two-dimensional thin-film flow on the inside of a circular cylinder is studied when the film surface is subject to mass and momentum transfer from impacting droplets. Asymptotic analysis is used systematically to identify distinguished limits that incorporate these transfer effects at leading order and to provide a new mathematical model. Applying both analytical and numerical approaches to the model, a set of stable steady, two-dimensional solutions that fit within the rational framework is determined. A number of these solutions feature steep fronts and associated recirculating pools, which are undesirable in an aeroengine since oil may be stripped away from the steep fronts when there is a core flow external to the film, and recirculation may lead to oil degradation. The model, however, provides a means of investigating whether the formation of the steep fronts on the film surface and of internal recirculation pools can be delayed, or inhibited altogether, by designing jets to deliver prescribed distributions of oil droplets or by the judicious siting of oil sinks. Moreover, by studying pathlines, oil-residence times can be predicted and systems optimized.

A geometric approach to non-linear correlations with intrinsic scatter

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2017-12-01

We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-σ correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is ∼6 for the data sets used, rather than the values in the range of ∼4-5 typically quoted in the literature for these data.

Reconfiguration of broad leaves into cones

NASA Astrophysics Data System (ADS)

Miller, Laura

2013-11-01

Flexible plants, fungi, and sessile animals are thought to reconfigure in the wind and water to reduce the drag forces that act upon them. Simple mathematical models of a flexible beam immersed in a two-dimensional flow will also exhibit this behavior. What is less understood is how the mechanical properties of a leaf in a three-dimensional flow will passively allow roll up and reduce drag. This presentation will begin by examining how leaves roll up into drag reducing shapes in strong flow. The dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia are described using particle image velocimetry. The flows around the leaves are compared with those of simplified sheets using 3D numerical simulations and physical models. For some reconfiguration shapes, large forces and oscillations due to strong vortex shedding are produced. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In physical and numerical models that reconfigure into cones, a similar recirculation zone is observed with both rigid and flexible tethers. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf.

Interrelated Dimensional Chains in Predicting Accuracy of Turbine Wheel Assembly Parameters

NASA Astrophysics Data System (ADS)

Yanyukina, M. V.; Bolotov, M. A.; Ruzanov, N. V.

2018-03-01

The working capacity of any device primarily depends on the assembly accuracy which, in its turn, is determined by the quality of each part manufactured, i.e., the degree of conformity between final geometrical parameters and the set ones. However, the assembly accuracy depends not only on a qualitative manufacturing process but also on the assembly process correctness. In this connection, there were preliminary calculations of assembly stages in terms of conformity to real geometrical parameters with their permissible values. This task is performed by means of the calculation of dimensional chains. The calculation of interrelated dimensional chains in the aircraft industry requires particular attention. The article considers the issues of dimensional chain calculation modelling by the example of the turbine wheel assembly process. The authors described the solution algorithm in terms of mathematical statistics implemented in Matlab. The paper demonstrated the results of a dimensional chain calculation for a turbine wheel in relation to the draw of turbine blades to the shroud ring diameter. Besides, the article provides the information on the influence of a geometrical parameter tolerance for the dimensional chain link elements on a closing one.

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Mathematical Approaches to Understanding and Imaging Atrial Fibrillation: Significance for Mechanisms and Management

PubMed Central

Trayanova, Natalia A

2014-01-01

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This articles aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention. PMID:24763468

Computer Programs For Automated Welding System

NASA Technical Reports Server (NTRS)

Agapakis, John E.

1993-01-01

Computer programs developed for use in controlling automated welding system described in MFS-28578. Together with control computer, computer input and output devices and control sensors and actuators, provide flexible capability for planning and implementation of schemes for automated welding of specific workpieces. Developed according to macro- and task-level programming schemes, which increases productivity and consistency by reducing amount of "teaching" of system by technician. System provides for three-dimensional mathematical modeling of workpieces, work cells, robots, and positioners.

A review of Reynolds stress models for turbulent shear flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.

1995-01-01

A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.

A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

NASA Astrophysics Data System (ADS)

Segal, Guus; Vuik, Kees; Vermolen, Fred

1998-03-01

The dissolution of a disk-likeAl2Cuparticle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically. First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms. This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of anAl2Cuparticle in anAl-Cualloy.

Pattern selection in solidification

NASA Technical Reports Server (NTRS)

Langer, J. S.

1984-01-01

Directional solidification of alloys produces a wide variety of cellular or lamellar structures which, depending upon growth conditions, may be reproducibly regular or may behave chaotically. It is not well understood how these patterns are selected and controlled or even whether there ever exist sharp selection mechanisms. A related phenomenon is the spatial propagation of a pattern into a system which has been caused to become unstable against pattern-forming deformations. This phenomenon has some features in common with the propagation of sidebranching modes in dendritic solidification. In a class of one-dimensional models, the nonlinear system can be shown to select the propagating mode in which the leading edge of the pattern is just marginally stable. This stability principle, when applicable, predicts both the speed of propagation and the geometrical characteristics of the pattern which forms behind the moving front. A boundary-layer model for fully two or three dimensional solidification problems appears to exhibit similar mathematical behavior.

Creep crack-growth: A new path-independent T sub o and computational studies

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1981-01-01

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations.

CAD system of design and engineering provision of die forming of compressor blades for aircraft engines

NASA Astrophysics Data System (ADS)

Khaimovich, I. N.

2017-10-01

The articles provides the calculation algorithms for blank design and die forming fitting to produce the compressor blades for aircraft engines. The design system proposed in the article allows generating drafts of trimming and reducing dies automatically, leading to significant reduction of work preparation time. The detailed analysis of the blade structural elements features was carried out, the taken limitations and technological solutions allowed forming generalized algorithms of forming parting stamp face over the entire circuit of the engraving for different configurations of die forgings. The author worked out the algorithms and programs to calculate three dimensional point locations describing the configuration of die cavity. As a result the author obtained the generic mathematical model of final die block in the form of three-dimensional array of base points. This model is the base for creation of engineering documentation of technological equipment and means of its control.

Hydrodynamic Influence Dabanhu River Bridge Holes Widening Based on Two-Dimensional Finite Element Numerical Model

NASA Astrophysics Data System (ADS)

Li, Dong Feng; Bai, Fu Qing; Nie, Hui

2018-06-01

In order to analyze the influence of bridge holes widening on hydrodynamic such as water level, a two-dimensional mathematical model was used to calculate the hydrodynamic factors, river network flow velocity vector distribution is given, water level and difference of bridge widening before and after is calculated and charted, water surface gradient in seven different river sections near the upper reaches of bridges is counted and revealed. The results of hydrodynamic calculation indicate that The Maximum and the minimum deducing numerical value of the water level after bridge widening is 0.028m, and 0.018m respective. the seven sections water surface gradient becomes smaller until it becomes negative, the influence of bridge widening on the upstream is basically over, the range of influence is about 450m from the bridge to the upstream. reach

Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhang, Fei

2018-02-01

We study susceptible-infected-recovered-susceptible epidemic model in weighted, regular, and random complex networks. We institute a pairwise-type mathematical model with a general transmission rate to evaluate the influence of the link-weight distribution on the spreading process. Furthermore, we develop a dimensionality reduction approach to derive the condition for the contagion outbreak. Finally, we analyze the influence of the heterogeneity of weight distribution on the outbreak condition for the scenario with a linear transmission rate. Our theoretical analysis is in agreement with stochastic simulations, showing that the heterogeneity of link-weight distribution can have a significant effect on the epidemic dynamics.

On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models.

PubMed

Kuritz, K; Stöhr, D; Pollak, N; Allgöwer, F

2017-02-07

Cyclic processes, in particular the cell cycle, are of great importance in cell biology. Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional "snapshot" data. Ergodic analysis can in general be applied to every process that exhibits a steady state distribution. By combining ergodic analysis with age structured population models we furthermore provide the theoretic basis for extensions of ergodic principles to distribution that deviate from their steady state. Copyright © 2016 Elsevier Ltd. All rights reserved.

A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness

PubMed Central

Stride, E.; Cheema, U.

2017-01-01

The growth of bubbles within the body is widely believed to be the cause of decompression sickness (DCS). Dive computer algorithms that aim to prevent DCS by mathematically modelling bubble dynamics and tissue gas kinetics are challenging to validate. This is due to lack of understanding regarding the mechanism(s) leading from bubble formation to DCS. In this work, a biomimetic in vitro tissue phantom and a three-dimensional computational model, comprising a hyperelastic strain-energy density function to model tissue elasticity, were combined to investigate key areas of bubble dynamics. A sensitivity analysis indicated that the diffusion coefficient was the most influential material parameter. Comparison of computational and experimental data revealed the bubble surface's diffusion coefficient to be 30 times smaller than that in the bulk tissue and dependent on the bubble's surface area. The initial size, size distribution and proximity of bubbles within the tissue phantom were also shown to influence their subsequent dynamics highlighting the importance of modelling bubble nucleation and bubble–bubble interactions in order to develop more accurate dive algorithms. PMID:29263127

The systems biology simulation core algorithm

PubMed Central

2013-01-01

Background With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases. Results This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database. Conclusions The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net. PMID:23826941

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

PubMed

Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef

2013-01-01

Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

Response function of a moving contact line

NASA Astrophysics Data System (ADS)

Perrin, H.; Belardinelli, D.; Sbragaglia, M.; Andreotti, B.

2018-04-01

The hydrodynamics of a liquid-vapor interface in contact with a heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified one-dimensional time-dependent models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to explore contact line motion through a disordered energy landscape.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

One-dimensional collision carts computer model and its design ideas for productive experiential learning

NASA Astrophysics Data System (ADS)

Wee, Loo Kang

2012-05-01

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a consistent simulation world view with a pen and paper representation, (2) a data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and (3) a game for simple concept testing that can further support learning. We also suggest using a physical world setup augmented by simulation by highlighting three advantages of real collision carts equipment such as a tacit 3D experience, random errors in measurement and the conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes.

The numerical study of the coextrusion process of polymer melts in the cable head

NASA Astrophysics Data System (ADS)

Kozitsyna, M. V.; Trufanova, N. M.

2017-06-01

The process of coextrusion consists in a simultaneous creation of all necessary insulating layers of different polymers in the channel of a special forming tool. The main focus of this study is the analysis of technological, geometrical and rheological characteristics on the values of the layer’s thickness. In this paper are considered three geometries of cable head on the three-dimensional and two-dimensional representation. The mathematical models of separate and joint flow of polymer melts have been implemented by the finite element method in Ansys software package. The velocity fields, temperature, pressure in the cross-sections of the channel and by the length have been obtained. The influence of some thickness characteristics of insulation layers has been identified.

CFRP composite mirrors for space telescopes and their micro-dimensional stability

NASA Astrophysics Data System (ADS)

Utsunomiya, Shin; Kamiya, Tomohiro; Shimizu, Ryuzo

2010-07-01

Ultra-lightweight and high-accuracy CFRP (carbon fiber reinforced plastics) mirrors for space telescopes were fabricated to demonstrate their feasibility for light wavelength applications. The CTE (coefficient of thermal expansion) of the all- CFRP sandwich panels was tailored to be smaller than 1×10-7/K. The surface accuracy of mirrors of 150 mm in diameter was 1.8 um RMS as fabricated and the surface smoothness was improved to 20 nm RMS by using a replica technique. Moisture expansion was considered the largest in un-predictable surface preciseness errors. The moisture expansion affected not only homologous shape change but also out-of-plane distortion especially in unsymmetrical compositions. Dimensional stability due to the moisture expansion was compared with a structural mathematical model.

Peristaltic motion of magnetohydrodynamic viscous fluid in a curved circular tube

NASA Astrophysics Data System (ADS)

Yasmeen, Shagufta; Okechi, Nnamdi Fidelis; Anjum, Hafiz Junaid; Asghar, Saleem

In this paper we investigate the peristaltic flow of viscous fluid through three-dimensional curved tube in the presence of the applied magnetic field. We present a mathematical model and an asymptotic solution for the three dimensional Navier-Stokes equations under the assumption of small inertial forces and long wavelength approximation. The effects of the curvature of the tube are investigated with particular interest. The solution is sought in terms of regular perturbation expansion for small curvature parameter. It is noted that the velocity field is more sensitive to the curvature of tube in comparison to the pressure gradient. It is shown that peristaltic magnetohydrodynamic (MHD) flow in a straight tube is the limiting case of this study.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

Dimensional synthesis of a leg mechanism

NASA Astrophysics Data System (ADS)

Pop, F.; Lovasz, E.-Ch; Pop, C.; Dolga, V.

2016-08-01

An eight bar leg mechanism dimensional synthesis is presented. The mathematical model regarding the synthesis is described and the results obtained after computation are verified with help of 2D mechanism simulation in Matlab. This mechanism, inspired from proposed solution of Theo Jansen, is integrated into the structure of a 2 DOF quadruped robot. With help of the kinematic synthesis method described, it is tried to determine new dimensions for the mechanism, based on a set of initial conditions. These are established by taking into account the movement of the end point of the leg mechanism, which enters in contact with the ground, during walking. An optimization process based on the results obtained can be conducted further in order to find a better solution for the leg mechanism.

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions

PubMed Central

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation. PMID:26150807

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions.

PubMed

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation.

Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance

NASA Astrophysics Data System (ADS)

Rosestolato, M.; Święch, A.

2017-02-01

We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.

An Assessment of the Dimensionality of SAT-Mathematical.

ERIC Educational Resources Information Center

Lawrence, Ida M.; Dorans, Neil J.

Six editions of Scholastic Aptitude Test-Mathematical (SAT-M) were factor analyzed using confirmatory and exploratory methods. Confirmatory factor analyses (using the LISREL VI program) were conducted on correlation matrices among item parcels--sums of scores on a small subset of items. Item parcels were constructed to yield correlation matrices…

Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics

ERIC Educational Resources Information Center

Miyazaki, Mikio; Kimiho, Chino; Katoh, Ryuhei; Arai, Hitoshi; Ogihara, Fumihiro; Oguchi, Yuichi; Morozumi, Tatsuo; Kon, Mayuko; Komatsu, Kotaro

2012-01-01

Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…

On the application of copula in modeling maintenance contract

NASA Astrophysics Data System (ADS)

Iskandar, B. P.; Husniah, H.

2016-02-01

This paper deals with the application of copula in maintenance contracts for a nonrepayable item. Failures of the item are modeled using a two dimensional approach where age and usage of the item and this requires a bi-variate distribution to modelling failures. When the item fails then corrective maintenance (CM) is minimally repaired. CM can be outsourced to an external agent or done in house. The decision problem for the owner is to find the maximum total profit whilst for the agent is to determine the optimal price of the contract. We obtain the mathematical models of the decision problems for the owner as well as the agent using a Nash game theory formulation.

Three Dimensional Flow and Pressure Patterns in a Single Pocket of a Hydrostatic Journal Bearing

NASA Technical Reports Server (NTRS)

Braun, M. Jack; Dzodzo, Milorad B.

1996-01-01

The flow in a hydrostatic pocket is described by a mathematical model that uses the three dimensional Navier-Stokes equations written in terms of the primary variables, u, v, w, and p. Using a conservative formulation, a finite volume multi-block method is applied through a collocated, body fitted grid. The flow is simulated in a shallow pocket with a depth/length ratio of 0.02. The flow structures obtained and described by the authors in their previous two dimensional models are made visible in their three dimensional aspect for the Couette flow. It has been found that the flow regimes formed central and secondary vortical cells with three dimensional corkscrew-like structures that lead the fluid on an outward bound path in the axial direction of the pocket. The position of the central vortical cell center is at the exit region of the capillary restrictor feedline. It has also been determined that a fluid turn around zone occupies all the upstream space between the floor of the pocket and the runner, thus preventing any flow exit through the upstream port. The corresponding pressure distribution under the shaft presented as well. It was clearly established that for the Couette dominated case the pressure varies significantly in the pocket in the circumferential direction, while its variation is less pronounced axially.

Numerical Solution of a 3-D Advection-Dispersion Model for Dissolved Oxygen Distribution in Facultative Ponds

NASA Astrophysics Data System (ADS)

Sunarsih; Sasongko, Dwi P.; Sutrisno

2018-02-01

This paper describes a mathematical model for the dissolved oxygen distribution in the plane of a facultative pond with a certain depth. The purpose of this paper is to determine the variation of dissolved oxygen concentration in facultative ponds. The 3-dimensional advection-diffusion equation is solved using the finite difference method Forward Time Central Space (FTCS). Numerical results show that the aerator greatly affects the occurrence of oxygen concentration variations in the facultative pond in the certain depth. The concentration of dissolved oxygen decreases as the depth of the pond increases.

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, Charles E.

1990-01-01

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Mathematical simulation of the process of condensing natural gas

NASA Astrophysics Data System (ADS)

Tastandieva, G. M.

2015-01-01

Presents a two-dimensional unsteady model of heat transfer in terms of condensation of natural gas at low temperatures. Performed calculations of the process heat and mass transfer of liquefied natural gas (LNG) storage tanks of cylindrical shape. The influence of model parameters on the nature of heat transfer. Defined temperature regimes eliminate evaporation by cooling liquefied natural gas. The obtained dependence of the mass flow rate of vapor condensation gas temperature. Identified the possibility of regulating the process of "cooling down" liquefied natural gas in terms of its partial evaporation with low cost energy.

Modelling short channel mosfets for use in VLSI

NASA Technical Reports Server (NTRS)

Klafter, Alex; Pilorz, Stuart; Polosa, Rosa Loguercio; Ruddock, Guy; Smith, Andrew

1986-01-01

In an investigation of metal oxide semiconductor field effect transistor (MOFSET) devices, a one-dimensional mathematical model of device dynamics was prepared, from which an accurate and computationally efficient drain current expression could be derived for subsequent parameter extraction. While a critical review revealed weaknesses in existing 1-D models (Pao-Sah, Pierret-Shields, Brews, and Van de Wiele), this new model in contrast was found to allow all the charge distributions to be continuous, to retain the inversion layer structure, and to include the contribution of current from the pinched-off part of the device. The model allows the source and drain to operate in different regimes. Numerical algorithms used for the evaluation of surface potentials in the various models are presented.

Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.

A Non Local Electron Heat Transport Model for Multi-Dimensional Fluid Codes

NASA Astrophysics Data System (ADS)

Schurtz, Guy

2000-10-01

Apparent inhibition of thermal heat flow is one of the most ancient problems in computational Inertial Fusion and flux-limited Spitzer-Harm conduction has been a mainstay in multi-dimensional hydrodynamic codes for more than 25 years. Theoretical investigation of the problem indicates that heat transport in laser produced plasmas has to be considered as a non local process. Various authors contributed to the non local theory and proposed convolution formulas designed for practical implementation in one-dimensional fluid codes. Though the theory, confirmed by kinetic calculations, actually predicts a reduced heat flux, it fails to explain the very small limiters required in two-dimensional simulations. Fokker-Planck simulations by Epperlein, Rickard and Bell [PRL 61, 2453 (1988)] demonstrated that non local effects could lead to a strong reduction of heat flow in two dimensions, even in situations where a one-dimensional analysis suggests that the heat flow is nearly classical. We developed at CEA/DAM a non local electron heat transport model suitable for implementation in our two-dimensional radiation hydrodynamic code FCI2. This model may be envisionned as the first step of an iterative solution of the Fokker-Planck equations; it takes the mathematical form of multigroup diffusion equations, the solution of which yields both the heat flux and the departure of the electron distribution function to the Maxwellian. Although direct implementation of the model is straightforward, formal solutions of it can be expressed in convolution form, exhibiting a three-dimensional tensor propagator. Reduction to one dimension retrieves the original formula of Luciani, Mora and Virmont [PRL 51, 1664 (1983)]. Intense magnetic fields may be generated by thermal effects in laser targets; these fields, as well as non local effects, will inhibit electron conduction. We present simulations where both effects are taken into account and shortly discuss the coupling strategy between them.

Dispersive shock waves and modulation theory

NASA Astrophysics Data System (ADS)

El, G. A.; Hoefer, M. A.

2016-10-01

There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.

An integrated mathematical model for chemical oxygen demand (COD) removal in moving bed biofilm reactors (MBBR) including predation and hydrolysis.

PubMed

Revilla, Marta; Galán, Berta; Viguri, Javier R

2016-07-01

An integrated mathematical model is proposed for modelling a moving bed biofilm reactor (MBBR) for removal of chemical oxygen demand (COD) under aerobic conditions. The composite model combines the following: (i) a one-dimensional biofilm model, (ii) a bulk liquid model, and (iii) biological processes in the bulk liquid and biofilm considering the interactions among autotrophic, heterotrophic and predator microorganisms. Depending on the values for the soluble biodegradable COD loading rate (SCLR), the model takes into account a) the hydrolysis of slowly biodegradable compounds in the bulk liquid, and b) the growth of predator microorganisms in the bulk liquid and in the biofilm. The integration of the model and the SCLR allows a general description of the behaviour of COD removal by the MBBR under various conditions. The model is applied for two in-series MBBR wastewater plant from an integrated cellulose and viscose production and accurately describes the experimental concentrations of COD, total suspended solids (TSS), nitrogen and phosphorous obtained during 14 months working at different SCLRs and nutrient dosages. The representation of the microorganism group distribution in the biofilm and in the bulk liquid allow for verification of the presence of predator microorganisms in the second reactor under some operational conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

Radiant heat exchange calculations in radiantly heated and cooled enclosures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chapman, K.S.; Zhang, P.

1995-08-01

This paper presents the development of a three-dimensional mathematical model to compute the radiant heat exchange between surfaces separated by a transparent and/or opaque medium. The model formulation accommodates arbitrary arrangements of the interior surfaces, as well as arbitrary placement of obstacles within the enclosure. The discrete ordinates radiation model is applied and has the capability to analyze the effect of irregular geometries and diverse surface temperatures and radiative properties. The model is verified by comparing calculated heat transfer rates to heat transfer rates determined from the exact radiosity method for four different enclosures. The four enclosures were selected tomore » provide a wide range of verification. This three-dimensional model based on the discrete ordinates method can be applied to a building to assist the design engineer in sizing a radiant heating system. By coupling this model with a convective and conductive heat transfer model and a thermal comfort model, the comfort levels throughout the room can be easily and efficiently mapped for a given radiant heater location. In addition, objects such as airplanes, trucks, furniture, and partitions can be easily incorporated to determine their effect on the performance of the radiant heating system.« less

Diagnostic tools for mixing models of stream water chemistry

USGS Publications Warehouse

Hooper, Richard P.

2003-01-01

Mixing models provide a useful null hypothesis against which to evaluate processes controlling stream water chemical data. Because conservative mixing of end‐members with constant concentration is a linear process, a number of simple mathematical and multivariate statistical methods can be applied to this problem. Although mixing models have been most typically used in the context of mixing soil and groundwater end‐members, an extension of the mathematics of mixing models is presented that assesses the “fit” of a multivariate data set to a lower dimensional mixing subspace without the need for explicitly identified end‐members. Diagnostic tools are developed to determine the approximate rank of the data set and to assess lack of fit of the data. This permits identification of processes that violate the assumptions of the mixing model and can suggest the dominant processes controlling stream water chemical variation. These same diagnostic tools can be used to assess the fit of the chemistry of one site into the mixing subspace of a different site, thereby permitting an assessment of the consistency of controlling end‐members across sites. This technique is applied to a number of sites at the Panola Mountain Research Watershed located near Atlanta, Georgia.

Illusions of Space: Charting Three Dimensions

ERIC Educational Resources Information Center

Glasser, Leslie

2014-01-01

We introduce various methods which are used to depict three-dimensional objects on two-dimensional surfaces. Many of these are artistic and not conducive to exact interpretation. Instead, the scientific and engineering practices and mathematics of orthographic projection are introduced, and illustrated in an accompanying interactive Excel…

Creating Three-Dimensional Scenes

ERIC Educational Resources Information Center

Krumpe, Norm

2005-01-01

Persistence of Vision Raytracer (POV-Ray), a free computer program for creating photo-realistic, three-dimensional scenes and a link for Mathematica users interested in generating POV-Ray files from within Mathematica, is discussed. POV-Ray has great potential in secondary mathematics classrooms and helps in strengthening students' visualization…

Prediction of the partitioning behaviour of proteins in aqueous two-phase systems using only their amino acid composition.

PubMed

Salgado, J Cristian; Andrews, Barbara A; Ortuzar, Maria Fernanda; Asenjo, Juan A

2008-01-18

The prediction of the partition behaviour of proteins in aqueous two-phase systems (ATPS) using mathematical models based on their amino acid composition was investigated. The predictive models are based on the average surface hydrophobicity (ASH). The ASH was estimated by means of models that use the three-dimensional structure of proteins and by models that use only the amino acid composition of proteins. These models were evaluated for a set of 11 proteins with known experimental partition coefficient in four-phase systems: polyethylene glycol (PEG) 4000/phosphate, sulfate, citrate and dextran and considering three levels of NaCl concentration (0.0% w/w, 0.6% w/w and 8.8% w/w). The results indicate that such prediction is feasible even though the quality of the prediction depends strongly on the ATPS and its operational conditions such as the NaCl concentration. The ATPS 0 model which use the three-dimensional structure obtains similar results to those given by previous models based on variables measured in the laboratory. In addition it maintains the main characteristics of the hydrophobic resolution and intrinsic hydrophobicity reported before. Three mathematical models, ATPS I-III, based only on the amino acid composition were evaluated. The best results were obtained by the ATPS I model which assumes that all of the amino acids are completely exposed. The performance of the ATPS I model follows the behaviour reported previously, i.e. its correlation coefficients improve as the NaCl concentration increases in the system and, therefore, the effect of the protein hydrophobicity prevails over other effects such as charge or size. Its best predictive performance was obtained for the PEG/dextran system at high NaCl concentration. An increase in the predictive capacity of at least 54.4% with respect to the models which use the three-dimensional structure of the protein was obtained for that system. In addition, the ATPS I model exhibits high correlation coefficients in that system being higher than 0.88 on average. The ATPS I model exhibited correlation coefficients higher than 0.67 for the rest of the ATPS at high NaCl concentration. Finally, we tested our best model, the ATPS I model, on the prediction of the partition coefficient of the protein invertase. We found that the predictive capacities of the ATPS I model are better in PEG/dextran systems, where the relative error of the prediction with respect to the experimental value is 15.6%.

Molecular Sieve Bench Testing and Computer Modeling

NASA Technical Reports Server (NTRS)

Mohamadinejad, Habib; DaLee, Robert C.; Blackmon, James B.

1995-01-01

The design of an efficient four-bed molecular sieve (4BMS) CO2 removal system for the International Space Station depends on many mission parameters, such as duration, crew size, cost of power, volume, fluid interface properties, etc. A need for space vehicle CO2 removal system models capable of accurately performing extrapolated hardware predictions is inevitable due to the change of the parameters which influences the CO2 removal system capacity. The purpose is to investigate the mathematical techniques required for a model capable of accurate extrapolated performance predictions and to obtain test data required to estimate mass transfer coefficients and verify the computer model. Models have been developed to demonstrate that the finite difference technique can be successfully applied to sorbents and conditions used in spacecraft CO2 removal systems. The nonisothermal, axially dispersed, plug flow model with linear driving force for 5X sorbent and pore diffusion for silica gel are then applied to test data. A more complex model, a non-darcian model (two dimensional), has also been developed for simulation of the test data. This model takes into account the channeling effect on column breakthrough. Four FORTRAN computer programs are presented: a two-dimensional model of flow adsorption/desorption in a packed bed; a one-dimensional model of flow adsorption/desorption in a packed bed; a model of thermal vacuum desorption; and a model of a tri-sectional packed bed with two different sorbent materials. The programs are capable of simulating up to four gas constituents for each process, which can be increased with a few minor changes.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation.

PubMed

Augustin, Moritz; Ladenbauer, Josef; Baumann, Fabian; Obermayer, Klaus

2017-06-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation

PubMed Central

Baumann, Fabian; Obermayer, Klaus

2017-01-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models. PMID:28644841

Atmospheric Carbon Dioxide and the Global Carbon Cycle: The Key Uncertainties

DOE R&D Accomplishments Database

Peng, T. H.; Post, W. M.; DeAngelis, D. L.; Dale, V. H.; Farrell, M. P.

1987-12-01

The biogeochemical cycling of carbon between its sources and sinks determines the rate of increase in atmospheric CO{sub 2} concentrations. The observed increase in atmospheric CO{sub 2} content is less than the estimated release from fossil fuel consumption and deforestation. This discrepancy can be explained by interactions between the atmosphere and other global carbon reservoirs such as the oceans, and the terrestrial biosphere including soils. Undoubtedly, the oceans have been the most important sinks for CO{sub 2} produced by man. But, the physical, chemical, and biological processes of oceans are complex and, therefore, credible estimates of CO{sub 2} uptake can probably only come from mathematical models. Unfortunately, one- and two-dimensional ocean models do not allow for enough CO{sub 2} uptake to accurately account for known releases. Thus, they produce higher concentrations of atmospheric CO{sub 2} than was historically the case. More complex three-dimensional models, while currently being developed, may make better use of existing tracer data than do one- and two-dimensional models and will also incorporate climate feedback effects to provide a more realistic view of ocean dynamics and CO{sub 2} fluxes. The instability of current models to estimate accurately oceanic uptake of CO{sub 2} creates one of the key uncertainties in predictions of atmospheric CO{sub 2} increases and climate responses over the next 100 to 200 years.

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

NASA Technical Reports Server (NTRS)

Beech, G. S.; Hampton, R. D.; Rupert, J. K.

2004-01-01

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Design and realization of retina-like three-dimensional imaging based on a MOEMS mirror

NASA Astrophysics Data System (ADS)

Cao, Jie; Hao, Qun; Xia, Wenze; Peng, Yuxin; Cheng, Yang; Mu, Jiaxing; Wang, Peng

2016-07-01

To balance conflicts for high-resolution, large-field-of-view and real-time imaging, a retina-like imaging method based on time-of flight (TOF) is proposed. Mathematical models of 3D imaging based on MOEMS are developed. Based on this method, we perform simulations of retina-like scanning properties, including compression of redundant information and rotation and scaling invariance. To validate the theory, we develop a prototype and conduct relevant experiments. The preliminary results agree well with the simulations.

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

NASA Astrophysics Data System (ADS)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

Pilot plant operation of a nonadiabatic methanation reactor. [15 refs. ; Raney nickel catalyst

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schehl, R.R.; Pennline, H.W.; Strakey, J.P.

The design and operation of a pilot plant scale hybrid methanation reactor is discussed. The hybrid methanator, utilizing a finned, Raney nickel coated insert, consolidates features of the tube-wall and hot-gas-recycle methanation reactors. Data are presented from four tests lasting from 3/sup 1///sub 2/ weeks to three months. Topics discussed include conversion, product yields, catalyst properties, and reactor temperature profiles. A one-dimensional mathematical model capable of explaining reactor performance trends is employed.

[Characteristics of Waves Generated Beneath the Solar Convection Zone by Penetrative Overshoot

NASA Technical Reports Server (NTRS)

Julien, Keith

2000-01-01

The goal of this project was to theoretically and numerically characterize the waves generated beneath the solar convection zone by penetrative overshoot. Three dimensional model simulations were designed to isolate the effects of rotation and shear. In order to overcome the numerically imposed limitations of finite Reynolds numbers (Re) below solar values, series of simulations were designed to elucidate the Reynolds-number dependence (hoped to exhibit mathematically simple scaling on Re) so that one could cautiously extrapolate to solar values.

Agent-Based Phytoplankton Models of Cellular and Population Processes: Fostering Individual-Based Learning in Undergraduate Research

NASA Astrophysics Data System (ADS)

Berges, J. A.; Raphael, T.; Rafa Todd, C. S.; Bate, T. C.; Hellweger, F. L.

2016-02-01

Engaging undergraduate students in research projects that require expertise in multiple disciplines (e.g. cell biology, population ecology, and mathematical modeling) can be challenging because they have often not developed the expertise that allows them to participate at a satisfying level. Use of agent-based modeling can allow exploration of concepts at more intuitive levels, and encourage experimentation that emphasizes processes over computational skills. Over the past several years, we have involved undergraduate students in projects examining both ecological and cell biological aspects of aquatic microbial biology, using the freely-downloadable, agent-based modeling environment NetLogo (https://ccl.northwestern.edu/netlogo/). In Netlogo, actions of large numbers of individuals can be simulated, leading to complex systems with emergent behavior. The interface features appealing graphics, monitors, and control structures. In one example, a group of sophomores in a BioMathematics program developed an agent-based model of phytoplankton population dynamics in a pond ecosystem, motivated by observed macroscopic changes in cell numbers (due to growth and death), and driven by responses to irradiance, temperature and a limiting nutrient. In a second example, junior and senior undergraduates conducting Independent Studies created a model of the intracellular processes governing stress and cell death for individual phytoplankton cells (based on parameters derived from experiments using single-cell culturing and flow cytometry), and then this model was embedded in the agents in the pond ecosystem model. In our experience, students with a range of mathematical abilities learned to code quickly and could use the software with varying degrees of sophistication, for example, creation of spatially-explicit two and three-dimensional models. Skills developed quickly and transferred readily to other platforms (e.g. Matlab).

Promise of new imaging technologies for assessing ovarian function.

PubMed

Singh, Jaswant; Adams, Gregg P; Pierson, Roger A

2003-10-15

Advancements in imaging technologies over the last two decades have ushered a quiet revolution in research approaches to the study of ovarian structure and function. The most significant changes in our understanding of the ovary have resulted from the use of ultrasonography which has enabled sequential analyses in live animals. Computer-assisted image analysis and mathematical modeling of the dynamic changes within the ovary has permitted exciting new avenues of research with readily quantifiable endpoints. Spectral, color-flow and power Doppler imaging now facilitate physiologic interpretations of vascular dynamics over time. Similarly, magnetic resonance imaging (MRI) is emerging as a research tool in ovarian imaging. New technologies, such as three-dimensional ultrasonography and MRI, ultrasound-based biomicroscopy and synchrotron-based techniques each have the potential to enhance our real-time picture of ovarian function to the near-cellular level. Collectively, information available in ultrasonography, MRI, computer-assisted image analysis and mathematical modeling heralds a new era in our understanding of the basic processes of female and male reproduction.

Mathematical Modeling of Ischemia-Reperfusion Injury and Postconditioning Therapy.

PubMed

Fong, D; Cummings, L J

2017-11-01

Reperfusion (restoration of blood flow) after a period of ischemia (interruption of blood flow) can paradoxically place tissues at risk of further injury: so-called ischemia-reperfusion injury or IR injury. Recent studies have shown that postconditioning (intermittent periods of further ischemia applied during reperfusion) can reduce IR injury. We develop a mathematical model to describe the reperfusion and postconditioning process following an ischemic insult, treating the blood vessel as a two-dimensional channel, lined with a monolayer of endothelial cells that interact (respiration and mechanotransduction) with the blood flow. We investigate how postconditioning affects the total cell density within the endothelial layer, by varying the frequency of the pulsatile flow and the oxygen concentration at the inflow boundary. We find that, in the scenarios we consider, the pulsatile flow should be of high frequency to minimize cellular damage, while oxygen concentration at the inflow boundary should be held constant, or subject to only low-frequency variations, to maximize cell proliferation.

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls

NASA Astrophysics Data System (ADS)

Hossain, Shaolie S.; Hossainy, Syed F. A.; Bazilevs, Yuri; Calo, Victor M.; Hughes, Thomas J. R.

2012-02-01

The majority of heart attacks occur when there is a sudden rupture of atherosclerotic plaque, exposing prothrombotic emboli to coronary blood flow, forming clots that can cause blockages of the arterial lumen. Diseased arteries can be treated with drugs delivered locally to vulnerable plaques. The objective of this work was to develop a computational tool-set to support the design and analysis of a catheter-based nanoparticulate drug delivery system to treat vulnerable plaques and diffuse atherosclerosis. A three-dimensional mathematical model of coupled mass transport of drug and drug-encapsulated nanoparticles was developed and solved numerically utilizing isogeometric finite element analysis. Simulations were run on a patient-specific multilayered coronary artery wall segment with a vulnerable plaque and the effect of artery and plaque inhomogeneity was analyzed. The method captured trends observed in local drug delivery and demonstrated potential for optimizing drug design parameters, including delivery location, nanoparticle surface properties, and drug release rate.

Characterization and modeling of an advanced flexible thermal protection material for space applications

NASA Technical Reports Server (NTRS)

Clayton, Joseph P.; Tinker, Michael L.

1991-01-01

This paper describes experimental and analytical characterization of a new flexible thermal protection material known as Tailorable Advanced Blanket Insulation (TABI). This material utilizes a three-dimensional ceramic fabric core structure and an insulation filler. TABI is the leading candidate for use in deployable aeroassisted vehicle designs. Such designs require extensive structural modeling, and the most significant in-plane material properties necessary for model development are measured and analytically verified in this study. Unique test methods are developed for damping measurements. Mathematical models are developed for verification of the experimental modulus and damping data, and finally, transverse properties are described in terms of the inplane properties through use of a 12-dof finite difference model of a simple TABI configuration.

Two-dimensional CFD modeling of the heat and mass transfer process during sewage sludge drying in a solar dryer

NASA Astrophysics Data System (ADS)

Krawczyk, Piotr; Badyda, Krzysztof

2011-12-01

The paper presents key assumptions of the mathematical model which describes heat and mass transfer phenomena in a solar sewage drying process, as well as techniques used for solving this model with the Fluent computational fluid dynamics (CFD) software. Special attention was paid to implementation of boundary conditions on the sludge surface, which is a physical boundary between the gaseous phase - air, and solid phase - dried matter. Those conditions allow to model heat and mass transfer between the media during first and second drying stages. Selection of the computational geometry is also discussed - it is a fragment of the entire drying facility. Selected modelling results are presented in the final part of the paper.

Description of two-metal biosorption equilibria by Langmuir-type models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chong, K.H.; Volesky, B.

A biosorbent prepared from Ascophyllum nodosum seaweed biomass, FCAN2, was examined for its sorption capacity. Equilibrium batch sorption studies were performed using two-metal systems containing either (Cu+Zn), (Cu+Cd), or (Zn+Cd). In the evaluation of the two-metal sorption system performance, simple isotherm curves had to be replaced by three-dimensional sorption isotherm surfaces. In order to describe the isotherm surfaces mathematically, three Langmuir-type models were evaluated. The apparent one-parameter Langmuir constant (b) was used to quantify FCAN2 ``affinity`` for one metal in the presence of another one. The uptake of Zn decreased drastically when Cu of Cd were present. The uptake ofmore » Cd was much more sensitive to the presence of Cu than to that of Zn. The presence of Cd and Zn alter the ``affinity`` of FCAN2 for Cu the least at high Cu equilibrium concentrations. The mathematical model of the two-metal sorption system enabled quantitative estimation of one-metal (bio)sorption inhibition due to the influence of a second metal.« less

Preliminary testing of turbulence and radionuclide transport modeling in deep ocean environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Onishi, Y.; Dummuller, D.C.; Trent, D.S.

Pacific Northwest Laboratory (PNL) performed a study for the US Environmental Protection Agency's Office of Radiation Programs to (1) identify candidate models for regional modeling of low-level waste ocean disposal sites in the mid-Atlantic ocean; (2) evaluate mathematical representation of the model's eddy viscosity/dispersion coefficients; and (3) evaluate the adequacy of the k-{epsilon} turbulence model and the feasibility of one of the candidate models, TEMPEST{copyright}/FLESCOT{copyright}, to deep-ocean applications on a preliminary basis. PNL identified the TEMPEST{copyright}/FLESCOT{copyright}, FLOWER, Blumberg's, and RMA 10 models as appropriate candidates for the regional radionuclide modeling. Among these models, TEMPEST/FLESCOT is currently the only model thatmore » solves distributions of flow, turbulence (with the k-{epsilon} model), salinity, water temperature, sediment, dissolved contaminants, and sediment-sorbed contaminants. Solving the Navier-Stokes equations using higher order correlations is not practical for regional modeling because of the prohibitive computational requirements; therefore, the turbulence modeling is a more practical approach. PNL applied the three-dimensional code, TEMPEST{copyright}/FLESCOT{copyright} with the k-{epsilon} model, to a very simple, hypothetical, two-dimensional, deep-ocean case, producing at least qualitatively appropriate results. However, more detailed testing should be performed for the further testing of the code. 46 refs., 39 figs., 6 tabs.« less

Modelling the Cast Component Weight in Hot Chamber Die Casting using Combined Taguchi and Buckingham's π Approach

NASA Astrophysics Data System (ADS)

Singh, Rupinder

2018-02-01

Hot chamber (HC) die casting process is one of the most widely used commercial processes for the casting of low temperature metals and alloys. This process gives near-net shape product with high dimensional accuracy. However in actual field environment the best settings of input parameters is often conflicting as the shape and size of the casting changes and one have to trade off among various output parameters like hardness, dimensional accuracy, casting defects, microstructure etc. So for online inspection of the cast components properties (without affecting the production line) the weight measurement has been established as one of the cost effective method (as the difference in weight of sound and unsound casting reflects the possible casting defects) in field environment. In the present work at first stage the effect of three input process parameters (namely: pressure at 2nd phase in HC die casting; metal pouring temperature and die opening time) has been studied for optimizing the cast component weight `W' as output parameter in form of macro model based upon Taguchi L9 OA. After this Buckingham's π approach has been applied on Taguchi based macro model for the development of micro model. This study highlights the Taguchi-Buckingham based combined approach as a case study (for conversion of macro model into micro model) by identification of optimum levels of input parameters (based on Taguchi approach) and development of mathematical model (based on Buckingham's π approach). Finally developed mathematical model can be used for predicting W in HC die casting process with more flexibility. The results of study highlights second degree polynomial equation for predicting cast component weight in HC die casting and suggest that pressure at 2nd stage is one of the most contributing factors for controlling the casting defect/weight of casting.

Application of a Functional Mathematical Index to the Evaluation of the Nutritional Quality of Potatoes

USDA-ARS?s Scientific Manuscript database

This paper describes the derivation and application of a new functional mathematical index that was used to evaluate the nutritional, safety, and processing quality aspects of potatoes. The index introduces the concept of an “optimal potato”, using appropriate distance and N-dimensional parameter sp...

Generalized Full-Information Item Bifactor Analysis

PubMed Central

Cai, Li; Yang, Ji Seung; Hansen, Mark

2011-01-01

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than one group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker’s (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood only requires two-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. PMID:21534682

Semianalytical solutions for transport in aquifer and fractured clay matrix system

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2015-09-01

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

Extending topological surgery to natural processes and dynamical systems.

PubMed

Antoniou, Stathis; Lambropoulou, Sofia

2017-01-01

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

Extending topological surgery to natural processes and dynamical systems

PubMed Central

Antoniou, Stathis; Lambropoulou, Sofia

2017-01-01

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a ‘hole drilling’ behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood. PMID:28915271

The 1986 advances in bioengineering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lantz, S.A.; King, A.I.

1986-01-01

This book presents the papers given at a conference on biomedicine. Topics considered at the conference included a mathematical method for obtaining three-dimensional information from standard two-dimensional radiographs, the human lumbar spine, scoliosis and instrumentation, vehicle crashworthiness, lung mechanics, physiological fluid mechanics, microgravity, cardiovascular mechanics, and soft tissue.

Normal forms for reduced stochastic climate models

PubMed Central

Majda, Andrew J.; Franzke, Christian; Crommelin, Daan

2009-01-01

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen–Loéve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to low-frequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability. PMID:19228943

A quantitative evaluation of the three dimensional reconstruction of patients' coronary arteries.

PubMed

Klein, J L; Hoff, J G; Peifer, J W; Folks, R; Cooke, C D; King, S B; Garcia, E V

1998-04-01

Through extensive training and experience angiographers learn to mentally reconstruct the three dimensional (3D) relationships of the coronary arterial branches. Graphic computer technology can assist angiographers to more quickly visualize the coronary 3D structure from limited initial views and then help to determine additional helpful views by predicting subsequent angiograms before they are obtained. A new computer method for facilitating 3D reconstruction and visualization of human coronary arteries was evaluated by reconstructing biplane left coronary angiograms from 30 patients. The accuracy of the reconstruction was assessed in two ways: 1) by comparing the vessel's centerlines of the actual angiograms with the centerlines of a 2D projection of the 3D model projected into the exact angle of the actual angiogram; and 2) by comparing two 3D models generated by different simultaneous pairs on angiograms. The inter- and intraobserver variability of reconstruction were evaluated by mathematically comparing the 3D model centerlines of repeated reconstructions. The average absolute corrected displacement of 14,662 vessel centerline points in 2D from 30 patients was 1.64 +/- 2.26 mm. The average corrected absolute displacement of 3D models generated from different biplane pairs was 7.08 +/- 3.21 mm. The intraobserver variability of absolute 3D corrected displacement was 5.22 +/- 3.39 mm. The interobserver variability was 6.6 +/- 3.1 mm. The centerline analyses show that the reconstruction algorithm is mathematically accurate and reproducible. The figures presented in this report put these measurement errors into clinical perspective showing that they yield an accurate representation of the clinically relevant information seen on the actual angiograms. These data show that this technique can be clinically useful by accurately displaying in three dimensions the complex relationships of the branches of the coronary arterial tree.

The stationary flow in a heterogeneous compliant vessel network

NASA Astrophysics Data System (ADS)

Filoche, Marcel; Florens, Magali

2011-09-01

We introduce a mathematical model of the hydrodynamic transport into systems consisting in a network of connected flexible pipes. In each pipe of the network, the flow is assumed to be steady and one-dimensional. The fluid-structure interaction is described through tube laws which relate the pipe diameter to the pressure difference across the pipe wall. We show that the resulting one-dimensional differential equation describing the flow in the pipe can be exactly integrated if one is able to estimate averages of the Reynolds number along the pipe. The differential equation is then transformed into a non linear scalar equation relating pressures at both ends of the pipe and the flow rate in the pipe. These equations are coupled throughout the network with mass conservation equations for the flow and zero pressure losses at the branching points of the network. This allows us to derive a general model for the computation of the flow into very large inhomogeneous networks consisting of several thousands of flexible pipes. This model is then applied to perform numerical simulations of the human lung airway system at exhalation. The topology of the system and the tube laws are taken from morphometric and physiological data in the literature. We find good qualitative and quantitative agreement between the simulation results and flow-volume loops measured in real patients. In particular, expiratory flow limitation which is an essential characteristic of forced expiration is found to be well reproduced by our simulations. Finally, a mathematical model of a pathology (Chronic Obstructive Pulmonary Disease) is introduced which allows us to quantitatively assess the influence of a moderate or severe alteration of the airway compliances.

Self-aligning and compressed autosophy video databases

NASA Astrophysics Data System (ADS)

Holtz, Klaus E.

1993-04-01

Autosophy, an emerging new science, explains `self-assembling structures,' such as crystals or living trees, in mathematical terms. This research provides a new mathematical theory of `learning' and a new `information theory' which permits the growing of self-assembling data network in a computer memory similar to the growing of `data crystals' or `data trees' without data processing or programming. Autosophy databases are educated very much like a human child to organize their own internal data storage. Input patterns, such as written questions or images, are converted to points in a mathematical omni dimensional hyperspace. The input patterns are then associated with output patterns, such as written answers or images. Omni dimensional information storage will result in enormous data compression because each pattern fragment is only stored once. Pattern recognition in the text or image files is greatly simplified by the peculiar omni dimensional storage method. Video databases will absorb input images from a TV camera and associate them with textual information. The `black box' operations are totally self-aligning where the input data will determine their own hyperspace storage locations. Self-aligning autosophy databases may lead to a new generation of brain-like devices.

Development and external validation of new ultrasound-based mathematical models for preoperative prediction of high-risk endometrial cancer.

PubMed

Van Holsbeke, C; Ameye, L; Testa, A C; Mascilini, F; Lindqvist, P; Fischerova, D; Frühauf, F; Fransis, S; de Jonge, E; Timmerman, D; Epstein, E

2014-05-01

To develop and validate strategies, using new ultrasound-based mathematical models, for the prediction of high-risk endometrial cancer and compare them with strategies using previously developed models or the use of preoperative grading only. Women with endometrial cancer were prospectively examined using two-dimensional (2D) and three-dimensional (3D) gray-scale and color Doppler ultrasound imaging. More than 25 ultrasound, demographic and histological variables were analyzed. Two logistic regression models were developed: one 'objective' model using mainly objective variables; and one 'subjective' model including subjective variables (i.e. subjective impression of myometrial and cervical invasion, preoperative grade and demographic variables). The following strategies were validated: a one-step strategy using only preoperative grading and two-step strategies using preoperative grading as the first step and one of the new models, subjective assessment or previously developed models as a second step. One-hundred and twenty-five patients were included in the development set and 211 were included in the validation set. The 'objective' model retained preoperative grade and minimal tumor-free myometrium as variables. The 'subjective' model retained preoperative grade and subjective assessment of myometrial invasion. On external validation, the performance of the new models was similar to that on the development set. Sensitivity for the two-step strategy with the 'objective' model was 78% (95% CI, 69-84%) at a cut-off of 0.50, 82% (95% CI, 74-88%) for the strategy with the 'subjective' model and 83% (95% CI, 75-88%) for that with subjective assessment. Specificity was 68% (95% CI, 58-77%), 72% (95% CI, 62-80%) and 71% (95% CI, 61-79%) respectively. The two-step strategies detected up to twice as many high-risk cases as preoperative grading only. The new models had a significantly higher sensitivity than did previously developed models, at the same specificity. Two-step strategies with 'new' ultrasound-based models predict high-risk endometrial cancers with good accuracy and do this better than do previously developed models. Copyright © 2013 ISUOG. Published by John Wiley & Sons Ltd.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

NASA Technical Reports Server (NTRS)

Langer, J. S.; Hong, D. C.

1986-01-01

This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.

Modeling mass drug treatment and resistant filaria disease transmission

NASA Astrophysics Data System (ADS)

Fuady, A. M.; Nuraini, N.; Soewono, E.; Tasman, H.; Supriatna, A. K.

2014-03-01

It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.

Mathematical model investigation of long-term transport of ocean-dumped sewage sludge related to remote sensing

NASA Technical Reports Server (NTRS)

Kuo, C. Y.; Modena, T. D.

1979-01-01

An existing, three-dimensional, Eulerian-Lagrangian finite-difference model was modified and used to examine the transport processes of dumped sewage sludge in the New York Bight. Both in situ and laboratory data were utilized in an attempt to approximate model inputs such as mean current speed, horizontal diffusion coefficients, particle size distributions, and specific gravities. The results presented are a quantitative description of the fate of a negatively buoyant sewage sludge plume resulting from continuous and instantaneous barge releases. Concentrations of the sludge near the surface were compared qualitatively with those remotely sensed. Laboratory study was performed to investigate the behavior of sewage sludge dumping in various ambient density conditions.

On firework blasts and qualitative parameter dependency.

PubMed

Zohdi, T I

2016-01-01

In this paper, a mathematical model is developed to qualitatively simulate the progressive time-evolution of a blast from a simple firework. Estimates are made for the blast radius that one can expect for a given amount of detonation energy and pyrotechnic display material. The model balances the released energy from the initial blast pulse with the subsequent kinetic energy and then computes the trajectory of the material under the influence of the drag from the surrounding air, gravity and possible buoyancy. Under certain simplifying assumptions, the model can be solved for analytically. The solution serves as a guide to identifying key parameters that control the evolving blast envelope. Three-dimensional examples are given.

Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

NASA Astrophysics Data System (ADS)

Camacho, Erika T.; Radulescu, Anca; Wirkus, Stephen

2016-09-01

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

On firework blasts and qualitative parameter dependency

PubMed Central

Zohdi, T. I.

2016-01-01

In this paper, a mathematical model is developed to qualitatively simulate the progressive time-evolution of a blast from a simple firework. Estimates are made for the blast radius that one can expect for a given amount of detonation energy and pyrotechnic display material. The model balances the released energy from the initial blast pulse with the subsequent kinetic energy and then computes the trajectory of the material under the influence of the drag from the surrounding air, gravity and possible buoyancy. Under certain simplifying assumptions, the model can be solved for analytically. The solution serves as a guide to identifying key parameters that control the evolving blast envelope. Three-dimensional examples are given. PMID:26997903

Computational Methods for Inviscid and Viscous Two-and-Three-Dimensional Flow Fields.

DTIC Science & Technology

1975-01-01

Difference Equations Over a Network, Watson Sei. Comput. Lab. Report, 19U9. 173- Isaacson, E. and Keller, H. B., Analaysis of Numerical Methods...element method has given a new impulse to the old mathematical theory of multivariate interpolation. We first study the one-dimensional case, which

Three-Dimensional Printing: A Journey in Visualization

ERIC Educational Resources Information Center

Poetzel, Adam; Muskin, Joseph; Munroe, Anne; Russell, Craig

2012-01-01

Imagine high school students glued to computer screens--not playing video games but applying their mathematical knowledge of functions to the design of three-dimensional sculptures. Imagine these students engaging in rich discourse as they transform functions of their choosing to design unique creations. Now, imagine these students using…

Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.

DTIC Science & Technology

1987-01-01

Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept

Computational techniques to enable visualizing shapes of objects of extra spatial dimensions

NASA Astrophysics Data System (ADS)

Black, Don Vaughn, II

Envisioning extra dimensions beyond the three of common experience is a daunting challenge for three dimensional observers. Intuition relies on experience gained in a three dimensional environment. Gaining experience with virtual four dimensional objects and virtual three manifolds in four-space on a personal computer may provide the basis for an intuitive grasp of four dimensions. In order to enable such a capability for ourselves, it is first necessary to devise and implement a computationally tractable method to visualize, explore, and manipulate objects of dimension beyond three on the personal computer. A technology is described in this dissertation to convert a representation of higher dimensional models into a format that may be displayed in realtime on graphics cards available on many off-the-shelf personal computers. As a result, an opportunity has been created to experience the shape of four dimensional objects on the desktop computer. The ultimate goal has been to provide the user a tangible and memorable experience with mathematical models of four dimensional objects such that the user can see the model from any user selected vantage point. By use of a 4D GUI, an arbitrary convex hull or 3D silhouette of the 4D model can be rotated, panned, scrolled, and zoomed until a suitable dimensionally reduced view or Aspect is obtained. The 4D GUI then allows the user to manipulate a 3-flat hyperplane cutting tool to slice the model at an arbitrary orientation and position to extract or "pluck" an embedded 3D slice or "aspect" from the embedding four-space. This plucked 3D aspect can be viewed from all angles via a conventional 3D viewer using three multiple POV viewports, and optionally exported to a third party CAD viewer for further manipulation. Plucking and Manipulating the Aspect provides a tangible experience for the end-user in the same manner as any 3D Computer Aided Design viewing and manipulation tool does for the engineer or a 3D video game provides for the nascent student.

Mathematical Models for Controlled Drug Release Through pH-Responsive Polymeric Hydrogels.

PubMed

Manga, Ramya D; Jha, Prateek K

2017-02-01

Hydrogels consisting of weakly charged acidic/basic groups are ideal candidates for carriers in oral delivery, as they swell in response to pH changes in the gastrointestinal tract, resulting in drug entrapment at low pH conditions of the stomach and drug release at high pH conditions of the intestine. We have developed 1-dimensional mathematical models to study the drug release behavior through pH-responsive hydrogels. Models are developed for 3 different cases that vary in the level of rigor, which together can be applied to predict both in vitro (drug release from carrier) and in vivo (drug concentration in the plasma) behavior of hydrogel-drug formulations. A detailed study of the effect of hydrogel and drug characteristics and physiological conditions is performed to gain a fundamental insight into the drug release behavior, which may be useful in the design of pH-responsive drug carriers. Finally, we describe a successful application of these models to predict both in vitro and in vivo behavior of docetaxel-loaded micelle in a pH-responsive hydrogel, as reported in a recent experimental study. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

NASA Technical Reports Server (NTRS)

Fischbach, S. R.

2015-01-01

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and ? as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Pulse Phase Dynamic Thermal Tomography Investigation on the Defects of the Solid-Propellant Missile Engine Cladding Layer

NASA Astrophysics Data System (ADS)

Peng, Wei; Wang, Fei; Liu, Jun-yan; Xiao, Peng; Wang, Yang; Dai, Jing-min

2018-04-01

Pulse phase dynamic thermal tomography (PP-DTT) was introduced as a nondestructive inspection technique to detect the defects of the solid-propellant missile engine cladding layer. One-dimensional thermal wave mathematical model stimulated by pulse signal was developed and employed to investigate the thermal wave transmission characteristics. The pulse phase algorithm was used to extract the thermal wave characteristic of thermal radiation. Depth calibration curve was obtained by fuzzy c-means algorithm. Moreover, PP-DTT, a depth-resolved photothermal imaging modality, was employed to enable three-dimensional (3D) visualization of cladding layer defects. The comparison experiment between PP-DTT and classical dynamic thermal tomography was investigated. The results showed that PP-DTT can reconstruct the 3D topography of defects in a high quality.

Complexity and diversity.

PubMed

Doebeli, Michael; Ispolatov, Iaroslav

2010-04-23

The mechanisms for the origin and maintenance of biological diversity are not fully understood. It is known that frequency-dependent selection, generating advantages for rare types, can maintain genetic variation and lead to speciation, but in models with simple phenotypes (that is, low-dimensional phenotype spaces), frequency dependence needs to be strong to generate diversity. However, we show that if the ecological properties of an organism are determined by multiple traits with complex interactions, the conditions needed for frequency-dependent selection to generate diversity are relaxed to the point where they are easily satisfied in high-dimensional phenotype spaces. Mathematically, this phenomenon is reflected in properties of eigenvalues of quadratic forms. Because all living organisms have at least hundreds of phenotypes, this casts the potential importance of frequency dependence for the origin and maintenance of diversity in a new light.

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Development of a two-dimensional skin friction balance nulling circuit using multivariable control theory

NASA Technical Reports Server (NTRS)

Tripp, John S.; Patek, Stephen D.

1988-01-01

Measurement of planar skin friction forces in aerodynamic testing currently requires installation of two perpendicularly mounted, single-axis balances; consequently, force components must be sensed at two distinct locations. A two-axis instrument developed at the Langley Research Center to overcome this disadvantage allows measurement of a two-dimensional force at one location. This paper describes a feedback-controlled nulling circuit developed for the NASA two-axis balance which, without external compensation, is inherently unstable because of its low friction mechanical design. Linear multivariable control theory is applied to an experimentally validated mathematical model of the balance to synthesize a state-variable feedback control law. Pole placement techniques and computer simulation studies are employed to select eigenvalues which provide ideal transient response with decoupled sensing dynamics.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

APOLLO: a general code for transport, slowing-down and thermalization calculations in heterogeneous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kavenoky, A.

1973-01-01

From national topical meeting on mathematical models and computational techniques for analysis of nuclear systems; Ann Arbor, Michigan, USA (8 Apr 1973). In mathematical models and computational techniques for analysis of nuclear systems. APOLLO calculates the space-and-energy-dependent flux for a one dimensional medium, in the multigroup approximation of the transport equation. For a one dimensional medium, refined collision probabilities have been developed for the resolution of the integral form of the transport equation; these collision probabilities increase accuracy and save computing time. The interaction between a few cells can also be treated by the multicell option of APOLLO. The diffusionmore » coefficient and the material buckling can be computed in the various B and P approximations with a linearly anisotropic scattering law, even in the thermal range of the spectrum. Eventually this coefficient is corrected for streaming by use of Benoist's theory. The self-shielding of the heavy isotopes is treated by a new and accurate technique which preserves the reaction rates of the fundamental fine structure flux. APOLLO can perform a depletion calculation for one cell, a group of cells or a complete reactor. The results of an APOLLO calculation are the space-and-energy-dependent flux, the material buckling or any reaction rate; these results can also be macroscopic cross sections used as input data for a 2D or 3D depletion and diffusion code in reactor geometry. 10 references. (auth)« less

High dimensional model representation method for fuzzy structural dynamics

NASA Astrophysics Data System (ADS)

Adhikari, S.; Chowdhury, R.; Friswell, M. I.

2011-03-01

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.

General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, S., E-mail: skrishna.bhu@gmail.com; Shukla, A., E-mail: ashukla038@gmail.com; Malik, R.P., E-mail: rpmalik1995@gmail.com

2014-12-15

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSYmore » invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.« less

Three-dimensional orientation and location-dependent varying rules of radiographic angles of the acetabular cup.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Zhao, Zhe; Xiao, Ruo-Xiu; Zhang, Li-Cheng; Tang, Pei-Fu

2018-02-17

The aim of this study is to demonstrate the varying rules of radiographic angles following varying three-dimensional (3D) orientations and locations of cup using an accurate mathematical model. A cone model is established to address the quantitative relationship between the opening circle of cup and its ellipse projection on radiograph. The varying rules of two-dimensional (2D) radiographic anteversion (RA) and inclination (RI) angles can be analyzed. When the centre of cup is located above X-ray source, with proper 3D RI/RA angles, 2D RA angle can be equal to its 3D counterpart, and 2D RI angle is usually greater than its 3D counterpart. Except for the original point on hip-centered anterior-posterior radiograph, there is no area on radiograph where both 2D RA and RI angles are equal to their 3D counterparts simultaneously. This study proposes an innovative model for accurately explaining how 2D RA/RI angles of cup are varying following different 3D RA/RI angles and location of cup. The analysis results provide clinicians an intuitive grasp of knowledge about 2D RA/RI angles greater or smaller than their 3D counterparts post-operatively. The established model may allow determining the effects of pelvic rotations on 2D radiographic angles of cup.

The limitations of mathematical modeling in high school physics education

NASA Astrophysics Data System (ADS)

Forjan, Matej

The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems geometrical approach to solving differential equations is appropriate, while in dynamical systems of higher dimensions mathematical constraints are avoided by using a graphical oriented programs for modeling. Because in dealing with dynamical systems with four or more dimensions we may encounter problems in numerical solving, we also show how to overcome them. In the case of electrostatic pendulum we show the process of modeling the real dynamical system and we put a particular emphasize on the different phases of modeling and on the way of overcoming constraints on which we encounter in the development of the model.

Fuzzy Performance between Surface Fitting and Energy Distribution in Turbulence Runner

PubMed Central

Liang, Zhongwei; Liu, Xiaochu; Ye, Bangyan; Brauwer, Richard Kars

2012-01-01

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy parameters, several typical algorithms of complicated surface fitting are applied for constructing microkinetic energy distribution surface models in the objective turbulence runner with those obtained kinetic energy values. On the base of calculating the newly proposed mathematical features, we construct fuzzy evaluation data sequence and present a new three-dimensional fuzzy quantitative evaluation method; then the value change tendencies of kinetic energy distribution surface features can be clearly quantified, and the fuzzy performance mechanism discipline between the performance results of surface fitting algorithms, the spatial features of turbulence kinetic energy distribution surface, and their respective environmental parameter conditions can be quantitatively analyzed in detail, which results in the acquirement of final conclusions concerning the inherent turbulence kinetic energy distribution performance mechanism and its mathematical relation. A further turbulence energy quantitative study can be ensured. PMID:23213287