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.

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.

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.

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 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)

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

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.

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.

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

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.

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.

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.

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

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)

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.

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.

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 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.

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.

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.

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

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.

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

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.

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.

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.

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.

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.

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.

Application of Mathematical and Three-Dimensional Computer Modeling Tools in the Planning of Processes of Fuel and Energy Complexes

NASA Astrophysics Data System (ADS)

Aksenova, Olesya; Nikolaeva, Evgenia; Cehlár, Michal

2017-11-01

This work aims to investigate the effectiveness of mathematical and three-dimensional computer modeling tools in the planning of processes of fuel and energy complexes at the planning and design phase of a thermal power plant (TPP). A solution for purification of gas emissions at the design development phase of waste treatment systems is proposed employing mathematical and three-dimensional computer modeling - using the E-nets apparatus and the development of a 3D model of the future gas emission purification system. Which allows to visualize the designed result, to select and scientifically prove economically feasible technology, as well as to ensure the high environmental and social effect of the developed waste treatment system. The authors present results of a treatment of planned technological processes and the system for purifying gas emissions in terms of E-nets. using mathematical modeling in the Simulink application. What allowed to create a model of a device from the library of standard blocks and to perform calculations. A three-dimensional model of a system for purifying gas emissions has been constructed. It allows to visualize technological processes and compare them with the theoretical calculations at the design phase of a TPP and. if necessary, make adjustments.

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…

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.

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

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.

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.

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.

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.

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.

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…

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)

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.

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.

Mathematical modeling of forest fire initiation in three dimensional setting

Treesearch

Valeriy Perminov

2007-01-01

In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

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…

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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…

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

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.

Examination of the Assumptions and Properties of the Graded Item Response Model: An Example Using a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1995-01-01

Over 5,000 students participated in a study of the dimensionality and stability of the item parameter estimates of a mathematics performance assessment developed for the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Project. Results demonstrate the test's dimensionality and illustrate ways to examine use of the…

Attitude determination of a high altitude balloon system. Part 1: Development of the mathematical model

NASA Technical Reports Server (NTRS)

Nigro, N. J.; Elkouh, A. F.; Shen, K. S.; Nimityongskul, P.; Jhaveri, V. N.; Sethi, A.

1975-01-01

A mathematical model for predicting the three dimensional motion of the balloon system is developed, which includes the effects of bounce, pendulation and spin of each subsystem. Boundary layer effects are also examined, along with the aerodynamic forces acting on the balloon. Various simplified forms of the system mathematical model were developed, based on an order of magnitude analysis.

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.

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.

Mathematical model for the simulation of Dynamic Docking Test System (DDST) active table motion

NASA Technical Reports Server (NTRS)

Gates, R. M.; Graves, D. L.

1974-01-01

The mathematical model developed to describe the three-dimensional motion of the dynamic docking test system active table is described. The active table is modeled as a rigid body supported by six flexible hydraulic actuators which produce the commanded table motions.

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.

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.

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.).

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.

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 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

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)

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.

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.

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.

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

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

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.

Mathematical model of a smoldering log.

Treesearch

Fernando de Souza Costa; David Sandberg

2004-01-01

A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

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…

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.

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.

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.

A tool for multi-scale modelling of the renal nephron

PubMed Central

Nickerson, David P.; Terkildsen, Jonna R.; Hamilton, Kirk L.; Hunter, Peter J.

2011-01-01

We present the development of a tool, which provides users with the ability to visualize and interact with a comprehensive description of a multi-scale model of the renal nephron. A one-dimensional anatomical model of the nephron has been created and is used for visualization and modelling of tubule transport in various nephron anatomical segments. Mathematical models of nephron segments are embedded in the one-dimensional model. At the cellular level, these segment models use models encoded in CellML to describe cellular and subcellular transport kinetics. A web-based presentation environment has been developed that allows the user to visualize and navigate through the multi-scale nephron model, including simulation results, at the different spatial scales encompassed by the model description. The Zinc extension to Firefox is used to provide an interactive three-dimensional view of the tubule model and the native Firefox rendering of scalable vector graphics is used to present schematic diagrams for cellular and subcellular scale models. The model viewer is embedded in a web page that dynamically presents content based on user input. For example, when viewing the whole nephron model, the user might be presented with information on the various embedded segment models as they select them in the three-dimensional model view. Alternatively, the user chooses to focus the model viewer on a cellular model located in a particular nephron segment in order to view the various membrane transport proteins. Selecting a specific protein may then present the user with a description of the mathematical model governing the behaviour of that protein—including the mathematical model itself and various simulation experiments used to validate the model against the literature. PMID:22670210

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.

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.

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.

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.

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

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

[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.

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.

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.

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

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.

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.

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

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

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.

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

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.

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.

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.

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…

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

NASA Astrophysics Data System (ADS)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Analysis of thermal stresses and metal movement during welding

NASA Technical Reports Server (NTRS)

Muraki, T.; Masubuchi, K.

1973-01-01

The research is reported concerning the development of a system of mathematical solutions and computer programs for one- and two-dimensional analyses for thermal stresses. Reports presented include: the investigation of thermal stress and buckling of tantalum and columbium sheet; and analysis of two dimensional thermal strains and metal movement during welding.

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.

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.

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

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.

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.

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

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

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.

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.

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…

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.

Let Students Derive, by Themselves, Two-Dimensional Atomic and Molecular Quantum Chemistry from Scratch

ERIC Educational Resources Information Center

Ge, Yingbin

2016-01-01

Hands-on exercises are designed for undergraduate physical chemistry students to derive two-dimensional quantum chemistry from scratch for the H atom and H[subscript 2] molecule, both in the ground state and excited states. By reducing the mathematical complexity of the traditional quantum chemistry teaching, these exercises can be completed…

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.

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.

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.

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.

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.

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.

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.

A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions

NASA Astrophysics Data System (ADS)

Rezaei, M. P.; Zamanian, M.

2017-01-01

In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler-Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.

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…

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

PubMed Central

Nayak, Alok Ranjan; Shajahan, T. K.; Panfilov, A. V.; Pandit, Rahul

2013-01-01

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities. PMID:24023798

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.

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

Bidirectional Elastic Image Registration Using B-Spline Affine Transformation

PubMed Central

Gu, Suicheng; Meng, Xin; Sciurba, Frank C.; Wang, Chen; Kaminski, Naftali; Pu, Jiantao

2014-01-01

A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-Spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bi-directional instead of the traditional unidirectional objective / cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210

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.

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.

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.

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.

Topics in Covariant Closed String Field Theory and Two-Dimensional Quantum Gravity

NASA Astrophysics Data System (ADS)

Saadi, Maha

1991-01-01

The closed string field theory based on the Witten vertex is found to be nonpolynomial in order to reproduce all tree amplitudes correctly. The interactions have a geometrical pattern of overlaps, which can be thought as the edges of a spherical polyhedron with face-perimeters equal to 2pi. At each vertex of the polyhedron there are three faces, thus all elementary interactions are cubic in the sense that at most three strings can coincide at a point. The quantum action is constructed by substracting counterterms which cancel the overcounting of moduli space, and by adding loop vertices in such a way no possible surfaces are missed. A counterterm that gives the correct one-string one-loop amplitude is formulated. The lowest order loop vertices are analyzed in the cases of genus one and two. Also, a one-loop two -string counterterm that restores BRST invariance to the respective scattering amplitude is constructed. An attempt to understand the formulation of two -dimensional pure gravity from the discrete representation of a two-dimensional surface is made. This is considered as a toy model of string theory. A well-defined mathematical model is used. Its continuum limit cannot be naively interpreted as pure gravity because each term of the sum over surfaces is not positive definite. The model, however, could be considered as an analytic continuation of the standard matrix model formulation of gravity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

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.

Mathematical investigation of tsunami-like long waves interaction with submerge dike of different thickness

NASA Astrophysics Data System (ADS)

Zhiltsov, Konstantin; Kostyushin, Kirill; Kagenov, Anuar; Tyryshkin, Ilya

2017-11-01

This paper presents a mathematical investigation of the interaction of a long tsunami-type wave with a submerge dike. The calculations were performed by using the freeware package OpenFOAM. Unsteady two-dimensional Navier-Stokes equations were used for mathematical modeling of incompressible two-phase medium. The Volume of Fluid (VOF) method is used to capture the free surface of a liquid. The effects caused by long wave of defined amplitude motion through a submerged dike of varying thickness were discussed in detail. Numerical results show that after wave passing through the barrier, multiple vortex structures were formed behind. Intensity of vortex depended on the size of the barrier. The effectiveness of the submerge barrier was estimated by evaluating the wave reflection and transmission coefficients using the energy integral method. Then, the curves of the dependences of the reflection and transmission coefficients were obtained for the interaction of waves with the dike. Finally, it was confirmed that the energy of the wave could be reduced by more than 50% when it passed through the barrier.

Cell Protrusion and Retraction Driven by Fluctuations in Actin Polymerization: A Two-Dimensional Model

PubMed Central

Ryan, Gillian L.; Holz, Danielle; Yamashiro, Sawako; Taniguchi, Daisuke; Watanabe, Naoki; Vavylonis, Dimitrios

2017-01-01

Animal cells that spread onto a surface often rely on actin-rich lamellipodial extensions to execute protrusion. Many cell types recently adhered on a two-dimensional substrate exhibit protrusion and retraction of their lamellipodia, even though the cell is not translating. Traveling waves of protrusion have also been observed, similar to those observed in crawling cells. These regular patterns of protrusion and retraction allow quantitative analysis for comparison to mathematical models. The periodic fluctuations in leading edge position of XTC cells have been linked to excitable actin dynamics using a one-dimensional model of actin dynamics, as a function of arc-length along the cell. In this work we extend this earlier model of actin dynamics into two dimensions (along the arc-length and radial directions of the cell) and include a model membrane that protrudes and retracts in response to the changing number of free barbed ends of actin filaments near the membrane. We show that if the polymerization rate at the barbed ends changes in response to changes in their local concentration at the leading edge and/or the opposing force from the cell membrane, the model can reproduce the patterns of membrane protrusion and retraction seen in experiment. We investigate both Brownian ratchet and switch-like force-velocity relationships between the membrane load forces and actin polymerization rate. The switch-like polymerization dynamics recover the observed patterns of protrusion and retraction as well as the fluctuations in F-actin concentration profiles. The model generates predictions for the behavior of cells after local membrane tension perturbations. PMID:28752950

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.

Diatom Valve Three-Dimensional Representation: A New Imaging Method Based on Combined Microscopies

PubMed Central

Ferrara, Maria Antonietta; De Tommasi, Edoardo; Coppola, Giuseppe; De Stefano, Luca; Rea, Ilaria; Dardano, Principia

2016-01-01

The frustule of diatoms, unicellular microalgae, shows very interesting photonic features, generally related to its complicated and quasi-periodic micro- and nano-structure. In order to simulate light propagation inside and through this natural structure, it is important to develop three-dimensional (3D) models for synthetic replica with high spatial resolution. In this paper, we present a new method that generates images of microscopic diatoms with high definition, by merging scanning electron microscopy and digital holography microscopy or atomic force microscopy data. Starting from two digital images, both acquired separately with standard characterization procedures, a high spatial resolution (Δz = λ/20, Δx = Δy ≅ 100 nm, at least) 3D model of the object has been generated. Then, the two sets of data have been processed by matrix formalism, using an original mathematical algorithm implemented on a commercially available software. The developed methodology could be also of broad interest in the design and fabrication of micro-opto-electro-mechanical systems. PMID:27690008

Trends and techniques for space base electronics. [mathematical models, ion implantation, and semiconductors

NASA Technical Reports Server (NTRS)

Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.

1978-01-01

A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

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.

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.

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.

Getting out of Flatland

ERIC Educational Resources Information Center

Popelka, Susan R.; Langlois, Joshua

2018-01-01

"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…

Maximizing kinetic energy transfer in one-dimensional many-body collisions

NASA Astrophysics Data System (ADS)

Ricardo, Bernard; Lee, Paul

2015-03-01

The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions.

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.

Matrix decompositions of two-dimensional nuclear magnetic resonance spectra.

PubMed

Havel, T F; Najfeld, I; Yang, J X

1994-08-16

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given.

Matrix decompositions of two-dimensional nuclear magnetic resonance spectra.

PubMed Central

Havel, T F; Najfeld, I; Yang, J X

1994-01-01

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given. PMID:8058742

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…

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.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

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.

Target recognition for ladar range image using slice image

NASA Astrophysics Data System (ADS)

Xia, Wenze; Han, Shaokun; Wang, Liang

2015-12-01

A shape descriptor and a complete shape-based recognition system using slice images as geometric feature descriptor for ladar range images are introduced. A slice image is a two-dimensional image generated by three-dimensional Hough transform and the corresponding mathematical transformation. The system consists of two processes, the model library construction and recognition. In the model library construction process, a series of range images are obtained after the model object is sampled at preset attitude angles. Then, all the range images are converted into slice images. The number of slice images is reduced by clustering analysis and finding a representation to reduce the size of the model library. In the recognition process, the slice image of the scene is compared with the slice image in the model library. The recognition results depend on the comparison. Simulated ladar range images are used to analyze the recognition and misjudgment rates, and comparison between the slice image representation method and moment invariants representation method is performed. The experimental results show that whether in conditions without noise or with ladar noise, the system has a high recognition rate and low misjudgment rate. The comparison experiment demonstrates that the slice image has better representation ability than moment invariants.

Topographic evolution of orogens: The long term perspective

NASA Astrophysics Data System (ADS)

Robl, Jörg; Hergarten, Stefan; Prasicek, Günther

2017-04-01

The landscape of mountain ranges reflects the competition of tectonics and climate, that build up and destroy topography, respectively. While there is a broad consensus on the acting processes, there is a vital debate whether the topography of individual orogens reflects stages of growth, steady-state or decay. This debate is fuelled by the million-year time scales hampering direct observations on landscape evolution in mountain ranges, the superposition of various process patterns and the complex interactions among different processes. In this presentation we focus on orogen-scale landscape evolution based on time-dependent numerical models and explore model time series to constrain the development of mountain range topography during an orogenic cycle. The erosional long term response of rivers and hillslopes to uplift can be mathematically formalised by the stream power and mass diffusion equations, respectively, which enables us to describe the time-dependent evolution of topography in orogens. Based on a simple one-dimensional model consisting of two rivers separated by a watershed we explain the influence of uplift rate and rock erodibility on steady-state channel profiles and show the time-dependent development of the channel - drainage divide system. The effect of dynamic drainage network reorganization adds additional complexity and its effect on topography is explored on the basis of two-dimensional models. Further complexity is introduced by coupling a mechanical model (thin viscous sheet approach) describing continental collision, crustal thickening and topography formation with a stream power-based landscape evolution model. Model time series show the impact of crustal deformation on drainage networks and consequently on the evolution of mountain range topography (Robl et al., in review). All model outcomes, from simple one-dimensional to coupled two dimensional models are presented as movies featuring a high spatial and temporal resolution. Robl, J., S. Hergarten, and G. Prasicek (in review), The topographic state of mountain ranges, Earth Science Reviews.

Three essays on multi-level optimization models and applications

NASA Astrophysics Data System (ADS)

Rahdar, Mohammad

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader's action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones.

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.

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.

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.

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.

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.

Origami Instruction in the Middle School Mathematics Classroom: Its Impact on Spatial Visualization and Geometry Knowledge of Students

ERIC Educational Resources Information Center

Boakes, Norma J.

2009-01-01

Within the study of geometry in the middle school curriculum is the natural development of students' spatial visualization, the ability to visualize two- and three-dimensional objects. The national mathematics standards call specifically for the development of such skills through hands-on experiences. A commonly accepted method is through the…

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.

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.

Thermal loading of natural streams

USGS Publications Warehouse

Jackman, Alan P.; Yotsukura, Nobuhiro

1977-01-01

The impact of thermal loading on the temperature regime of natural streams is investigated by mathematical models, which describe both transport (convection-diffusion) and decay (surface dissipation) of waste heat over 1-hour or shorter time intervals. The models are derived from the principle of conservation of thermal energy for application to one- and two-dimensional spaces. The basic concept in these models is to separate water temperature into two parts, (1) excess temperature due to thermal loading and (2) natural (ambient) temperature. This separation allows excess temperature to be calculated from the models without incoming radiation data. Natural temperature may either be measured in prototypes or calculated from the model. If use is made of the model, however, incoming radiation is required as input data. Comparison of observed and calculated temperatures in seven natural streams shows that the models are capable of predicting transient temperature regimes satisfactorily in most cases. (Woodard-USGS)

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.

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.

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 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.

Foundations of chaotic mixing.

PubMed

Wiggins, Stephen; Ottino, Julio M

2004-05-15

The simplest mixing problem corresponds to the mixing of a fluid with itself; this case provides a foundation on which the subject rests. The objective here is to study mixing independently of the mechanisms used to create the motion and review elements of theory focusing mostly on mathematical foundations and minimal models. The flows under consideration will be of two types: two-dimensional (2D) 'blinking flows', or three-dimensional (3D) duct flows. Given that mixing in continuous 3D duct flows depends critically on cross-sectional mixing, and that many microfluidic applications involve continuous flows, we focus on the essential aspects of mixing in 2D flows, as they provide a foundation from which to base our understanding of more complex cases. The baker's transformation is taken as the centrepiece for describing the dynamical systems framework. In particular, a hierarchy of characterizations of mixing exist, Bernoulli --> mixing --> ergodic, ordered according to the quality of mixing (the strongest first). Most importantly for the design process, we show how the so-called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing. Extensions of these concepts lead to first-principle-based designs without resorting to lengthy computations.

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.

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.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

On the motion of one-dimensional double pendulum

NASA Astrophysics Data System (ADS)

Burian, S. N.; Kalnitsky, V. S.

2018-05-01

A two-dimensional dynamic Lagrangian system of a double mathematical pendulum with one special constraint is considered. Configuration spaces for a given constraints (ellipses) are studied. The diagrams of paths and reactions in the course of motion along them are shown. The calculations of the transversal intersection case and in the case of tangency are given.

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.

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...

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.

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. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds.

PubMed

Herlin, Antoine; Jacquemet, Vincent

2012-05-01

Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.

Current algebra, statistical mechanics and quantum models

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2017-11-01

Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

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.

Fullerenes and disk-fullerenes

NASA Astrophysics Data System (ADS)

Deza, M.; Dutour Sikirić, M.; Shtogrin, M. I.

2013-08-01

A geometric fullerene, or simply a fullerene, is the surface of a simple closed convex 3-dimensional polyhedron with only 5- and 6-gonal faces. Fullerenes are geometric models for chemical fullerenes, which form an important class of organic molecules. These molecules have been studied intensively in chemistry, physics, crystallography, and so on, and their study has led to the appearance of a vast literature on fullerenes in mathematical chemistry and combinatorial and applied geometry. In particular, several generalizations of the notion of a fullerene have been given, aiming at various applications. Here a new generalization of this notion is proposed: an n-disk-fullerene. It is obtained from the surface of a closed convex 3-dimensional polyhedron which has one n-gonal face and all other faces 5- and 6-gonal, by removing the n-gonal face. Only 5- and 6-disk-fullerenes correspond to geometric fullerenes. The notion of a geometric fullerene is therefore generalized from spheres to compact simply connected two-dimensional manifolds with boundary. A two-dimensional surface is said to be unshrinkable if it does not contain belts, that is, simple cycles consisting of 6-gons each of which has two neighbours adjacent at a pair of opposite edges. Shrinkability of fullerenes and n-disk-fullerenes is investigated. Bibliography: 87 titles.

Dimensional coordinate measurements: application in characterizing cervical spine motion

NASA Astrophysics Data System (ADS)

Zheng, Weilong; Li, Linan; Wang, Shibin; Wang, Zhiyong; Shi, Nianke; Xue, Yuan

2014-06-01

Cervical spine as a complicated part in the human body, the form of its movement is diverse. The movements of the segments of vertebrae are three-dimensional, and it is reflected in the changes of the angle between two joint and the displacement in different directions. Under normal conditions, cervical can flex, extend, lateral flex and rotate. For there is no relative motion between measuring marks fixed on one segment of cervical vertebra, the cervical vertebrae with three marked points can be seen as a body. Body's motion in space can be decomposed into translational movement and rotational movement around a base point .This study concerns the calculation of dimensional coordinate of the marked points pasted to the human body's cervical spine by an optical method. Afterward, these measures will allow the calculation of motion parameters for every spine segment. For this study, we choose a three-dimensional measurement method based on binocular stereo vision. The object with marked points is placed in front of the CCD camera. Through each shot, we will get there two parallax images taken from different cameras. According to the principle of binocular vision we can be realized three-dimensional measurements. Cameras are erected parallelly. This paper describes the layout of experimental system and a mathematical model to get the coordinates.

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

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

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.

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

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.

A User's Guide for the Differential Reduced Ejector/Mixer Analysis "DREA" Program. 1.0

NASA Technical Reports Server (NTRS)

DeChant, Lawrence J.; Nadell, Shari-Beth

1999-01-01

A system of analytical and numerical two-dimensional mixer/ejector nozzle models that require minimal empirical input has been developed and programmed for use in conceptual and preliminary design. This report contains a user's guide describing the operation of the computer code, DREA (Differential Reduced Ejector/mixer Analysis), that contains these mathematical models. This program is currently being adopted by the Propulsion Systems Analysis Office at the NASA Glenn Research Center. A brief summary of the DREA method is provided, followed by detailed descriptions of the program input and output files. Sample cases demonstrating the application of the program are presented.

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

NASA Astrophysics Data System (ADS)

Chiu, Mei-Shiu

2016-12-01

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 prior learning experiences of trigonometry in mathematics. The perspectives of three curriculum developers, 22 mathematics and physics teachers, two principals, and 45 science students were obtained by interview. The results of qualitative data analysis revealed six challenges and suggested likely solutions. The national level includes political and social challenges, resolved by respecting teachers as professionals; the teacher level includes knowledge and teaching challenges, resolved by increasing teacher trans-literal capacities; and the student level includes learning and justice challenges, resolved by focusing on students' diverse developments in cross-domain learning.

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.

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.

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.

Free boundary problems in shock reflection/diffraction and related transonic flow problems

PubMed Central

Chen, Gui-Qiang; Feldman, Mikhail

2015-01-01

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws. PMID:26261363

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.

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

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.

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.

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.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts.

PubMed

Nayak, Alok Ranjan; Shajahan, T K; Panfilov, A V; Pandit, Rahul

2013-01-01

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as [Formula: see text], the fibroblast resting-membrane potential, the fibroblast conductance [Formula: see text], and the MF gap-junctional coupling [Formula: see text]. Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as [Formula: see text], and [Formula: see text], and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity [Formula: see text] decreases as a function of [Formula: see text], for zero-sided and one-sided couplings; however, for two-sided coupling, [Formula: see text] decreases initially and then increases as a function of [Formula: see text], and, eventually, we observe that conduction failure occurs for low values of [Formula: see text]. In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling [Formula: see text] or [Formula: see text]. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacón, L.; Cappello, S.

2010-08-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacón, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code in cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

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

Bonfiglio, Daniele; Chacon, Luis; Cappello, Susanna

2010-01-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacon, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code inmore » cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.« less

SEMI-ANALYTIC CALCULATION OF THE TEMPERATURE DISTRIBUTION IN A PERFORATED CIRCLE

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

Kennedy, J.M.; Fowler, J.K.

The flow of heat in a tube-in-shell fuel element is closely related to the two-dimensional heat flow in a circular region perforated by a number of circular holes. Mathematical expressions for the two-dimensional temperature distribution were obtained in terms of sources and sinks of increasing complexity located within the holes and beyond the outer circle. A computer program, TINS, which solves the temperature problem for an array of one or two rings of holes, with or without a center hole, is also described. (auth)

Modeling and simulation of electronic structure, material interface and random doping in nano electronic devices

PubMed Central

Chen, Duan; Wei, Guo-Wei

2010-01-01

The miniaturization of nano-scale electronic devices, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. Modeling and simulation of this class of problems have emerged as an important topic in applied and computational mathematics. This work presents mathematical models and computational algorithms for the simulation of nano-scale MOSFETs. We introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential of the nano-electronic device. This framework enables us to put microscopic and macroscopic descriptions in an equal footing at nano scale. By optimization of the energy functional, we derive consistently-coupled Poisson-Kohn-Sham equations. Additionally, layered structures are crucial to the electrostatic and transport properties of nano transistors. A material interface model is proposed for more accurate description of the electrostatics governed by the Poisson equation. Finally, a new individual dopant model that utilizes the Dirac delta function is proposed to understand the random doping effect in nano electronic devices. Two mathematical algorithms, the matched interface and boundary (MIB) method and the Dirichlet-to-Neumann mapping (DNM) technique, are introduced to improve the computational efficiency of nano-device simulations. Electronic structures are computed via subband decomposition and the transport properties, such as the I-V curves and electron density, are evaluated via the non-equilibrium Green's functions (NEGF) formalism. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our three-dimensional numerical simulations. For these devices, the current fluctuation and voltage threshold lowering effect induced by the discrete dopant model are explored. Numerical convergence and model well-posedness are also investigated in the present work. PMID:20396650

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%.

Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy

PubMed Central

Sápi, Johanna; Kovács, Levente; Drexler, Dániel András; Kocsis, Pál; Gajári, Dávid; Sápi, Zoltán

2015-01-01

Background Bevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol. Materials and Methods We have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis. Results In the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model. Conclusion Our results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration. PMID:26540189

Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy.

PubMed

Sápi, Johanna; Kovács, Levente; Drexler, Dániel András; Kocsis, Pál; Gajári, Dávid; Sápi, Zoltán

2015-01-01

Bevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol. We have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis. In the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model. Our results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration.

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.

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.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

NASA Astrophysics Data System (ADS)

Matsevityi, Yu. M.; Alekhina, S. V.; Borukhov, V. T.; Zayats, G. M.; Kostikov, A. O.

2017-11-01

The problem of identifying the time-dependent thermal conductivity coefficient in the initial-boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.

Divergence thrust loss calculations for convergent-divergent nozzles: Extensions to the classical case

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

1991-01-01

The analytical derivations of the non-axial thrust divergence losses for convergent-divergent nozzles are described as well as how these calculations are embodied in the Navy/NASA engine computer program. The convergent-divergent geometries considered are simple classic axisymmetric nozzles, two dimensional rectangular nozzles, and axisymmetric and two dimensional plug nozzles. A simple, traditional, inviscid mathematical approach is used to deduce the influence of the ineffectual non-axial thrust as a function of the nozzle exit divergence angle.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

SIERRA/Aero Theory Manual Version 4.46.

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

Sierra Thermal/Fluid Team

2017-09-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

SIERRA/Aero Theory Manual Version 4.44

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

Sierra Thermal /Fluid Team

2017-04-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

Application of kinetic flux vector splitting scheme for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

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

In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form 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 kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

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.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers.

PubMed

Nayak, Alok Ranjan; Panfilov, A V; Pandit, Rahul

2017-02-01

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

NASA Astrophysics Data System (ADS)

Nayak, Alok Ranjan; Panfilov, A. V.; Pandit, Rahul

2017-02-01

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

How High Is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity

ERIC Educational Resources Information Center

Yoon, Caroline; Dreyfus, Tommy; Thomas, Michael O. J.

2010-01-01

Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

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...

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.

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.

Limitations in the 2D description of the electromagnetic waves propagation in thin dielectric and magnetic layers

NASA Astrophysics Data System (ADS)

Radożycki, Tomasz; Bargieła, Piotr

2018-07-01

The propagation of electromagnetic waves trapped within dielectric and magnetic layers is considered. The description within the three-dimensional theory is compared to the simplified analysis in two dimensions. Two distinct media configurations of different topology are dealt with: a plane slab and a hollow cylinder. Choosing the appropriate values for the geometrical parameters (layer thickness, radius of the cylinder) and for the electromagnetic properties of the media one can trap exactly one mode corresponding to that obtained within the two-dimensional electromagnetism. However, the symmetry between electric and magnetic fields suggests, that the two versions of the simplified electromagnetism ought to be equally considered. Its usual form is incomplete to describe all modes. It is also found that there exists a domain of optimal values of parameters for which the 2D model works relatively correctly. However, in the case of a cylindrical surface we observe several differences which may be attributed to the curvature of the layer, and which exclude the propagation of evanescent modes. The two-dimensional electrodynamics, whichever form is used, turns out still too poor to describe the so-called 'hybrid modes' excited in a real layer. The obtained results can be essential for proper description of the propagating waves within thin layers for which 3D approach is not available due to mathematical complexity and reducing the layer to a lower dimensional structure seems the only possible option.

Generalized Weierstrass-Mandelbrot Function Model for Actual Stocks Markets Indexes with Nonlinear Characteristics

NASA Astrophysics Data System (ADS)

Zhang, L.; Yu, C.; Sun, J. Q.

2015-03-01

It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.

General flat four-dimensional world pictures and clock systems

NASA Technical Reports Server (NTRS)

Hsu, J. P.; Underwood, J. A.

1978-01-01

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincare-Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. The connection between the properties of light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework.

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

Two-dimensional echo-cardiographic estimation of left atrial volume and volume load in patients with congenital heart disease.

PubMed

Kawaguchi, A; Linde, L M; Imachi, T; Mizuno, H; Akutsu, H

1983-12-01

To estimate the left atrial volume (LAV) and pulmonary blood flow in patients with congenital heart disease (CHD), we employed two-dimensional echocardiography (TDE). The LAV was measured in dimensions other than those obtained in conventional M-mode echocardiography (M-mode echo). Mathematical and geometrical models for LAV calculation using the standard long-axis, short-axis and apical four-chamber planes were devised and found to be reliable in a preliminary study using porcine heart preparations, although length (10%), area (20%) and volume (38%) were significantly and consistently underestimated with echocardiography. Those models were then applied and correlated with angiocardiograms (ACG) in 25 consecutive patients with suspected CHD. In terms of the estimation of the absolute LAV, accuracy seemed commensurate with the number of the dimensions measured. The correlation between data obtained by TDE and ACG varied with changing hemodynamics such as cardiac cycle, absolute LAV and presence or absence of volume load. The left atrium was found to become spherical and progressively underestimated with TDE at ventricular endsystole, in larger LAV and with increased volume load. Since this tendency became less pronounced in measuring additional dimensions, reliable estimation of the absolute LAV and volume load was possible when 2 or 3 dimensions were measured. Among those calculation models depending on 2 or 3 dimensional measurements, there was only a small difference in terms of accuracy and predictability, although algorithm used varied from one model to another. This suggests that accurate cross-sectional area measurement is critically important for volume estimation rather than any particular algorithm involved. Cross-sectional area measurement by TDE integrated into a three dimensional equivalent allowed a reliable estimate of the LAV or volume load in a variety of hemodynamic situations where M-mode echo was not reliable.

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.

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.

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.

Finite element meshing approached as a global minimization process

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

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

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.

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.

A Framework for Assessing Reading Comprehension of Geometric Construction Texts

ERIC Educational Resources Information Center

Yang, Kai-Lin; Li, Jian-Lin

2018-01-01

This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three…

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.

The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

NASA Astrophysics Data System (ADS)

Belloni, M.; Robinett, R. W.

2014-07-01

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law ‘tail’.More recently, Tan [43] and others [44,45] have noted that for condensed matter or atomic systems with a large scattering length, so that the short-range interactions can actually be modeled as singular δ-functions, the momentum distribution also exhibits a large momentum ‘tail’ which falls off as C/k4. The constant of proportionality, C (or contact as it has come to be known), encodes important information on the microscopic physics, in much the way that the constants in Eq. (5) are related to the details of the 1D potential. In fact, in one review [46] of these developments, this connection has been described as “How the tail wags the dog in ultracold atomic gases”. Just as with the H-atom momentum distribution, experiments have verified this power-law behavior for both fermion [47,48] and more recently Bose systems [49].It is these connections, namely of exemplary results derived in simpler one-dimensional systems such as the ISW and DDF potentials which find parallels in more fundamental physical realizations, that motivate us to review many of the basic mathematical and physical results of these two ‘benchmark’ model potentials. We hope that both students and instructors alike involved in advanced undergraduate and graduate courses in quantum mechanics will find this survey useful. We trust that it will aid readers in exploring a wide array of physical effects, using rigorous mathematical methods, in the context of familiar one-dimensional systems, making use of otherwise hard-to-find results.

Performance analysis of successive over relaxation method for solving glioma growth model

NASA Astrophysics Data System (ADS)

Hussain, Abida; Faye, Ibrahima; Muthuvalu, Mohana Sundaram

2016-11-01

Brain tumor is one of the prevalent cancers in the world that lead to death. In light of the present information of the properties of gliomas, mathematical models have been developed by scientists to quantify the proliferation and invasion dynamics of glioma. In this study, one-dimensional glioma growth model is considered, and finite difference method is used to discretize the problem. Then, two stationary methods, namely Gauss-Seidel (GS) and Successive Over Relaxation (SOR) are used to solve the governing algebraic system. The performance of the methods are evaluated in terms of number of iteration and computational time. On the basis of performance analysis, SOR method is shown to be more superior compared to GS method.

Tension waves in tethered satellite cables

NASA Technical Reports Server (NTRS)

Lallman, F. J.

1984-01-01

A one-degree-of-freedom simulation of the Tethered Satellite System (TSS) was programmed using a distributed system model of the tether based on the one-dimensional wave equation. This model represents the time varying tension profile along the tether as the sum of two traveling waves of tension moving in opposite directions. A control loop was devised which combines a deployment rate command with the measured tension at the deployer to produce a smooth, stable rate of deployment of the subsatellite. Simulation results show a buildup of periodic bursts of high frequency oscillation in tension. This report covers the mathematical modelling and simulation results and explains the reason for the observed oscillations. The design of a possible vibration damping device is discussed.

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.

Physics of the Lorentz Group

NASA Astrophysics Data System (ADS)

Başkal, Sibel

2015-11-01

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

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.

Utility-free heuristic models of two-option choice can mimic predictions of utility-stage models under many conditions

PubMed Central

Piantadosi, Steven T.; Hayden, Benjamin Y.

2015-01-01

Economists often model choices as if decision-makers assign each option a scalar value variable, known as utility, and then select the option with the highest utility. It remains unclear whether as-if utility models describe real mental and neural steps in choice. Although choices alone cannot prove the existence of a utility stage, utility transformations are often taken to provide the most parsimonious or psychologically plausible explanation for choice data. Here, we show that it is possible to mathematically transform a large set of common utility-stage two-option choice models (specifically ones in which dimensions are can be decomposed into additive functions) into a heuristic model (specifically, a dimensional prioritization heuristic) that has no utility computation stage. We then show that under a range of plausible assumptions, both classes of model predict similar neural responses. These results highlight the difficulties in using neuroeconomic data to infer the existence of a value stage in choice. PMID:25914613

Automatic Reconstruction of Spacecraft 3D Shape from Imagery

NASA Astrophysics Data System (ADS)

Poelman, C.; Radtke, R.; Voorhees, H.

We describe a system that computes the three-dimensional (3D) shape of a spacecraft from a sequence of uncalibrated, two-dimensional images. While the mathematics of multi-view geometry is well understood, building a system that accurately recovers 3D shape from real imagery remains an art. A novel aspect of our approach is the combination of algorithms from computer vision, photogrammetry, and computer graphics. We demonstrate our system by computing spacecraft models from imagery taken by the Air Force Research Laboratory's XSS-10 satellite and DARPA's Orbital Express satellite. Using feature tie points (each identified in two or more images), we compute the relative motion of each frame and the 3D location of each feature using iterative linear factorization followed by non-linear bundle adjustment. The "point cloud" that results from this traditional shape-from-motion approach is typically too sparse to generate a detailed 3D model. Therefore, we use the computed motion solution as input to a volumetric silhouette-carving algorithm, which constructs a solid 3D model based on viewpoint consistency with the image frames. The resulting voxel model is then converted to a facet-based surface representation and is texture-mapped, yielding realistic images from arbitrary viewpoints. We also illustrate other applications of the algorithm, including 3D mensuration and stereoscopic 3D movie generation.

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.

Mathematical modeling of a dynamic thin plate deformation in acoustoelasticity problems

NASA Astrophysics Data System (ADS)

Badriev, I. B.; Paimuhin, V. N.

2018-01-01

The coupled problem of planar acoustic wave propagation through a composite plate covered with a second damping layer with a large logarithmic decrement of oscillations is formulated. The aerohydrodynamic interaction of a plate with external acoustic environment is described by three-dimensional wave equations and the mechanical behavior of a two-layer plate by the classical Kirchhoff-Love model. An exact analytic solution of the problem is found for the case of hinged support of the edges of a plate. On the basis of this, the parameters of the covering damping layer were found, under which it is possible to achieve a practically complete damping of the plate vibration under resonant modes of its acoustic loading.

Coupling of Transport and Chemical Processes in Catalytic Combustion

NASA Technical Reports Server (NTRS)

Bracco, F. V.; Bruno, C.; Royce, B. S. H.; Santavicca, D. A.; Sinha, N.; Stein, Y.

1983-01-01

Catalytic combustors have demonstrated the ability to operate efficiently over a much wider range of fuel air ratios than are imposed by the flammability limits of conventional combustors. Extensive commercial use however needs the following: (1) the design of a catalyst with low ignition temperature and high temperature stability, (2) reducing fatigue due to thermal stresses during transient operation, and (3) the development of mathematical models that can be used as design optimization tools to isolate promising operating ranges for the numerous operating parameters. The current program of research involves the development of a two dimensional transient catalytic combustion model and the development of a new catalyst with low temperature light-off and high temperature stablity characteristics.

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

NASA Technical Reports Server (NTRS)

Olson, Erik D.

2015-01-01

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

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.

Extension and application of the Preissmann slot model to 2D transient mixed flows

NASA Astrophysics Data System (ADS)

Maranzoni, Andrea; Dazzi, Susanna; Aureli, Francesca; Mignosa, Paolo

2015-08-01

This paper presents an extension of the Preissmann slot concept for the modeling of highly transient two-dimensional (2D) mixed flows. The classic conservative formulation of the 2D shallow water equations for free surface flows is adapted by assuming that two fictitious vertical slots, aligned along the two Cartesian plane directions and normally intersecting, are added on the ceiling of each integration element. Accordingly, transitions between free surface and pressurized flow can be handled in a natural and straightforward way by using the same set of governing equations. The opportunity of coupling free surface and pressurized flows is actually useful not only in one-dimensional (1D) problems concerning sewer systems but also for modeling 2D flooding phenomena in which the pressurization of bridges, culverts, or other crossing hydraulic structures can be expected. Numerical simulations are performed by using a shock-capturing MUSCL-Hancock finite volume scheme combined with the FORCE (First-Order Centred) solver for the evaluation of the numerical fluxes. The validation of the mathematical model is accomplished on the basis of both exact solutions of 1D discontinuous initial value problems and reference radial solutions of idealized test cases with cylindrical symmetry. Furthermore, the capability of the model to deal with practical field-scale applications is assessed by simulating the transit of a bore under an arch bridge. Numerical results show that the proposed model is suitable for the prediction of highly transient 2D mixed flows.

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

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.

Linear Static Behavior of Damaged Laminated Composite Plates and Shells

PubMed Central

2017-01-01

A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software. PMID:28773170

Kinematic reconstruction in cardiovascular imaging.

PubMed

Bastarrika, G; Huebra Rodríguez, I J González de la; Calvo-Imirizaldu, M; Suárez Vega, V M; Alonso-Burgos, A

2018-05-17

Advances in clinical applications of computed tomography have been accompanied by improvements in advanced post-processing tools. In addition to multiplanar reconstructions, curved planar reconstructions, maximum intensity projections, and volumetric reconstructions, very recently kinematic reconstruction has been developed. This new technique, based on mathematical models that simulate the propagation of light beams through a volume of data, makes it possible to obtain very realistic three dimensional images. This article illustrates examples of kinematic reconstructions and compares them with classical volumetric reconstructions in patients with cardiovascular disease in a way that makes it easy to establish the differences between the two types of reconstruction. Kinematic reconstruction is a new method for representing three dimensional images that facilitates the explanation and comprehension of the findings. Copyright © 2018 SERAM. Publicado por Elsevier España, S.L.U. All rights reserved.

Design of horizontal-axis wind turbine using blade element momentum method

NASA Astrophysics Data System (ADS)

Bobonea, Andreea; Pricop, Mihai Victor

2013-10-01

The study of mathematical models applied to wind turbine design in recent years, principally in electrical energy generation, has become significant due to the increasing use of renewable energy sources with low environmental impact. Thus, this paper shows an alternative mathematical scheme for the wind turbine design, based on the Blade Element Momentum (BEM) Theory. The results from the BEM method are greatly dependent on the precision of the lift and drag coefficients. The basic of BEM method assumes the blade can be analyzed as a number of independent element in spanwise direction. The induced velocity at each element is determined by performing the momentum balance for a control volume containing the blade element. The aerodynamic forces on the element are calculated using the lift and drag coefficient from the empirical two-dimensional wind tunnel test data at the geometric angle of attack (AOA) of the blade element relative to the local flow velocity.

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.

Numerical investigation of cryogen re-gasification in a plate heat exchanger

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Płuszka, Paweł; Brenk, Arkadiusz

2017-12-01

The efficient re-gasification of cryogen is a crucial process in many cryogenic installations. It is especially important in the case of LNG evaporators used in stationary and mobile applications (e.g. marine and land transport). Other gases, like nitrogen or argon can be obtained at highest purity after re-gasification from their liquid states. Plate heat exchangers (PHE) are characterized by a high efficiency. Application of PHE for liquid gas vaporization processes can be beneficial. PHE design and optimization can be significantly supported by numerical modelling. Such calculations are very challenging due to very high computational demands and complexity related to phase change modelling. In the present work, a simplified mathematical model of a two phase flow with phase change was introduced. To ensure fast calculations a simplified two-dimensional (2D) numerical model of a real PHE was developed. It was validated with experimental measurements and finally used for LNG re-gasification modelling. The proposed numerical model showed to be orders of magnitude faster than its full 3D original.

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

Thermal analysis of underground power cable system

NASA Astrophysics Data System (ADS)

Rerak, Monika; Ocłoń, Paweł

2017-10-01

The paper presents the application of Finite Element Method in thermal analysis of underground power cable system. The computations were performed for power cables buried in-line in the ground at a depth of 2 meters. The developed mathematical model allows determining the two-dimensional temperature distribution in the soil, thermal backfill and power cables. The simulations studied the effect of soil and cable backfill thermal conductivity on the maximum temperature of the cable conductor. Also, the effect of cable diameter on the temperature of cable core was studied. Numerical analyses were performed based on a program written in MATLAB.

Application of thermal scanning to the study of transverse mixing in rivers

NASA Technical Reports Server (NTRS)

Eheart, J. W.

1975-01-01

Remote sensing has shown itself to be a valuable research tool in the study of transverse mixing in rivers. It is desirable, for a number of reasons, to study and predict the two-dimensional movement of pollutants in the region just downstream of a pollutant discharge point. While many of the more common pollutants do not exhibit a spectral signature, it was shown that the temperature difference between the pollutant and the receiving water could be successfully exploited by applying a mathematical model of mass transport processes to heat transport, and testing and calibrating it with thermal scanning data.

Knot invariants and M-theory: Proofs and derivations

NASA Astrophysics Data System (ADS)

Errasti Díez, Verónica

2018-01-01

We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to K. Dasgupta, V. Errasti Díez, P. Ramadevi, and R. Tatar, Phys. Rev. D 95, 026010 (2017), 10.1103/PhysRevD.95.026010, covering all but Sec. III C. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in the first paper, but is self-contained and can be read independently.

Three-dimensional automatic computer-aided evaluation of pleural effusions on chest CT images

NASA Astrophysics Data System (ADS)

Bi, Mark; Summers, Ronald M.; Yao, Jianhua

2011-03-01

The ability to estimate the volume of pleural effusions is desirable as it can provide information about the severity of the condition and the need for thoracentesis. We present here an improved version of an automated program to measure the volume of pleural effusions using regular chest CT images. First, the lungs are segmented using region growing, mathematical morphology, and anatomical knowledge. The visceral and parietal layers of the pleura are then extracted based on anatomical landmarks, curve fitting and active contour models. The liver and compressed tissues are segmented out using thresholding. The pleural space is then fitted to a Bezier surface which is subsequently projected onto the individual two-dimensional slices. Finally, the volume of the pleural effusion is quantified. Our method was tested on 15 chest CT studies and validated against three separate manual tracings. The Dice coefficients were 0.74+/-0.07, 0.74+/-0.08, and 0.75+/-0.07 respectively, comparable to the variation between two different manual tracings.

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.

Direct integration of the inverse Radon equation for X-ray computed tomography.

PubMed

Libin, E E; Chakhlov, S V; Trinca, D

2016-11-22

A new mathematical appoach using the inverse Radon equation for restoration of images in problems of linear two-dimensional x-ray tomography is formulated. In this approach, Fourier transformation is not used, and it gives the chance to create the practical computing algorithms having more reliable mathematical substantiation. Results of software implementation show that for especially for low number of projections, the described approach performs better than standard X-ray tomographic reconstruction algorithms.

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Investigation of possible observable e ects in a proposed theory of physics

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

Freidan, Daniel

2015-03-31

The work supported by this grant produced rigorous mathematical results on what is possible in quantum field theory. Quantum field theory is the well-established mathematical language for fundamental particle physics, for critical phenomena in condensed matter physics, and for Physical Mathematics (the numerous branches of Mathematics that have benefitted from ideas, constructions, and conjectures imported from Theoretical Physics). Proving rigorous constraints on what is possible in quantum field theories thus guides the field, puts actual constraints on what is physically possible in physical or mathematical systems described by quantum field theories, and saves the community the effort of trying tomore » do what is proved impossible. Results were obtained in two dimensional qft (describing, e.g., quantum circuits) and in higher dimensional qft. Rigorous bounds were derived on basic quantities in 2d conformal field theories, i.e., in 2d critical phenomena. Conformal field theories are the basic objects in quantum field theory, the scale invariant theories describing renormalization group fixed points from which all qfts flow. The first known lower bounds on the 2d boundary entropy were found. This is the entropy- information content- in junctions in critical quantum circuits. For dimensions d > 2, a no-go theorem was proved on the possibilities of Cauchy fields, which are the analogs of the holomorphic fields in d = 2 dimensions, which have had enormously useful applications in Physics and Mathematics over the last four decades. This closed o the possibility of finding analogously rich theories in dimensions above 2. The work of two postdoctoral research fellows was partially supported by this grant. Both have gone on to tenure track positions.« less

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.

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.

Three-dimensional electrical impedance tomography: a topology optimization approach.

PubMed

Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

2008-02-01

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Computer-aided light sheet flow visualization using photogrammetry

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1994-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and a visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) results, was chosen to interactively display the reconstructed light sheet images with the numerical surface geometry for the model or aircraft under study. The photogrammetric reconstruction technique and the image processing and computer graphics techniques and equipment are described. Results of the computer-aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images with CFD solutions in the same graphics environment is also demonstrated.

Computer-Aided Light Sheet Flow Visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Computer-aided light sheet flow visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Early MIMD experience on the CRAY X-MP

NASA Astrophysics Data System (ADS)

Rhoades, Clifford E.; Stevens, K. G.

1985-07-01

This paper describes some early experience with converting four physics simulation programs to the CRAY X-MP, a current Multiple Instruction, Multiple Data (MIMD) computer consisting of two processors each with an architecture similar to that of the CRAY-1. As a multi-processor, the CRAY X-MP together with the high speed Solid-state Storage Device (SSD) in an ideal machine upon which to study MIMD algorithms for solving the equations of mathematical physics because it is fast enough to run real problems. The computer programs used in this study are all FORTRAN versions of original production codes. They range in sophistication from a one-dimensional numerical simulation of collisionless plasma to a two-dimensional hydrodynamics code with heat flow to a couple of three-dimensional fluid dynamics codes with varying degrees of viscous modeling. Early research with a dual processor configuration has shown speed-ups ranging from 1.55 to 1.98. It has been observed that a few simple extensions to FORTRAN allow a typical programmer to achieve a remarkable level of efficiency. These extensions involve the concept of memory local to a concurrent subprogram and memory common to all concurrent subprograms.

Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy.

PubMed

Foryś, U; Bodnar, M; Kogan, Y

2016-10-01

In the case of some specific cancers, immunotherapy is one of the possible treatments that can be considered. Our study is based on a mathematical model of patient-specific immunotherapy proposed in Kronik et al. (PLoS One 5(12):e15,482, 2010). This model was validated for clinical trials presented in Michael et al. (Clin Cancer Res 11(12):4469-4478, 2005). It consists of seven ordinary differential equations and its asymptotic dynamics can be described by some t-periodic one-dimensional dynamical system. In this paper we propose a generalised version of this t-periodic system and study the dynamics of the proposed model. We show that there are three possible types of the model behaviour: the solution either converges to zero, or diverges to infinity, or it is periodic. Moreover, the periodic solution is unique, and it divides the phase space into two sub-regions. The general results are applied to the PC specific case, which allow to derive conditions guaranteeing successful as well as unsuccessful treatment. The results indicate that a single vaccination is not sufficient to cure the cancer.

Analytical method for optimal source reduction with monitored natural attenuation in contaminated aquifers

USGS Publications Warehouse

Widdowson, M.A.; Chapelle, F.H.; Brauner, J.S.; ,

2003-01-01

A method is developed for optimizing monitored natural attenuation (MNA) and the reduction in the aqueous source zone concentration (??C) required to meet a site-specific regulatory target concentration. The mathematical model consists of two one-dimensional equations of mass balance for the aqueous phase contaminant, to coincide with up to two distinct zones of transformation, and appropriate boundary and intermediate conditions. The solution is written in terms of zone-dependent Peclet and Damko??hler numbers. The model is illustrated at a chlorinated solvent site where MNA was implemented following source treatment using in-situ chemical oxidation. The results demonstrate that by not taking into account a variable natural attenuation capacity (NAC), a lower target ??C is predicted, resulting in unnecessary source concentration reduction and cost with little benefit to achieving site-specific remediation goals.

Adaptive behaviour and multiple equilibrium states in a predator-prey model.

PubMed

Pimenov, Alexander; Kelly, Thomas C; Korobeinikov, Andrei; O'Callaghan, Michael J A; Rachinskii, Dmitrii

2015-05-01

There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. Phenomenological mathematical models which exhibit such properties can be constructed rather straightforwardly. For instance, for a predator-prey system this result can be achieved through the use of non-monotonic functional response for the predator. However, while formal formulation of such a model is not a problem, the biological justification for such functional responses and models is usually inconclusive. In this note, we explore a conjecture that a multitude of equilibrium states can be caused by an adaptation of animal behaviour to changes of environmental conditions. In order to verify this hypothesis, we consider a simple predator-prey model, which is a straightforward extension of the classic Lotka-Volterra predator-prey model. In this model, we made an intuitively transparent assumption that the prey can change a mode of behaviour in response to the pressure of predation, choosing either "safe" of "risky" (or "business as usual") behaviour. In order to avoid a situation where one of the modes gives an absolute advantage, we introduce the concept of the "cost of a policy" into the model. A simple conceptual two-dimensional predator-prey model, which is minimal with this property, and is not relying on odd functional responses, higher dimensionality or behaviour change for the predator, exhibits two stable co-existing equilibrium states with basins of attraction separated by a separatrix of a saddle point. Copyright © 2015 Elsevier Inc. All rights reserved.

Modelling the behaviour of additives in gun barrels

NASA Astrophysics Data System (ADS)

Rhodes, N.; Ludwig, J. C.

1986-01-01

A mathematical model which predicts the flow and heat transfer in a gun barrel is described. The model is transient, two-dimensional and equations are solved for velocities and enthalpies of a gas phase, which arises from the combustion of propellant and cartridge case, for particle additives which are released from the case; volume fractions of the gas and particles. Closure of the equations is obtained using a two-equation turbulence model. Preliminary calculations are described in which the proportions of particle additives in the cartridge case was altered. The model gives a good prediction of the ballistic performance and the gas to wall heat transfer. However, the expected magnitude of reduction in heat transfer when particles are present is not predicted. The predictions of gas flow invalidate some of the assumptions made regarding case and propellant behavior during combustion and further work is required to investigate these effects and other possible interactions, both chemical and physical, between gas and particles.

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...

Evaluating the morphological completeness of a training image.

PubMed

Gao, Mingliang; Teng, Qizhi; He, Xiaohai; Feng, Junxi; Han, Xue

2017-05-01

Understanding the three-dimensional (3D) stochastic structure of a porous medium is helpful for studying its physical properties. A 3D stochastic structure can be reconstructed from a two-dimensional (2D) training image (TI) using mathematical modeling. In order to predict what specific morphology belonging to a TI can be reconstructed at the 3D orthogonal slices by the method of 3D reconstruction, this paper begins by introducing the concept of orthogonal chords. After analyzing the relationship among TI morphology, orthogonal chords, and the 3D morphology of orthogonal slices, a theory for evaluating the morphological completeness of a TI is proposed for the cases of three orthogonal slices and of two orthogonal slices. The proposed theory is evaluated using four TIs of porous media that represent typical but distinct morphological types. The significance of this theoretical evaluation lies in two aspects: It allows special morphologies, for which the attributes of a TI can be reconstructed at a special orthogonal slice of a 3D structure, to be located and quantified, and it can guide the selection of an appropriate reconstruction method for a special TI.

Synthetic river valleys: Creating prescribed topography for form-process inquiry and river rehabilitation design

NASA Astrophysics Data System (ADS)

Brown, R. A.; Pasternack, G. B.; Wallender, W. W.

2014-06-01

The synthesis of artificial landforms is complementary to geomorphic analysis because it affords a reflection on both the characteristics and intrinsic formative processes of real world conditions. Moreover, the applied terminus of geomorphic theory is commonly manifested in the engineering and rehabilitation of riverine landforms where the goal is to create specific processes associated with specific morphology. To date, the synthesis of river topography has been explored outside of geomorphology through artistic renderings, computer science applications, and river rehabilitation design; while within geomorphology it has been explored using morphodynamic modeling, such as one-dimensional simulation of river reach profiles, two-dimensional simulation of river networks, and three-dimensional simulation of subreach scale river morphology. To date, no approach allows geomorphologists, engineers, or river rehabilitation practitioners to create landforms of prescribed conditions. In this paper a method for creating topography of synthetic river valleys is introduced that utilizes a theoretical framework that draws from fluvial geomorphology, computer science, and geometric modeling. Such a method would be valuable to geomorphologists in understanding form-process linkages as well as to engineers and river rehabilitation practitioners in developing design surfaces that can be rapidly iterated. The method introduced herein relies on the discretization of river valley topography into geometric elements associated with overlapping and orthogonal two-dimensional planes such as the planform, profile, and cross section that are represented by mathematical functions, termed geometric element equations. Topographic surfaces can be parameterized independently or dependently using a geomorphic covariance structure between the spatial series of geometric element equations. To illustrate the approach and overall model flexibility examples are provided that are associated with mountain, lowland, and hybrid synthetic river valleys. To conclude, recommended advances such as multithread channels are discussed along with potential applications.

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.

Microfluidic circuit analysis II: implications of ion conservation for microchannels connected in series.

PubMed

Biscombe, Christian J C; Davidson, Malcolm R; Harvie, Dalton J E

2012-01-01

A mathematical framework for analysing electrokinetic flow in microchannel networks is outlined. The model is based on conservation of volume and total charge at network junctions, but in contrast to earlier theories also incorporates conservation of ion charge there. The model is applied to mixed pressure-driven/electro-osmotic flows of binary electrolytes through homogeneous microchannels as well as a 4:1:4 contraction-expansion series network. Under conditions of specified volumetric flow rate and ion currents, non-linear steady-state phenomena may arise: when the direction of the net co-ion flux is opposite to the direction of the net volumetric flow, two different fully developed, steady-state flow solutions may be obtained. Model predictions are compared with two-dimensional computational fluid dynamics (CFD) simulations. For systems where two steady states are realisable, the ultimate steady behaviour is shown to depend in part upon the initial state of the system. Copyright © 2011 Elsevier Inc. All rights reserved.

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,…

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).

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

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.

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case

NASA Astrophysics Data System (ADS)

Michael, L.; Nikiforakis, N.

2018-02-01

This work is concerned with the effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The main objective is to understand the origin of localised temperature peaks (hot spots) which play a leading order role at the early stages of ignition. To this end, we perform two- and three-dimensional numerical simulations of shock-induced single gas-cavity collapse in liquid nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. In order to understand the relative contribution between these two processes, we consider in this first part of the work the evolution of the physical system in the absence of chemical reactions. We employ a multi-phase mathematical formulation which can account for the large density difference across the gas-liquid material interface without generating spurious temperature peaks. The mathematical and physical models are validated against experimental, analytic, and numerical data. Previous inert studies have identified the impact of the upwind (relative to the direction of the incident shock wave) side of the cavity wall to the downwind one as the main reason for the generation of a hot spot outside of the cavity, something which is also observed in this work. However, it is also apparent that the topology of the temperature field is more complex than previously thought and additional hot spot locations exist, which arise from the generation of Mach stems rather than jet impact. To explain the generation mechanisms and topology of the hot spots, we carefully follow the complex wave patterns generated in the collapse process and identify specifically the temperature elevation or reduction generated by each wave. This enables tracking each hot spot back to its origins. It is shown that the highest hot spot temperatures can be more than twice the post-incident shock temperature of the neat material and can thus lead to ignition. By comparing two-dimensional and three-dimensional simulation results in the context of the maximum temperature observed in the domain, it is apparent that three-dimensional calculations are necessary in order to avoid belated ignition times in reactive scenarios.

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.

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

Geodynamics for Everyone: Robust Finite-Difference Heat Transfer Models using MS Excel 2007 Spreadsheets

NASA Astrophysics Data System (ADS)

Grose, C. J.

2008-05-01

Numerical geodynamics models of heat transfer are typically thought of as specialized topics of research requiring knowledge of specialized modelling software, linux platforms, and state-of-the-art finite-element codes. I have implemented analytical and numerical finite-difference techniques with Microsoft Excel 2007 spreadsheets to solve for complex solid-earth heat transfer problems for use by students, teachers, and practicing scientists without specialty in geodynamics modelling techniques and applications. While implementation of equations for use in Excel spreadsheets is occasionally cumbersome, once case boundary structure and node equations are developed, spreadsheet manipulation becomes routine. Model experimentation by modifying parameter values, geometry, and grid resolution makes Excel a useful tool whether in the classroom at the undergraduate or graduate level or for more engaging student projects. Furthermore, the ability to incorporate complex geometries and heat-transfer characteristics makes it ideal for first and occasionally higher order geodynamics simulations to better understand and constrain the results of professional field research in a setting that does not require the constraints of state-of-the-art modelling codes. The straightforward expression and manipulation of model equations in excel can also serve as a medium to better understand the confusing notations of advanced mathematical problems. To illustrate the power and robustness of computation and visualization in spreadsheet models I focus primarily on one-dimensional analytical and two-dimensional numerical solutions to two case problems: (i) the cooling of oceanic lithosphere and (ii) temperatures within subducting slabs. Excel source documents will be made available.

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.

An investigation on a two-dimensional problem of Mode-I crack in a thermoelastic medium

NASA Astrophysics Data System (ADS)

Kant, Shashi; Gupta, Manushi; Shivay, Om Namha; Mukhopadhyay, Santwana

2018-04-01

In this work, we consider a two-dimensional dynamical problem of an infinite space with finite linear Mode-I crack and employ a recently proposed heat conduction model: an exact heat conduction with a single delay term. The thermoelastic medium is taken to be homogeneous and isotropic. However, the boundary of the crack is subjected to a prescribed temperature and stress distributions. The Fourier and Laplace transform techniques are used to solve the problem. Mathematical modeling of the present problem reduces the solution of the problem into the solution of a system of four dual integral equations. The solution of these equations is equivalent to the solution of the Fredholm's integral equation of the first kind which has been solved by using the regularization method. Inverse Laplace transform is carried out by using the Bellman method, and we obtain the numerical solution for all the physical field variables in the physical domain. Results are shown graphically, and we highlight the effects of the presence of crack in the behavior of thermoelastic interactions inside the medium in the present context, and its results are compared with the results of the thermoelasticity of type-III.

Advances in modeling the pressure correlation terms in the second moment equations

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Shabbir, Aamir; Lumley, John L.

1991-01-01

In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.

3-D characterization of weathered building limestones by high resolution synchrotron X-ray microtomography.

PubMed

Rozenbaum, O

2011-04-15

Understanding the weathering processes of building stones and more generally of their transfer properties requires detailed knowledge of the porosity characteristics. This study aims at analyzing three-dimensional images obtained by X-ray microtomography of building stones. In order to validate these new results a weathered limestone previously characterised (Rozenbaum et al., 2007) by two-dimensional image analysis was selected. The 3-D images were analysed by a set of mathematical tools that enable the description of the pore and solid phase distribution. Results show that 3-D image analysis is a powerful technique to characterise the morphological, structural and topological differences due to weathering. The paper also discusses criteria for mathematically determining whether a stone is weathered or not. Copyright © 2011 Elsevier B.V. All rights reserved.

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Faithfulness of Recurrence Plots: A Mathematical Proof

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; Komuro, Motomasa; Horai, Shunsuke; Aihara, Kazuyuki

It is practically known that a recurrence plot, a two-dimensional visualization of time series data, can contain almost all information related to the underlying dynamics except for its spatial scale because we can recover a rough shape for the original time series from the recurrence plot even if the original time series is multivariate. We here provide a mathematical proof that the metric defined by a recurrence plot [Hirata et al., 2008] is equivalent to the Euclidean metric under mild conditions.

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

Chaotic dynamics and thermodynamics of periodic systems with long-range forces

NASA Astrophysics Data System (ADS)

Kumar, Pankaj

Gravitational and electromagnetic interactions form the backbone of our theoretical understanding of the universe. While, in general, such interactions are analytically inexpressible for three-dimensional infinite systems, one-dimensional modeling allows one to treat the long-range forces exactly. Not only are one-dimensional systems of profound intrinsic interest, physicists often rely on one-dimensional models as a starting point in the analysis of their more complicated higher-dimensional counterparts. In the analysis of large systems considered in cosmology and plasma physics, periodic boundary conditions are a natural choice and have been utilized in the study of one dimensional Coulombic and gravitational systems. Such studies often employ numerical simulations to validate the theoretical predictions, and in cases where theoretical relations have not been mathematically formulated, numerical simulations serve as a powerful method in characterizing the system's physical properties. In this dissertation, analytic techniques are formulated to express the exact phase-space dynamics of spatially-periodic one-dimensional Coulombic and gravitational systems. Closed-form versions of the Hamiltonian and the electric field are derived for single-component and two-component Coulombic systems, placing the two on the same footing as the gravitational counterpart. Furthermore, it is demonstrated that a three-body variant of the spatially-periodic Coulombic or gravitational system may be reduced isomorphically to a periodic system of a single particle in a two-dimensional rhombic potential. The analytic results are utilized for developing and implementing efficient computational tools to study the dynamical and the thermodynamic properties of the systems without resorting to numerical approximations. Event-driven algorithms are devised to obtain Lyapunov spectra, radial distribution function, pressure, caloric curve, and Poincare surface of section through an N-body molecular-dynamics approach. The simulation results for the three-body systems show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. The results for the large versions of the single-component and two-component Coulombic systems show no clear-cut indication of a phase transition. However, as predicted by the theoretical treatment, the simulated temperature dependencies of energy, pressure as well as Lyapunov exponent for the gravitational system indicate a phase transition and the critical temperature obtained in simulation agrees well with that from the theory.

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, ...

Convective fluid flows in a horizontal channel with evaporation: analytical and experimental investigations

NASA Astrophysics Data System (ADS)

Lyulin, Y. V.; Rezanova, E. V.

2017-11-01

Heat- and mass transfer processes in a two-layer system of the liquid and gas are studied with respect to evaporation at interface. The stationary convective flows of two immiscible viscous incompressible fluids filling an infinite channel and being under action of the transverse gravitation field are studied analytically. Mathematical modeling of the flows is carried out with the help of the Navier-Stokes equations in Boussinesq approximation. The Dufour and Soret effects are taken into consideration in the gas-vapor phase. In the two-dimensional case the exact solutions of special type are constructed under condition of a given specific gas flow rate. Comparison of the analytical results with results of the physical experiments with the “liquid-gas” system like “ethanol-air” are presented.

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

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

Plechac, Petr; Vlachos, Dionisios G.

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems,more » etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.« less

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.

Technology Modeling by Mathematics Professors in Required Courses for Secondary Mathematics Pre-Service Teachers: A Case Study in Two Universities

ERIC Educational Resources Information Center

Asing-Cashman, Joyce G.

2011-01-01

The purpose of this qualitative case study was to examine the modeling of technology by mathematics professors in two universities in teaching required courses for secondary level pre-service mathematics teachers. Six professors participated in this case study. Their responses were documented in pre- and post-interviews and data were gathered from…

Simulation of action potential propagation in plants.

PubMed

Sukhov, Vladimir; Nerush, Vladimir; Orlova, Lyubov; Vodeneev, Vladimir

2011-12-21

Action potential is considered to be one of the primary responses of a plant to action of various environmental factors. Understanding plant action potential propagation mechanisms requires experimental investigation and simulation; however, a detailed mathematical model of plant electrical signal transmission is absent. Here, the mathematical model of action potential propagation in plants has been worked out. The model is a two-dimensional system of excitable cells; each of them is electrically coupled with four neighboring ones. Ion diffusion between excitable cell apoplast areas is also taken into account. The action potential generation in a single cell has been described on the basis of our previous model. The model simulates active and passive signal transmission well enough. It has been used to analyze theoretically the influence of cell to cell electrical conductivity and H(+)-ATPase activity on the signal transmission in plants. An increase in cell to cell electrical conductivity has been shown to stimulate an increase in the length constant, the action potential propagation velocity and the temperature threshold, while the membrane potential threshold being weakly changed. The growth of H(+)-ATPase activity has been found to induce the increase of temperature and membrane potential thresholds and the reduction of the length constant and the action potential propagation velocity. Copyright © 2011 Elsevier Ltd. All rights reserved.

On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1987-01-01

This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.

Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

NASA Astrophysics Data System (ADS)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

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 and includes the relationship with traditional point-vortex studies, 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. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Modeling glacial climates

NASA Technical Reports Server (NTRS)

North, G. R.; Crowley, T. J.

1984-01-01

Mathematical climate modelling has matured as a discipline to the point that it is useful in paleoclimatology. As an example a new two dimensional energy balance model is described and applied to several problems of current interest. The model includes the seasonal cycle and the detailed land-sea geographical distribution. By examining the changes in the seasonal cycle when external perturbations are forced upon the climate system it is possible to construct hypotheses about the origin of midlatitude ice sheets and polar ice caps. In particular the model predicts a rather sudden potential for glaciation over large areas when the Earth's orbital elements are only slightly altered. Similarly, the drift of continents or the change of atmospheric carbon dioxide over geological time induces radical changes in continental ice cover. With the advance of computer technology and improved understanding of the individual components of the climate system, these ideas will be tested in far more realistic models in the near future.

Conditional Covariance Theory and DETECT for Polytomous Items. Research Report. ETS RR-04-50

ERIC Educational Resources Information Center

Zhang, Jinming

2004-01-01

This paper extends the theory of conditional covariances to polytomous items. It has been mathematically proven that under some mild conditions, commonly assumed in the analysis of response data, the conditional covariance of two items, dichotomously or polytomously scored, is positive if the two items are dimensionally homogeneous and negative…

Embodied Semiotic Activities and Their Role in the Construction of Mathematical Meaning of Motion Graphs

ERIC Educational Resources Information Center

Botzer, Galit; Yerushalmy, Michal

2008-01-01

This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…

Structural analysis of online handwritten mathematical symbols based on support vector machines

NASA Astrophysics Data System (ADS)

Simistira, Foteini; Papavassiliou, Vassilis; Katsouros, Vassilis; Carayannis, George

2013-01-01

Mathematical expression recognition is still a very challenging task for the research community mainly because of the two-dimensional (2d) structure of mathematical expressions (MEs). In this paper, we present a novel approach for the structural analysis between two on-line handwritten mathematical symbols of a ME, based on spatial features of the symbols. We introduce six features to represent the spatial affinity of the symbols and compare two multi-class classification methods that employ support vector machines (SVMs): one based on the "one-against-one" technique and one based on the "one-against-all", in identifying the relation between a pair of symbols (i.e. subscript, numerator, etc). A dataset containing 1906 spatial relations derived from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 training dataset is constructed to evaluate the classifiers and compare them with the rule-based classifier of the ILSP-1 system participated in the contest. The experimental results give an overall mean error rate of 2.61% for the "one-against-one" SVM approach, 6.57% for the "one-against-all" SVM technique and 12.31% error rate for the ILSP-1 classifier.

The combined effects of longitudinal heat conduction, flow nonuniformity and temperature nonuniformity in crossflow plate-fin heat exchangers

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

Ranganayakulu, C.; Seetharamu, K.N.

An analysis of a crossflow plate-fin compact heat exchanger, accounting for the combined effects of two-dimensional longitudinal heat conduction through the exchanger wall and nonuniform inlet fluid flow and temperature distribution is carried out using a finite element method. A mathematical equation is developed to generate different types of fluid flow/temperature maldistribution models considering the possible deviations in fluid flow. Using these models, the exchanger effectiveness and its deterioration due to the combined effects of longitudinal heat conduction, flow nonuniformity and temperature nonuniformity are calculated for various design and operating conditions of the exchanger. It was found that the performancemore » variations are quite significant in some typical applications.« less

Electro-magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity

NASA Astrophysics Data System (ADS)

Ezzat, M. A.; El-Bary, A. A.

2018-01-01

A unified mathematical model of Green-Naghdi's thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

Mathematical modeling of damage in unidirectional composites

NASA Technical Reports Server (NTRS)

Goree, J. G.; Dharani, L. R.; Jones, W. F.

1983-01-01

Extending the work of Goree and Gross (1979), solutions are given for a two-dimensional region of unidirectional fibers embedded in an elastic matrix whose initial flaw may take the form of a transverse notch, a rectangular cutout, or a circular hole. Subsequent flaw-induced damage is generated by remote stresses acting parallel to the fibers. For the case of such ductile matrix composites as boron/aluminum, present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Little difference is found for the three types of initial damage considered. In all cases, the presence of additional damage changes the nature of stress distribution through the unbroken fibers.

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

NASA Technical Reports Server (NTRS)

Strelkov, S. A.; Sushkevich, T. A.

1983-01-01

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Spatial Localization in Dissipative Systems

NASA Astrophysics Data System (ADS)

Knobloch, E.

2015-03-01

Spatial localization is a common feature of physical systems, occurring in both conservative and dissipative systems. This article reviews the theoretical foundations of our understanding of spatial localization in forced dissipative systems, from both a mathematical point of view and a physics perspective. It explains the origin of the large multiplicity of simultaneously stable spatially localized states present in a parameter region called the pinning region and its relation to the notion of homoclinic snaking. The localized states are described as bound states of fronts, and the notions of front pinning, self-pinning, and depinning are emphasized. Both one-dimensional and two-dimensional systems are discussed, and the reasons behind the differences in behavior between dissipative systems with conserved and nonconserved dynamics are explained. The insights gained are specific to forced dissipative systems and are illustrated here using examples drawn from fluid mechanics (convection and shear flows) and a simple model of crystallization.

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.

Analysis of precision in chemical oscillators: implications for circadian clocks

NASA Astrophysics Data System (ADS)

d'Eysmond, Thomas; De Simone, Alessandro; Naef, Felix

2013-10-01

Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms.

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model.

PubMed

Bytchenkoff, Dimitri; Rodts, Stéphane

2011-01-01

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data. Copyright © 2010 Elsevier Inc. All rights reserved.

Hierarchical classification in high dimensional numerous class cases

NASA Technical Reports Server (NTRS)

Kim, Byungyong; Landgrebe, D. A.

1990-01-01

As progress in new sensor technology continues, increasingly high resolution imaging sensors are being developed. These sensors give more detailed and complex data for each picture element and greatly increase the dimensionality of data over past systems. Three methods for designing a decision tree classifier are discussed: a top down approach, a bottom up approach, and a hybrid approach. Three feature extraction techniques are implemented. Canonical and extended canonical techniques are mainly dependent upon the mean difference between two classes. An autocorrelation technique is dependent upon the correlation differences. The mathematical relationship between sample size, dimensionality, and risk value is derived.

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

Airflow and Particle Transport Through Human Airways: A Systematic Review

NASA Astrophysics Data System (ADS)

Kharat, S. B.; Deoghare, A. B.; Pandey, K. M.

2017-08-01

This paper describes review of the relevant literature about two phase analysis of air and particle flow through human airways. An emphasis of the review is placed on elaborating the steps involved in two phase analysis, which are Geometric modelling methods and Mathematical models. The first two parts describes various approaches that are followed for constructing an Airway model upon which analysis are conducted. Broad two categories of geometric modelling viz. Simplified modelling and Accurate modelling using medical scans are discussed briefly. Ease and limitations of simplified models, then examples of CT based models are discussed. In later part of the review different mathematical models implemented by researchers for analysis are briefed. Mathematical models used for Air and Particle phases are elaborated separately.

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

Dynamics from a mathematical model of a two-state gas laser

NASA Astrophysics Data System (ADS)

Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A.

2018-05-01

Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger's equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger's equation, with no evidence of shock formation or loss of regularity.

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

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

On the Mathematical Modeling of Single and Multiple Scattering of Ultrasonic Guided Waves by Small Scatterers: A Structural Health Monitoring Measurement Model

NASA Astrophysics Data System (ADS)

Strom, Brandon William

In an effort to assist in the paradigm shift from schedule based maintenance to conditioned based maintenance, we derive measurement models to be used within structural health monitoring algorithms. Our models are physics based, and use scattered Lamb waves to detect and quantify pitting corrosion. After covering the basics of Lamb waves and the reciprocity theorem, we develop a technique for the scattered wave solution. The first application is two-dimensional, and is employed in two different ways. The first approach integrates a traction distribution and replaces it by an equivalent force. The second approach is higher order and uses the actual traction distribution. We find that the equivalent force version of the solution technique holds well for small pits at low frequencies. The second application is three-dimensional. The equivalent force caused by the scattered wave of an arbitrary equivalent force is calculated. We obtain functions for the scattered wave displacements as a function of equivalent forces, equivalent forces as a function of incident wave, and scattered wave amplitudes as a function of incident amplitude. The third application uses self-consistency to derive governing equations for the scattered waves due to multiple corrosion pits. We decouple the implicit set of equations and solve explicitly by using a recursive series solution. Alternatively, we solve via an undetermined coefficient method which results in an interaction operator and solution via matrix inversion. The general solution is given for N pits including mode conversion. We show that the two approaches are equivalent, and give a solution for three pits. Various approximations are advanced to simplify the problem while retaining the leading order physics. As a final application, we use the multiple scattering model to investigate resonance of Lamb waves. We begin with a one-dimensional problem and progress to a three-dimensional problem. A directed graph enables interpretation of the interaction operator, and we show that a series solution converges due to loss of energy in the system. We see that there are four causes of resonance and plot the modulation depth as a function of spacing between the pits.

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

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models.

PubMed

Dagdeviren, Omur E

2018-08-03

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Experimental Study and a Mathematical Model of the Processes in Frozen Soil Under a Reservoir with a Hot Heat-Transfer Agent

NASA Astrophysics Data System (ADS)

Kislitsyn, A. A.; Shastunova, U. Yu.; Yanbikova, Yu. F.

2018-05-01

On an experimental setup, the authors have measured temperature fields in frozen soil during the filling of a reservoir with hot heat-transfer agent (oil), and also the change in the shape and position of the front of ice melting (isotherms T = 0°C) with time. The approximate solution of a two-dimensional Stefan problem on thawing of frozen soil has been given; it has been shown that satisfactory agreement with experimental results can only be obtained with account taken of the convective transfer of heat due to the water motion in the region of thawed soil.

Electron beam dispersion measurements in nitrogen using two-dimensional imaging of N2(+) fluorescence

NASA Technical Reports Server (NTRS)

Clapp, L. H.; Twiss, R. G.; Cattolica, R. J.

1991-01-01

Experimental results are presented related to the radial spread of fluorescence excited by 10 and 20 KeV electron beams passing through nonflowing rarefied nitrogen at 293 K. An imaging technique for obtaining species distributions from measured beam-excited fluorescence is described, based on a signal inversion scheme mathematically equivalent to the inversion of the Abel integral equation. From fluorescence image data, measurements of beam radius, integrated signal intensity, and spatially resolved distributions of N2(+) first-negative-band fluorescence-emitting species have been made. Data are compared with earlier measurements and with an heuristic beam spread model.

Experimental Study and a Mathematical Model of the Processes in Frozen Soil Under a Reservoir with a Hot Heat-Transfer Agent

NASA Astrophysics Data System (ADS)

Kislitsyn, A. A.; Shastunova, U. Yu.; Yanbikova, Yu. F.

2018-03-01

On an experimental setup, the authors have measured temperature fields in frozen soil during the filling of a reservoir with hot heat-transfer agent (oil), and also the change in the shape and position of the front of ice melting (isotherms T = 0°C) with time. The approximate solution of a two-dimensional Stefan problem on thawing of frozen soil has been given; it has been shown that satisfactory agreement with experimental results can only be obtained with account taken of the convective transfer of heat due to the water motion in the region of thawed soil.

Polar synthetic imaging

NASA Astrophysics Data System (ADS)

George, Jonathan K.

2013-05-01

In the search for low-cost wide spectrum imagers it may become necessary to sacrifice the expense of the focal plane array and revert to a scanning methodology. In many cases the sensor may be too unwieldy to physically scan and mirrors may have adverse effects on particular frequency bands. In these cases, photonic masks can be devised to modulate the incoming light field with a code over time. This is in essence code-division multiplexing of the light field into a lower dimension channel. In this paper a simple method for modulating the light field with masks of the Archimedes' spiral is presented and a mathematical model of the two-dimensional mask set is developed.

Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students' Mathematical Abilities

ERIC Educational Resources Information Center

An, Song; Capraro, Mary Margaret; Tillman, Daniel A.

2013-01-01

This article presents exploratory research investigating the way teachers integrate music into their regular mathematics lessons as well as the effects of music-mathematics interdisciplinary lessons on elementary school students' mathematical abilities of modeling, strategy and application. Two teachers and two classes of first grade and third…

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)

A network model for characterizing brine channels in sea ice

NASA Astrophysics Data System (ADS)

Lieblappen, Ross M.; Kumar, Deip D.; Pauls, Scott D.; Obbard, Rachel W.

2018-03-01

The brine pore space in sea ice can form complex connected structures whose geometry is critical in the governance of important physical transport processes between the ocean, sea ice, and surface. Recent advances in three-dimensional imaging using X-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.

Three-Dimensional Messages for Interstellar Communication

NASA Astrophysics Data System (ADS)

Vakoch, Douglas A.

One of the challenges facing independently evolved civilizations separated by interstellar distances is to communicate information unique to one civilization. One commonly proposed solution is to begin with two-dimensional pictorial representations of mathematical concepts and physical objects, in the hope that this will provide a foundation for overcoming linguistic barriers. However, significant aspects of such representations are highly conventional, and may not be readily intelligible to a civilization with different conventions. The process of teaching conventions of representation may be facilitated by the use of three-dimensional representations redundantly encoded in multiple formats (e.g., as both vectors and as rasters). After having illustrated specific conventions for representing mathematical objects in a three-dimensional space, this method can be used to describe a physical environment shared by transmitter and receiver: a three-dimensional space defined by the transmitter--receiver axis, and containing stars within that space. This method can be extended to show three-dimensional representations varying over time. Having clarified conventions for representing objects potentially familiar to both sender and receiver, novel objects can subsequently be depicted. This is illustrated through sequences showing interactions between human beings, which provide information about human behavior and personality. Extensions of this method may allow the communication of such culture-specific features as aesthetic judgments and religious beliefs. Limitations of this approach will be noted, with specific reference to ETI who are not primarily visual.

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.

Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model

NASA Astrophysics Data System (ADS)

Pathak, Jaideep; Wikner, Alexander; Fussell, Rebeckah; Chandra, Sarthak; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2018-04-01

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus, we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.

Assessment of Heterotrophic Growth Supported by Soluble Microbial Products in Anammox Biofilm using Multidimensional Modeling

PubMed Central

Liu, Yiwen; Sun, Jing; Peng, Lai; Wang, Dongbo; Dai, Xiaohu; Ni, Bing-Jie

2016-01-01

Anaerobic ammonium oxidation (anammox) is known to autotrophically convert ammonium to dinitrogen gas with nitrite as the electron acceptor, but little is known about their released microbial products and how these are relative to heterotrophic growth in anammox system. In this work, we applied a mathematical model to assess the heterotrophic growth supported by three key microbial products produced by bacteria in anammox biofilm (utilization associated products (UAP), biomass associated products (BAP), and decay released substrate). Both One-dimensional and two-dimensional numerical biofilm models were developed to describe the development of anammox biofilm as a function of the multiple bacteria–substrate interactions. Model simulations show that UAP of anammox is the main organic carbon source for heterotrophs. Heterotrophs are mainly dominant at the surface of the anammox biofilm with small fraction inside the biofilm. 1-D model is sufficient to describe the main substrate concentrations/fluxes within the anammox biofilm, while the 2-D model can give a more detailed biomass distribution. The heterotrophic growth on UAP is mainly present at the outside of anammox biofilm, their growth on BAP (HetB) are present throughout the biofilm, while the growth on decay released substrate (HetD) is mainly located in the inner layers of the biofilm. PMID:27273460

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.

A mathematical model for HIV and hepatitis C co-infection and its assessment from a statistical perspective.

PubMed

Castro Sanchez, Amparo Yovanna; Aerts, Marc; Shkedy, Ziv; Vickerman, Peter; Faggiano, Fabrizio; Salamina, Guiseppe; Hens, Niel

2013-03-01

The hepatitis C virus (HCV) and the human immunodeficiency virus (HIV) are a clear threat for public health, with high prevalences especially in high risk groups such as injecting drug users. People with HIV infection who are also infected by HCV suffer from a more rapid progression to HCV-related liver disease and have an increased risk for cirrhosis and liver cancer. Quantifying the impact of HIV and HCV co-infection is therefore of great importance. We propose a new joint mathematical model accounting for co-infection with the two viruses in the context of injecting drug users (IDUs). Statistical concepts and methods are used to assess the model from a statistical perspective, in order to get further insights in: (i) the comparison and selection of optional model components, (ii) the unknown values of the numerous model parameters, (iii) the parameters to which the model is most 'sensitive' and (iv) the combinations or patterns of values in the high-dimensional parameter space which are most supported by the data. Data from a longitudinal study of heroin users in Italy are used to illustrate the application of the proposed joint model and its statistical assessment. The parameters associated with contact rates (sharing syringes) and the transmission rates per syringe-sharing event are shown to play a major role. Copyright © 2013 Elsevier B.V. All rights reserved.

A gel as an array of channels.

PubMed

Zimm, B H

1996-06-01

We consider the theory of charged point molecules ('probes') being pulled by an electric field through a two-dimensional net of channels that represents a piece of gel. Associated with the position in the net is a free energy of interaction between the probe and the net; this free energy fluctuates randomly with the position of the probe in the net. The free energy is intended to represent weak interactions between the probe and the gel, such as entropy associated with the restriction of the freedom of motion of the probe by the gel, or electrostatic interactions between the probe and charges fixed to the gel. The free energy can be thought of as a surface with the appearance of a rough, hilly landscape spread over the net; the roughness is measured by the standard deviation of the free-energy distribution. Two variations of the model are examined: (1) the net is assumed to have all channels open, or (2) only channels parallel to the electric field are open and all the cross-connecting channels are closed. Model (1) is more realistic but presents a two-dimensional mathematical problem which can only be solved by slow iteration methods, while model (2) is less realistic but presents a one-dimensional problem that can be reduced to simple quadratures and is easy to solve by numerical integration. In both models the mobility of the probe decreases as the roughness parameter is increased, but the effect is larger in the less realistic model (2) if the same free-energy surface is used in both. The mobility in model (2) is reduced both by high points in the rough surface ('bumps') and by low points ('traps'), while in model (1) only the traps are effective, since the probes can flow around the bumps through the cross channels. The mobility in model (2) can be made to agree with model (1) simply by cutting off the bumps of the surface. Thus the simple model (2) can be used in place of the more realistic model (1) that is more difficult to compute.

Kinematics of swimming of the manta ray: three-dimensional analysis of open-water maneuverability.

PubMed

Fish, Frank E; Kolpas, Allison; Crossett, Andrew; Dudas, Michael A; Moored, Keith W; Bart-Smith, Hilary

2018-03-22

For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult, particularly in the field. To measure turning performance in a three-dimensional space for the manta ray ( Mobula birostris ), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65±16.66 deg s -1 and 2.05±1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies. © 2018. Published by The Company of Biologists Ltd.

Two-fluid models of turbulence

NASA Technical Reports Server (NTRS)

Spalding, D. B.

1985-01-01

The defects of turbulence models are summarized and the importance of so-called nongradient diffusion in turbulent fluxes is discussed. The mathematical theory of the flow of two interpenetrating continua is reviewed, and the mathematical formulation of the two fluid model is outlined. Results from plane wake, axisymmetric jet, and combustion studies are shown.

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.

"When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…

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.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

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.

The theory of n-scales

NASA Astrophysics Data System (ADS)

Dündar, Furkan Semih

2018-01-01

We provide a theory of n-scales previously called as n dimensional time scales. In previous approaches to the theory of time scales, multi-dimensional scales were taken as product space of two time scales [1, 2]. n-scales make the mathematical structure more flexible and appropriate to real world applications in physics and related fields. Here we define an n-scale as an arbitrary closed subset of ℝn. Modified forward and backward jump operators, Δ-derivatives and Δ-integrals on n-scales are defined.

A model for the kinetics of homotypic cellular aggregation under static conditions

NASA Technical Reports Server (NTRS)

Neelamegham, S.; Munn, L. L.; Zygourakis, K.; McIntire, L. V. (Principal Investigator)

1997-01-01

We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.

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.

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

NASA Astrophysics Data System (ADS)

F, M. Abbasi; M, Mustafa; S, A. Shehzad; M, S. Alhuthali; T, Hayat

2016-01-01

We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier’s law of heat conduction. Project supported by the Deanship of Scientific Research (DSR) King Abdulaziz University, Jeddah, Saudi Arabia (Grant No. 32-130-36-HiCi).

Water resources planning for rivers draining into mobile bay

NASA Technical Reports Server (NTRS)

Ng, S.; April, G. C.

1976-01-01

A hydrodynamic model describing water movement and tidal elevation is formulated, computed, and used to provide basic data about water quality in natural systems. The hydrodynamic model is based on two-dimensional, unsteady flow equations. The water mass is considered to be reasonably mixed such that integration (averaging) in the depth direction is a valid restriction. Convective acceleration, the Coriolis force, wind and bottom interactions are included as contributing terms in the momentum equations. The solution of the equations is applied to Mobile Bay, and used to investigate the influence that river discharge rate, wind direction and speed, and tidal condition have on water circulation and holdup within the bay. Storm surge conditions, oil spill transport, artificial island construction, dredging, and areas subject to flooding are other topics which could be investigated using the mathematical modeling approach.

Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.

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 Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

ERIC Educational Resources Information Center

Dalla Vecchia, Rodrigo

2015-01-01

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

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.

Supercritical wing sections 2, volume 108

NASA Technical Reports Server (NTRS)

Bauer, F.; Garabedian, P.; Korn, D.; Jameson, A.; Beckmann, M. (Editor); Kuenzi, H. P. (Editor)

1975-01-01

A mathematical theory for the design and analysis of supercritical wing sections was previously presented. Examples and computer programs showing how this method works were included. The work on transonics is presented in a more definitive form. For design, a better model of the trailing edge is introduced which should eliminate a loss of fifteen or twenty percent in lift experienced with previous heavily aft loaded models, which is attributed to boundary layer separation. How drag creep can be reduced at off-design conditions is indicated. A rotated finite difference scheme is presented that enables the application of Murman's method of analysis in more or less arbitrary curvilinear coordinate systems. This allows the use of supersonic as well as subsonic free stream Mach numbers and to capture shock waves as far back on an airfoil as desired. Moreover, it leads to an effective three dimensional program for the computation of transonic flow past an oblique wing. In the case of two dimensional flow, the method is extended to take into account the displacement thickness computed by a semi-empirical turbulent boundary layer correction.

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.

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.

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.

Teaching Polygons

ERIC Educational Resources Information Center

Scahill, Jillian

2006-01-01

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…

Designer: A Knowledge-Based Graphic Design Assistant.

ERIC Educational Resources Information Center

Weitzman, Louis

This report describes Designer, an interactive tool for assisting with the design of two-dimensional graphic interfaces for instructional systems. The system, which consists of a color graphics interface to a mathematical simulation, provides enhancements to the Graphics Editor component of Steamer (a computer-based training system designed to aid…

Harmonic oscillator states in aberration optics

NASA Technical Reports Server (NTRS)

Wolf, Kurt Bernardo

1993-01-01

The states of the three-dimensional quantum harmonic oscillator classify optical aberrations of axis-symmetric systems due to the isomorphism between the two mathematical structures. Cartesian quanta and angular momentum classifications have their corresponding aberration classifications. The operation of concatenation of optical elements introduces a new operation between harmonic oscillator states.

Using Two-Dimensional Colloidal Crystals to Understand Crystallography

ERIC Educational Resources Information Center

Bosse, Stephanie A.; Loening, Nikolaus M.

2008-01-01

X-ray crystallography is an essential technique for modern chemistry and biochemistry, but it is infrequently encountered by undergraduate students owing to lack of access to equipment, the time-scale for generating diffraction-quality molecular crystals, and the level of mathematics involved in analyzing the resulting diffraction patterns.…

Dimensionality of Upper Elementary Mathematics Instruction: Exploring Factors across Two Observational Instruments

ERIC Educational Resources Information Center

Blazar, David; Braslow, David; Charalambous, Charalambos Y.

2015-01-01

Over the past several years, research teams have developed observational instruments to measure the quality of teachers' instructional practices. Instruments such as Framework for Teaching (FFT) and the Classroom Assessment Scoring System (CLASS) assess general teaching practices, including student-teacher interactions, behavior management, and…

Fractional Quantization of the Hall Effect

DOE R&D Accomplishments Database

Laughlin, R. B.

1984-02-27

The Fractional Quantum Hall Effect is caused by the condensation of a two-dimensional electron gas in a strong magnetic field into a new type of macroscopic ground state, the elementary excitations of which are fermions of charge 1/m, where m is an odd integer. A mathematical description is presented.

Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.

Application of remote sensing to thermal pollution analysis. [satellite sea surface temperature measurement assessment

NASA Technical Reports Server (NTRS)

Hiser, H. W.; Lee, S. S.; Veziroglu, T. N.; Sengupta, S.

1975-01-01

A comprehensive numerical model development program for near-field thermal plume discharge and far field general circulation in coastal regions is being carried on at the University of Miami Clean Energy Research Institute. The objective of the program is to develop a generalized, three-dimensional, predictive model for thermal pollution studies. Two regions of specific application of the model are the power plants sites at the Biscayne Bay and Hutchinson Island area along the Florida coastline. Remote sensing from aircraft as well as satellites are used in parallel with in situ measurements to provide information needed for the development and verification of the mathematical model. This paper describes the efforts that have been made to identify problems and limitations of the presently available satellite data and to develop methods for enhancing and enlarging thermal infrared displays for mesoscale sea surface temperature measurements.

One-dimensional model for biogeochemical interactions and permeability reduction in soils during leachate permeation.

PubMed

Singhal, Naresh; Islam, Jahangir

2008-02-19

This paper uses the findings from a column study to develop a reactive model for exploring the interactions occurring in leachate-contaminated soils. The changes occurring in the concentrations of acetic acid, sulphate, suspended and attached biomass, Fe(II), Mn(II), calcium, carbonate ions, and pH in the column are assessed. The mathematical model considers geochemical equilibrium, kinetic biodegradation, precipitation-dissolution reactions, bacterial and substrate transport, and permeability reduction arising from bacterial growth and gas production. A two-step sequential operator splitting method is used to solve the coupled transport and biogeochemical reaction equations. The model gives satisfactory fits to experimental data and the simulations show that the transport of metals in soil is controlled by multiple competing biotic and abiotic reactions. These findings suggest that bioaccumulation and gas formation, compared to chemical precipitation, have a larger influence on hydraulic conductivity reduction.

[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.

Performance of a parallel code for the Euler equations on hypercube computers

NASA Technical Reports Server (NTRS)

Barszcz, Eric; Chan, Tony F.; Jesperson, Dennis C.; Tuminaro, Raymond S.

1990-01-01

The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.

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

A microfluidic chip containing multiple 3D nanofibrous scaffolds for culturing human pluripotent stem cells

NASA Astrophysics Data System (ADS)

Wertheim, Lior; Shapira, Assaf; Amir, Roey J.; Dvir, Tal

2018-04-01

In microfluidics-based lab-on-a-chip systems, which are used for investigating the effect of drugs and growth factors on cells, the latter are usually cultured within the device’s channels in two-dimensional, and not in their optimal three-dimensional (3D) microenvironment. Herein, we address this shortfall by designing a microfluidic system, comprised of two layers. The upper layer of the system consists of multiple channels generating a gradient of soluble factors. The lower layer is comprised of multiple wells, each deposited with 3D, nanofibrous scaffold. We first used a mathematical model to characterize the fluid flow within the system. We then show that induced pluripotent stem cells can be seeded within the 3D scaffolds and be exposed to a well-mixed gradient of soluble factors. We believe that utilizing such system may enable in the future to identify new differentiation factors, investigate drug toxicity, and eventually allow to perform analyses on patient-specific tissues, in order to fit the appropriate combination and concentration of drugs.

Theoretical study on the constricted flow phenomena in arteries

NASA Astrophysics Data System (ADS)

Sen, S.; Chakravarty, S.

2012-12-01

The present study is dealt with the constricted flow characteristics of blood in arteries by making use of an appropriate mathematical model. The constricted artery experiences the generated wall shear stress due to flow disturbances in the presence of constriction. The disturbed flow in the stenosed arterial segment causes malfunction of the cardiovascular system leading to serious health problems in the form of heart attack and stroke. The flowing blood contained in the stenosed artery is considered to be non-Newtonian while the flow is treated to be two-dimensional. The present pursuit also accounts for the motion of the arterial wall and its effect on local fluid mechanics. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for non-Newtonian fluid representing blood. An extensive quantitative analysis presented at the end of the paper based on large scale numerical computations of the quantities of major physiological significance enables one to estimate the constricted flow characteristics in the arterial system under consideration which deviates significantly from that of normal physiological flow conditions.

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.

Mathematical Modeling in the People's Republic of China--Indicators of Participation and Performance on COMAP's Modeling Contest

ERIC Educational Resources Information Center

Tian, Xiaoxi

2014-01-01

In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and…

Teachers as Managers of the Modelling Process

ERIC Educational Resources Information Center

Lingefjard, Thomas; Meier, Stephanie

2010-01-01

The work in the Comenius Network project Developing Quality in Mathematics Education II (DQME II) has a main focus on development and evaluation of modelling tasks. One reason is the gap between what mathematical modelling is and what is taught in mathematical classrooms. This article deals with one modelling task and focuses on how two teachers…

Mathematical modeling of fluxgate magnetic gradiometers

NASA Astrophysics Data System (ADS)

Milovzorov, D. G.; Yasoveev, V. Kh.

2017-07-01

Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

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

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Comparison of two-dimensional and quasi-one-dimensional scramjet models by the example of VAG experiment

NASA Astrophysics Data System (ADS)

Seleznev, R. K.

2017-02-01

In the paper two-dimensional and quasi-one dimensional models for scramjet combustion chamber are described. Comparison of the results of calculations for the two-dimensional and quasi-one dimensional code by the example of VAG experiment are presented.

D GIS for Flood Modelling in River Valleys

NASA Astrophysics Data System (ADS)

Tymkow, P.; Karpina, M.; Borkowski, A.

2016-06-01

The objective of this study is implementation of system architecture for collecting and analysing data as well as visualizing results for hydrodynamic modelling of flood flows in river valleys using remote sensing methods, tree-dimensional geometry of spatial objects and GPU multithread processing. The proposed solution includes: spatial data acquisition segment, data processing and transformation, mathematical modelling of flow phenomena and results visualization. Data acquisition segment was based on aerial laser scanning supplemented by images in visible range. Vector data creation was based on automatic and semiautomatic algorithms of DTM and 3D spatial features modelling. Algorithms for buildings and vegetation geometry modelling were proposed or adopted from literature. The implementation of the framework was designed as modular software using open specifications and partially reusing open source projects. The database structure for gathering and sharing vector data, including flood modelling results, was created using PostgreSQL. For the internal structure of feature classes of spatial objects in a database, the CityGML standard was used. For the hydrodynamic modelling the solutions of Navier-Stokes equations in two-dimensional version was implemented. Visualization of geospatial data and flow model results was transferred to the client side application. This gave the independence from server hardware platform. A real-world case in Poland, which is a part of Widawa River valley near Wroclaw city, was selected to demonstrate the applicability of proposed system.

Artificial neural network model for photosynthetic pigments identification using multi wavelength chromatographic data

NASA Astrophysics Data System (ADS)

Prilianti, K. R.; Hariyanto, S.; Natali, F. D. D.; Indriatmoko, Adhiwibawa, M. A. S.; Limantara, L.; Brotosudarmo, T. H. P.

2016-04-01

The development of rapid and automatic pigment characterization method become an important issue due to the fact that there are only less than 1% of plant pigments in the earth have been explored. In this research, a mathematical model based on artificial intelligence approach was developed to simplify and accelerate pigment characterization process from HPLC (high-performance liquid chromatography) procedure. HPLC is a widely used technique to separate and identify pigments in a mixture. Input of the model is chromatographic data from HPLC device and output of the model is a list of pigments which is the spectrum pattern is discovered in it. This model provides two dimensional (retention time and wavelength) fingerprints for pigment characterization which is proven to be more accurate than one dimensional fingerprint (fixed wavelength). Moreover, by mimicking interconnection of the neuron in the nervous systems of the human brain, the model have learning ability that could be replacing expert judgement on evaluating spectrum pattern. In the preprocessing step, principal component analysis (PCA) was used to reduce the huge dimension of the chromatographic data. The aim of this step is to simplify the model and accelerate the identification process. Six photosynthetic pigments i.e. zeaxantin, pheophytin a, α-carotene, β-carotene, lycopene and lutein could be well identified by the model with accuracy up to 85.33% and processing time less than 1 second.

Shadow-driven 4D haptic visualization.

PubMed

Zhang, Hui; Hanson, Andrew

2007-01-01

Just as we can work with two-dimensional floor plans to communicate 3D architectural design, we can exploit reduced-dimension shadows to manipulate the higher-dimensional objects generating the shadows. In particular, by taking advantage of physically reactive 3D shadow-space controllers, we can transform the task of interacting with 4D objects to a new level of physical reality. We begin with a teaching tool that uses 2D knot diagrams to manipulate the geometry of 3D mathematical knots via their projections; our unique 2D haptic interface allows the user to become familiar with sketching, editing, exploration, and manipulation of 3D knots rendered as projected imageson a 2D shadow space. By combining graphics and collision-sensing haptics, we can enhance the 2D shadow-driven editing protocol to successfully leverage 2D pen-and-paper or blackboard skills. Building on the reduced-dimension 2D editing tool for manipulating 3D shapes, we develop the natural analogy to produce a reduced-dimension 3D tool for manipulating 4D shapes. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the experience accessible to human beings. As far as we are aware, this paper reports the first interactive system with force-feedback that provides "4D haptic visualization" permitting the user to model and interact with 4D cloth-like objects.

Modeling of monolayer charge-stabilized colloidal crystals with static hexagonal crystal lattice

NASA Astrophysics Data System (ADS)

Nagatkin, A. N.; Dyshlovenko, P. E.

2018-01-01

The mathematical model of monolayer colloidal crystals of charged hard spheres in liquid electrolyte is proposed. The particles in the monolayer are arranged into the two-dimensional hexagonal crystal lattice. The model enables finding elastic constants of the crystals from the stress-strain dependencies. The model is based on the nonlinear Poisson-Boltzmann differential equation. The Poisson-Boltzmann equation is solved numerically by the finite element method for any spatial configuration. The model has five geometrical and electrical parameters. The model is used to study the crystal with particles comparable in size with the Debye length of the electrolyte. The first- and second-order elastic constants are found for a broad range of densities. The model crystal turns out to be stable relative to small uniform stretching and shearing. It is also demonstrated that the Cauchy relation is not fulfilled in the crystal. This means that the pair effective interaction of any kind is not sufficient to proper model the elasticity of colloids within the one-component approach.

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David

2000-01-01

Many microgravity space-science experiments require vibratory acceleration levels 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 (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. 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, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

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.

Modeling of leachate generation from MSW landfills by a 2-dimensional 2-domain approach

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

Fellner, Johann, E-mail: j.fellner@tuwien.ac.a; Brunner, Paul H., E-mail: paul.h.brunner@tuwien.ac.a

2010-11-15

The flow of water through Municipal Solid Waste (MSW) landfills is highly non-uniform and dominated by preferential pathways. Thus, concepts to simulate landfill behavior require that a heterogeneous flow regime is considered. Recent models are based on a 2-domain approach, differentiating between channel domain with high hydraulic conductivity, and matrix domain of slow water movement with high water retention capacity. These models focus on the mathematical description of rapid water flow in channel domain. The present paper highlights the importance of water exchange between the two domains, and expands the 1-dimensional, 2-domain flow model by taking into account water flowsmore » in two dimensions. A flow field consisting of a vertical path (channel domain) surrounded by the waste mass (matrix domain) is defined using the software HYDRUS-2D. When the new model is calibrated using data sets from a MSW-landfill site the predicted leachate generation corresponds well with the observed leachate discharge. An overall model efficiency in terms of r{sup 2} of 0.76 was determined for a simulation period of almost 4 years. The results confirm that water in landfills follows a preferential path way characterized by high permeability (K{sub s} = 300 m/d) and zero retention capacity, while the bulk of the landfill (matrix domain) is characterized by low permeability (K{sub s} = 0.1 m/d) and high retention capacity. The most sensitive parameters of the model are the hydraulic conductivities of the channel domain and the matrix domain, and the anisotropy of the matrix domain.« less

Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1982-01-01

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed 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 has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

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.

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%.