APROS 3-D core models for simulators and plant analyzers
International Nuclear Information System (INIS)
Puska, E.K.
1999-01-01
The 3-D core models of APROS simulation environment can be used in simulator and plant analyzer applications, as well as in safety analysis. The key feature of APROS models is that the same physical models can be used in all applications. For three-dimensional reactor cores the APROS models cover both quadratic BWR and PWR cores and the hexagonal lattice VVER-type cores. In APROS environment the user can select the number of flow channels in the core and either five- or six-equation thermal hydraulic model for these channels. The thermal hydraulic model and the channel description have a decisive effect on the calculation time of the 3-D core model and thus just these selection make at present the major difference between a safety analysis model and a training simulator model. The paper presents examples of various types of 3-D LWR-type core descriptions for simulator and plant analyzer use and discusses the differences of calculation speed and physical results between a typical safety analysis model description and a real-time simulator model description in transients. (author)
Modelling the horizontal steam generator with APROS
Energy Technology Data Exchange (ETDEWEB)
Ylijoki, J. [VTT Energy, Espoo (Finland); Palsinajaervi, C.; Porkholm, K. [IVO International Ltd, Vantaa (Finland)
1995-12-31
In this paper the capability of the five- and six-equation models of the simulation code APROS to simulate the behaviour of the horizontal steam generator is discussed. Different nodalizations are used in the modelling and the results of the stationary state runs are compared. Exactly the same nodalizations have been created for the five- and six-equation models. The main simulation results studied in this paper are void fraction and mass flow distributions in the secondary side of the steam generator. It was found that quite a large number of simulation volumes is required to simulate the distributions with a reasonable accuracy. The simulation results of the different models are presented and their validity is discussed. (orig.). 4 refs.
Modelling the horizontal steam generator with APROS
Energy Technology Data Exchange (ETDEWEB)
Ylijoki, J [VTT Energy, Espoo (Finland); Palsinajaervi, C; Porkholm, K [IVO International Ltd, Vantaa (Finland)
1996-12-31
In this paper the capability of the five- and six-equation models of the simulation code APROS to simulate the behaviour of the horizontal steam generator is discussed. Different nodalizations are used in the modelling and the results of the stationary state runs are compared. Exactly the same nodalizations have been created for the five- and six-equation models. The main simulation results studied in this paper are void fraction and mass flow distributions in the secondary side of the steam generator. It was found that quite a large number of simulation volumes is required to simulate the distributions with a reasonable accuracy. The simulation results of the different models are presented and their validity is discussed. (orig.). 4 refs.
Calculation of the 5th AER dynamic benchmark with APROS
International Nuclear Information System (INIS)
Puska, E.K.; Kontio, H.
1998-01-01
The model used for calculation of the 5th AER dynamic benchmark with APROS code is presented. In the calculation of the 5th AER dynamic benchmark the three-dimensional neutronics model of APROS was used. The core was divided axially into 20 nodes according to the specifications of the benchmark and each six identical fuel assemblies were placed into one one-dimensional thermal hydraulic channel. The five-equation thermal hydraulic model was used in the benchmark. The plant process and automation was described with a generic VVER-440 plant model created by IVO PE. (author)
Calculation of the fifth atomic energy research dynamic benchmark with APROS
International Nuclear Information System (INIS)
Puska Eija Karita; Kontio Harii
1998-01-01
The band-out presents the model used for calculation of the fifth atomic energy research dynamic benchmark with APROS code. In the calculation of the fifth atomic energy research dynamic benchmark the three-dimensional neutronics model of APROS was used. The core was divided axially into 20 nodes according to the specifications of the benchmark and each six identical fuel assemblies were placed into one one-dimensional thermal hydraulic channel. The five-equation thermal hydraulic model was used in the benchmark. The plant process and automation was described with a generic WWER-440 plant model created by IVO Power Engineering Ltd. - Finland. (Author)
Severe accident training simulator APROS SA
International Nuclear Information System (INIS)
Raiko, Eerikki; Salminen, Kai; Lundstroem, Petra; Harti, Mika; Routamo, Tomi
2003-01-01
APROS SA is a severe accident training simulator based on the APROS simulation environment. APROS SA has been developed in Fortum Nuclear Services Ltd to serve as a training tool for the personnel of the Loviisa NPP. Training with APROS SA gives the personnel a deeper understanding of the severe accident phenomena and thus it is an important part of the implementation of the severe accident management strategy. APROS SA consists of two parts, a comprehensive Loviisa plant model and an external severe accident model. The external model is an extension to the Loviisa plant model, which allows the simulation to proceed into the severe accident phase. The severe accident model has three submodels: the core melting and relocation model, corium pool model and fission product model. In addition to these, a new thermal-hydraulic solver is introduced to the core region of the Loviisa plant model to replace the more limited APROS thermal-hydraulic solver. The full APROS SA training simulator has a graphical user interface with visualizations of both severe accident management panels at the operator room and the important physical phenomena during the accident. This paper describes the background of the APROS SA training simulator, the severe accident submodels and the graphical user interface. A short description how APROS SA will be used as a training tool at the Loviisa NPP is also given
Evaluation of two-fluid and drift flux thermohydraulics in APROS code environment
International Nuclear Information System (INIS)
Miettinen, J.; Karppinen, I.; Haenninen, M.; Ylijoki, J.
1999-01-01
The characteristics of the thermohydraulic solutions in APROS are considered for the nuclear power plant modelling. The thermohydraulic model of the APROS plant analyzer includes three levels of solutions, homogeneous 3-equation model, 5-equation drift flux model and 6-equation two-fluid model. In practical modelling of versatile process systems different approaches are selected for different types of the power plant sections. The 3-equation model is used for turbines and auxiliary systems. The 5-equation model and 6-equation model are alternative models for main process sections of the primary and secondary sides. The 5-equation model has been typically selected for the real time applications and the 6-equation model for the safety analysis applications. The validation needs for both approaches are the same. Because the change of the solution mode is an easy task in APROS, the validation tasks are typically performed in parallel for 5-equation and 6-equation models. By calculating in parallel with both models systematic errors in solutions may be pointed out. The testing against both separate effects tests and integral tests is an essential part in the thermohydraulics. In different plant applications different physical features are important. The analysis requirements vary from one application to another. When nodalizations together with increased computer speed are growing up, the earlier validation cases may be insufficient. That is why the content of the code has to be known in detail. Such an expertise in the code development has to be gained that properties of the code against other thermohydraulics codes are known. (author)
APROS couplings from core to containment
International Nuclear Information System (INIS)
Puska, E.K.; Ylijoki, J.
2005-01-01
APROS simulation environment is able to describe the 1-D and 3-D neutronics of the reactor core. It is also able to describe the thermal hydraulics of the core and circuits either with 5- equation or 6-equation thermal hydraulics. It can also describe the plant automation and electrical systems, as well as the behaviour of the containment. The peculiar feature of APROS in comparison to other coupled systems is that all parts in the coupled system are described with the same code instead of coupling two or three separate codes together with information exchange between the separate codes. The most recent possibility is the coupled calculation of the process and the containment. The more traditional coupling, the coupling of the process containing both the process description and the automation description with more or less detailed description of the 3-D core either for safety analysis or real-time simulation purposes has been discussed in previous work. The paper presents and discusses the capabilities of the code in coupling the plant process and automation description with the plant containment description with two example transient cases. An improved boron concentration solution with second order upwind discretization has been recently included in APROS. An example on the increased accuracy acquired in the 3-D core model has been included. (authors)
APROS multifunctional simulator applications for VVER-440
International Nuclear Information System (INIS)
Porkholm, K.; Kantee, H.; Tiihonen, O.
2000-01-01
Fortum Engineering Ltd and the Technical Research Centre of Finland have developed APROS simulation software since 1986. APROS is a multifunctional simulator, which is used for process and automation design, safety analysis and training simulator applications. APROS has unique features and models developed especially for VVER-440 reactors. At first the paper gives a short overview of APROS multifunctional simulator. The rest of the paper deals with different kind of applications of APROS in VVER-440 reactors' improvement and operation development. (author)
Validation of new 3-D neutronics model in APROS for hexagonal geometry
International Nuclear Information System (INIS)
Rintala, J.
2010-01-01
APROS - Advanced PROcess Simulation environment-is a widely used simulation tool for nuclear power plant modelling. Earlier the three-dimensional neutronics calculation has been based on model using the difference method. The original three-dimensional core model is mainly used in power plant simulator applications, where it fits well because of its speed. For safety analysis purposes, however, a new model was considered to be an important improvement to meet the accuracy requirements. A sophisticated nodal model used already in HEXTRAN and TRAB-3D was decided to be implemented into APROS. The hexagonal part of the model has now been implemented and tested. For practical reasons, the model was programmed from scratch into APROS and also some small improvements were added and thus, an extensive validation program was necessary to prove the correct behaviour of the model. In this paper, the most important results from AER kinetic benchmarks 2 and 3 calculations are shown as well as the calculation results against data achieved LR-0 test reactor space-time kinetic experiments. Since the model is similar to the one in HEXTRAN, the results in benchmarks are compared to the results by it. In LR-0 calculations, results by both, original and new model are presented and compared to the measurements. The results shows that the implementation of the model has been successful and the new model improves the accuracy of three-dimensional neutronics calculation in APROS into the level required in safety analyses. (Author)
APROS - A multifunctional modelling environment
International Nuclear Information System (INIS)
Juslin, K.; Paljakka, M.
1999-01-01
The Advanced Process Simulation (APROS) environment has after more than a decade of dedicated product development and intense commercial use reached a level of maturity that is difficult to find with regard to similar products. One of the basic ideas behind this software tool is its multifunctional concept. The concept requires that the tool is suitable for modelling and simulation of the dynamics of a process plant during all phases of its life-span from pre-design to training and model supported operation and control. The implementation of this concept had a significant impact on the software structure. Several, sometimes contradictory requirements had to be encompassed. It should be suitable both for small simple models and full scope simulators. It should facilitate time-steps from milliseconds to minutes, for the same models, just depending on the scope of study. It should combine several modelling paradigms such as continuous, discrete, mechanistic and empirical. The intrinsic model building blocks should be comprehensively verified, but users' model equations should be accepted, as well. It should be easy to connect to external models or hardware, and to use both in master or slave mode. It should be easy to study and modify the internals of the models, their structures and parameters, but it should also be possible to disclose all delicate model information from unwanted access. The calculation should be optimised for current computer hardware, but the model specifications should be easily transportable to new platforms. And finally, it should be suited both for researchers, engineers and plant operators. How did we succeed? We had 20 years of comprehensive thermal hydraulic modelling tradition before starting the project. We had the key experts with the key knowledge. We dedicated more than 100 man years of efforts for the new software developments. Presently, we have a superb team maintaining and improving the software, complemented with new enthusiastic
Progress in implementation of the neutronics model of HEXTRAN into APROS
International Nuclear Information System (INIS)
Rintala, J.
2009-01-01
A new three-dimensional nodal model for neutronics calculation is currently under implementation into APROS - Advanced PROcess Simulation environment - to conform the increasing accuracy requirements. The new model is based on an advanced nodal code HEXTRAN and its static version HEXBU-3D by VTT, Technical Research Centre of Finland. However, several improvements for the model are made and the whole model has been reprogrammed. They don't change the theory basement of the method, but rather makes the implementation more flexible. Currently the computational part of the program is ready and current work concentrates on testing and validation. User interface details and usability issues need also work in the future. In this paper, general information about the improvements of the theory is explained first. Then the latest validation results are given. Currently the dynamical characteristics are tested by calculating the AER's kinetic benchmarks for VVER-440 reactors. In this paper, the results for the first benchmark are shown for two version of the code. The first version is fully HEXTRAN-comparable code to test that the basic structure works as wanted. The second version is the actual improved model for APROS. (author)
Progress in implementation of the neutronics model of HEXTRAN into APROS
International Nuclear Information System (INIS)
Jukka Rintala
2009-01-01
A new three-dimensional nodal model for neutronics calculation is currently under implementation into APROS - Advanced PROcess Simulation environment - to conform the increasing accuracy requirements. The new model is based on an advanced nodal code HEXTRAN and its static version HEXBU-3D by VTT, Technical Research Centre of Finland. However, several improvements for the model are made and the whole model has been reprogrammed. They don't change the theory basement of the method, but rather makes the implementation more flexible. Currently the computational part of the program is ready and current work concentrates on testing and validation. User interface details and usability issues need also work in the future. In this paper, general information about the improvements of the theory is explained first. Then the latest validation results are given. Currently the dynamical characteristics are tested by calculating the atomic energy research's kinetic benchmarks for WWER-440 reactors. In this paper, the results for the first benchmark are shown for two version of the code. The first version is fully HEXTRAN-comparable code to test that the basic structure works as wanted. The second version is the actual improved model for APROS. (Authors)
Implementation of the neutronics model of HEXTRAN/HEXBU-3D into APROS for WWER calculations
International Nuclear Information System (INIS)
Rintala, J.
2008-01-01
A new three-dimensional nodal model for neutronics calculation is currently under implementation into APROS - Advanced PROcess Simulation environment - to conform the increasing accuracy requirements. The new model is based on an advanced nodal code HEXTRAN and its static version HEXBU-3D by VTT, Technical Research Centre of Finland. Currently the new APROS is under a testing programme. Later a systematic validation will be performed. In the first phase, a goal is to obtain a fully validated model for VVER-440 calculations. Thus, all the current test calculations are performed by using Loviisa NPP's VVER-440 model of APROS. In future, the model is planned to be applied for the calculations of VVER-1000 type reactors as well as in rectangular fuel geometry. The paper outlines first the general aspects of the method, and then the current situation of the implementation. Because of the identical model with the models of HEXTRAN and HEXBU-3D, the results in the test calculations are compared to the results of those. In the paper, results of two static test calculations are shown. Currently the model works well already in static analyses. Only minor problems with the control assemblies of VVER-440 type reactor still exist but the reasons are known and will be corrected in near future. Dynamical characteristics of the model are up to now tested only by some empirical tests. (author)
Analysis of a small break loss-of-coolant accident of pressurized water reactor by APROS
Energy Technology Data Exchange (ETDEWEB)
Al-Falahi, A. [Helsinki Univ. of Technology, Espoo (Finland); Haennine, M. [VTT Energy, Espoo (Finland); Porkholm, K. [IVO International, Ltd., Vantaa (Finland)
1995-09-01
The purpose of this paper is to study the capability of APROS (Advanced PROcess Simulator) code to simulate the real plant thermal-hydraulic transient of a Small Break Loss-Of-Coolant Accident (SBLOCA) of Loss-Of-Fluid Test (LOFT) facility. The LOFT is a scaled model of a Pressurized Water Reactor (PWR). This work is a part of a larger validation of the APROS thermal-hydraulic models. The results of SBLOCA transient calculated by APROS showed a reasonable agreement with the measured data.
Nuclear reactor core modelling in multifunctional simulators
International Nuclear Information System (INIS)
Puska, E.K.
1999-01-01
The thesis concentrates on the development of nuclear reactor core models for the APROS multifunctional simulation environment and the use of the core models in various kinds of applications. The work was started in 1986 as a part of the development of the entire APROS simulation system. The aim was to create core models that would serve in a reliable manner in an interactive, modular and multifunctional simulator/plant analyser environment. One-dimensional and three-dimensional core neutronics models have been developed. Both models have two energy groups and six delayed neutron groups. The three-dimensional finite difference type core model is able to describe both BWR- and PWR-type cores with quadratic fuel assemblies and VVER-type cores with hexagonal fuel assemblies. The one- and three-dimensional core neutronics models can be connected with the homogeneous, the five-equation or the six-equation thermal hydraulic models of APROS. The key feature of APROS is that the same physical models can be used in various applications. The nuclear reactor core models of APROS have been built in such a manner that the same models can be used in simulator and plant analyser applications, as well as in safety analysis. In the APROS environment the user can select the number of flow channels in the three-dimensional reactor core and either the homogeneous, the five- or the six-equation thermal hydraulic model for these channels. The thermal hydraulic model and the number of flow channels have a decisive effect on the calculation time of the three-dimensional core model and thus, at present, these particular selections make the major difference between a safety analysis core model and a training simulator core model. The emphasis on this thesis is on the three-dimensional core model and its capability to analyse symmetric and asymmetric events in the core. The factors affecting the calculation times of various three-dimensional BWR, PWR and WWER-type APROS core models have been
Nuclear reactor core modelling in multifunctional simulators
Energy Technology Data Exchange (ETDEWEB)
Puska, E.K. [VTT Energy, Nuclear Energy, Espoo (Finland)
1999-06-01
The thesis concentrates on the development of nuclear reactor core models for the APROS multifunctional simulation environment and the use of the core models in various kinds of applications. The work was started in 1986 as a part of the development of the entire APROS simulation system. The aim was to create core models that would serve in a reliable manner in an interactive, modular and multifunctional simulator/plant analyser environment. One-dimensional and three-dimensional core neutronics models have been developed. Both models have two energy groups and six delayed neutron groups. The three-dimensional finite difference type core model is able to describe both BWR- and PWR-type cores with quadratic fuel assemblies and VVER-type cores with hexagonal fuel assemblies. The one- and three-dimensional core neutronics models can be connected with the homogeneous, the five-equation or the six-equation thermal hydraulic models of APROS. The key feature of APROS is that the same physical models can be used in various applications. The nuclear reactor core models of APROS have been built in such a manner that the same models can be used in simulator and plant analyser applications, as well as in safety analysis. In the APROS environment the user can select the number of flow channels in the three-dimensional reactor core and either the homogeneous, the five- or the six-equation thermal hydraulic model for these channels. The thermal hydraulic model and the number of flow channels have a decisive effect on the calculation time of the three-dimensional core model and thus, at present, these particular selections make the major difference between a safety analysis core model and a training simulator core model. The emphasis on this thesis is on the three-dimensional core model and its capability to analyse symmetric and asymmetric events in the core. The factors affecting the calculation times of various three-dimensional BWR, PWR and WWER-type APROS core models have been
Analyzing Program Termination and Complexity Automatically with AProVE
DEFF Research Database (Denmark)
Giesl, Jürgen; Aschermann, Cornelius; Brockschmidt, Marc
2017-01-01
In this system description, we present the tool AProVE for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and rewrite systems. In addition to classical term rewrite systems (TRSs), AProVE also supports rewrite systems containing built-in integers (int-TRSs). To analyze...... programs in high-level languages, AProVE automatically converts them to (int-)TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting rewrite systems. The generated proofs can be exported to check their correctness using automatic certifiers...
Design and analysis of nuclear processes with the APROS
International Nuclear Information System (INIS)
Haenninen, M.; Puska, E.K.; Nystroem, P.
1987-01-01
APROS (Advanced Process Simulator) is the product being developed in the process simulators project of Imatran Voima Co. and Technical Research Centre of Finland. The aim is to design and construct an efficient and easy to use computer simulation system for process and automation system design, evaluation, analysis, testing and training purposes. As halfway of this project a working system exists with a large number of proven routines and models. However, a lot of development is still foreseen before the project will be finished. This article gives an overview of the APROS in general and of the nuclear features in particular. The calculational capabilities of the system are presented with the help of one example. (orig.)
Capability of APROS in design and validation of I and C systems
International Nuclear Information System (INIS)
Kantee, H.; Porkholm, K.
2004-01-01
There are two WWER-440 type reactors in Loviisa. The first unit was commissioned in 1977 and the second in 1980. The availability of the plant as well as the operational experiences of the Instrumentation and control systems are good. However, it is obvious that the lifetime of the original I and C systems is not sufficient to guarantee the good availability of the plant in the future. Due to this fact a project for the renewal of the existing I and C systems has been started at Loviisa Nuclear Power Plant (NPP). In the project the analog I and C systems will be replaced with a digital I and C systems in four phases during from 2006-2014. Simulators will be utilized extensively in the project to assure that the renewal of I and C systems can be realized safely and economically. The engineering simulator will be used in the design and validation of the modernized I and C systems. The development simulator is aimed for the design, testing and acceptance of the new Man Machine Interface (MMI). The testing simulator will used for the testing of the new I and C systems and for retuning of the controllers mainly during the Factory Acceptance Tests. The training simulator will be used to familiarize the operators and other technical personnel to the operation of the new monitor-based control room facilities. APROS simulation software will be the main simulation tool in development and assessing of the new I and C configuration as well as in training of the plant personnel. First a brief description of the APROS code and APROS model of Loviisa plant including the model validation extent is discussed. Then the development and design of the new I and C system of Loviisa NPP is presented. As an example the application where trip of three reactor coolant pumps (RCP) assuming different failures during the transient is presented. An essential APROS feature in this study is the capability of the code to simulate the control rod movement. This feature is needed especially in WWER
International Nuclear Information System (INIS)
Henttonen, T.; Paananen, M.
2010-01-01
This paper presents a computer model and simulation results for a long-distance heat transport system. The system can be used e.g. to transport heat from a nuclear power plant with combined heat and power (CHP) production. CHP production is considered for new build NPP projects in Finland. Emphasis is on the environmental conditions during a hot water pipeline break in a service tunnel. The modelled pipeline system is designed to transport 1000 MW of heat over a distance of 77 km for district heating purposes. The hot water pipeline is assumed to be 1200 mm diameter with a water temperature of 120 deg. C. Cooled water returns with a temperature of 55 - 60 deg. C in a similar 1200 mm diameter pipe. Both pipelines are installed to a service tunnel which is excavated into bedrock and divided into 2 kilometres long compartments. Both the 77 km long pipeline and the tunnel are modelled with Apros simulation software. A leak is modelled from the pipeline to the tunnel and the results are analyzed. This paper includes three different leak sizes (1 %, 10 % and 100 % of the pipeline's cross-sectional area). The leaks are calculated with water temperatures of 95 deg. C and 120 deg. C in the pipeline. Apros calculates dynamically the phenomena inside the pipeline with two-phase 6-equation calculation model. The tunnel conditions are calculated with a lumped parameter model. The size of the leak has a substantial effect on the leak's consequences in the tunnel. Also the water temperature in the pipeline influences the results strongly. If the water temperature is over 100 deg. C, a considerable amount of the water boils as it leaks to the tunnel. The boiling of water makes the conditions in the tunnel much more severe than they would otherwise be. If there is a substantial flow out of the tunnel, the air in the tunnel can be replaced by hot steam. Obviously, this can mean hazardous conditions in the tunnel. (authors)
International Nuclear Information System (INIS)
Finch, P.E.; Dancer, K.A.; Isaac, P.S.; Links, J.
2011-01-01
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the two-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.
Properties of linear integral equations related to the six-vertex model with disorder parameter II
International Nuclear Information System (INIS)
Boos, Hermann; Göhmann, Frank
2012-01-01
We study certain functions arising in the context of the calculation of correlation functions of the XXZ spin chain and of integrable field theories related to various scaling limits of the underlying six-vertex model. We show that several of these functions that are related to linear integral equations can be obtained by acting with (deformed) difference operators on a master function Φ. The latter is defined in terms of a functional equation and of its asymptotic behavior. Concentrating on the so-called temperature case, we show that these conditions uniquely determine the high-temperature series expansions of the master function. This provides an efficient calculation scheme for the high-temperature expansions of the derived functions as well. (paper)
Simulation of Thermal Hydraulic at Supercritical Pressures with APROS
Energy Technology Data Exchange (ETDEWEB)
Kurki, Joona [VTT Technical Research Centre of Finland, P.O. Box 1000, FI02044 VTT (Finland)
2008-07-01
The proposed concepts for the fourth generation of nuclear reactors include a reactor operating with water at thermodynamically supercritical state, the Supercritical Water Reactor (SCWR). For the design and safety demonstrations of such a reactor, the possibility to accurately simulate the thermal hydraulics of the supercritical coolant is an absolute prerequisite. For this purpose, the one-dimensional two-phase thermal hydraulics solution of APROS process simulation software was developed to function at the supercritical pressure region. Software modifications included the redefinition of some parameters that have physical significance only at the subcritical pressures, improvement of the steam tables, and addition of heat transfer and friction correlations suitable for the supercritical pressure region. (author)
Six-Degree-of-Freedom Sensor Fish Design: Governing Equations and Motion Modeling
Energy Technology Data Exchange (ETDEWEB)
Deng, Zhiqun; Richmond, Marshall C.; Simmons, Carver S.; Carlson, Thomas J.
2004-08-19
The Sensor Fish device is being used at Northwest hydropower projects to better understand the conditions fish experience during passage through hydroturbines and other dam bypass alternatives. Since its initial development in 1997, the Sensor Fish has undergone numerous design changes to improve its function and extend the range of its use. The most recent Sensor Fish design, the three degree of freedom (3DOF) device, has been used successfully to characterize the environment fish experience when passing through turbines, in spill, or in engineered fish bypass facilities at dams. Pacific Northwest National Laboratory (PNNL) is in the process of redesigning the current 3DOF Sensor Fish device package to improve its field performance. Rate gyros will be added to the new six degree of freedom (6DOF) device so that it will be possible to observe the six linear and angular accelerations of the Sensor Fish as it passes the dam. Before the 6DOF Sensor Fish device can be developed and deployed, governing equations of motion must be developed in order to understand the design implications of instrument selection and placement within the body of the device. In this report, we describe a fairly general formulation for the coordinate systems, equations of motion, force and moment relationships necessary to simulate the 6DOF movement of an underwater body. Some simplifications are made by considering the Sensor Fish device to be a rigid, axisymmetric body. The equations of motion are written in the body-fixed frame of reference. Transformations between the body-fixed and interial reference frames are performed using a formulation based on quaternions. Force and moment relationships specific to the Sensor Fish body are currently not available. However, examples of the trajectory simulations using the 6DOF equations are presented using existing low and high-Reynolds number force and moment correlations. Animation files for the test cases are provided in an attached CD. The next
Six-degree-of-freedom Sensor Fish design - Governing equations and motion modeling
Energy Technology Data Exchange (ETDEWEB)
Zeng, D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Richmond, M. C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Simmons, C. S. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Carlson, T. J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2004-07-01
The Sensor Fish device is being used at Northwest hydropower projects to better understand the conditions fish experience during passage through hydro turbines and other dam bypass alternatives. Since its initial development in 1997, the Sensor Fish has undergone numerous design changes to improve its function and extend the range of its use. The most recent Sensor Fish design, the three degree of freedom (3DOF) device, has been used successfully to characterize the environment fish experience when passing through turbines, in spill, or in engineered fish bypass facilities at dams. Pacific Northwest National Laboratory (PNNL) is in the process of redesigning the current 3DOF Sensor Fish device package to improve its field performance. Rate gyros will be added to the new six degree of freedom (6DOF) device so that it will be possible to observe the six linear and angular accelerations of the Sensor Fish as it passes the dam. Before the 6DOF Sensor Fish device can be developed and deployed, governing equations of motion must be developed in order to understand the design implications of instrument selection and placement within the body of the device. The report describes a fairly general formulation for the coordinate systems, equations of motion, force and moment relationships necessary to simulate the 6DOF movement of an underwater body.
Energy Technology Data Exchange (ETDEWEB)
Virtanen, E.; Haapalehto, T. [Lappeenranta Univ. of Technology, Lappeenranta (Finland); Kouhia, J. [VTT Energy, Nuclear Energy, Lappeenranta (Finland)
1995-09-01
Three experiments were conducted to study the behavior of the new horizontal steam generator construction of the PACTEL test facility. In the experiments the secondary side coolant level was reduced stepwise. The experiments were calculated with two computer codes RELAP5/MOD3.1 and APROS version 2.11. A similar nodalization scheme was used for both codes to that the results may be compared. Only the steam generator was modelled and the rest of the facility was given as a boundary condition. The results show that both codes calculate well the behaviour of the primary side of the steam generator. On the secondary side both codes calculate lower steam temperatures in the upper part of the heat exchange tube bundle than was measured in the experiments.
International Nuclear Information System (INIS)
Virtanen, E.; Haapalehto, T.; Kouhia, J.
1997-01-01
Three experiments were conducted to study the behaviour of the new horizontal steam generator construction of the PACTEL test facility. In the experiments the secondary side coolant level was reduced stepwise. The experiments were calculated with two computer codes RELAP5/MOD3.1 and APROS version 2.11. A similar nodalization scheme was used for both codes so that the results may be compared. Only the steam generator was modeled and the rest of the facility was given as a boundary condition. The results show that both codes calculate well the behaviour of the primary side of the steam generator. On the secondary side both codes calculate lower steam temperatures in the upper part of the heat exchange tube bundle than was measured in the experiments. (orig.)
Electromagnetic-field equations in the six-dimensional space-time R6
International Nuclear Information System (INIS)
Teli, M.T.; Palaskar, D.
1984-01-01
Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts
The hyper-Kaehler supersymmetric sigma-model in six dimensions
International Nuclear Information System (INIS)
Sierra, G.; Townsend, P.K.
1983-01-01
The maximally supersymmetric, hyper-Kaehler, sigma-model is given in six-dimensional superfield form. The hyper-Kaehler condition follows from the requirements that the equations of motion be derivable from an action. (orig.)
Application of a Lorentz transformation in six dimensions to an extension of dirac equation
International Nuclear Information System (INIS)
Sabry, A.A.
2000-01-01
On applying a six dimensional Lorentz transformation (by adding three time components to the usual 3 space components) a covariant extended Dirac equation in this six dimensional space is suggested. From the free field solution of the extended equation we obtained four solutions for E , the first component of energy which depends on very big masses M and M 0 . The observed masses of the leptons and their corresponding neutrinos satisfying the same free field equation, can then be obtained on using second quantisation procedures on the field operators
Directory of Open Access Journals (Sweden)
A. Sakabekov
2016-01-01
Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.
Equations for predicting biomass of six introduced tree species, island of Hawaii
Thomas H. Schukrt; Robert F. Strand; Thomas G. Cole; Katharine E. McDuffie
1988-01-01
Regression equations to predict total and stem-only above-ground dry biomass for six species (Acacia melanoxylon, Albizio falcataria, Eucalyptus globulus, E. grandis, E. robusta, and E. urophylla) were developed by felling and measuring 2- to 6-year-old...
Lai, C M; Mak, K K; Watanabe, H; Jeong, J; Kim, D; Bahar, N; Ramos, M; Chen, S H; Cheng, C
2015-09-01
This study examines the associations of Internet addiction with social anxiety, depression, and psychosocial well-being among Asian adolescents. A self-medication model conceptualizing Internet addiction as a mediating role in relating depression and social anxiety to negative psychosocial well-being was tested. A cross-sectional survey. In the Asian Adolescent Risk Behavior Survey (AARBS), 5366 adolescents aged 12-18 years from six Asian countries (China, Hong Kong, Japan, South Korea, Malaysia, and Philippines) completed a questionnaire with items of the Internet Addiction Test (IAT), Social Anxiety Scale for Adolescents (SAS-A), Center for Epidemiological Studies Depression Scale (CESD), Self-Rated Health of the Nation Outcome Scales for Children and Adolescents (HoNOSCA-SR) in the 2012-2013 school year. Structural equation modelling was used to examine the mediating role of Internet addiction in depression, social anxiety, and subjective psychosocial well-being. Significant differences on the scores of IAT, SAS-A, CESD, and HoNOSCA-SR across the six countries were found. The proposed self-medication model of Internet addiction received satisfactory goodness-of-fit with data of all countries. After the path from social anxiety to Internet addiction had been discarded in the revised model, there was a significant improvement of the goodness-of-fit in the models for Japan, South Korea, and the Philippines. Depression and social anxiety reciprocally influenced, whereas depression associated with poorer psychosocial well-being directly and indirectly through Internet addiction in all six countries. Internet addiction mediated the association between social anxiety and poor psychosocial well-being in China, Hong Kong, and Malaysia. Copyright © 2015 The Royal Society for Public Health. Published by Elsevier Ltd. All rights reserved.
Equation of state for neutron matter in the Quark Compound Bag model
Krivoruchenko, M. I.
2017-11-01
The equation of state for neutron matter is derived in the framework of the Quark Compound Bag model, in which the nucleon-nucleon interaction is generated by the s-channel exchange of six-quark Jaffe-Low primitives.
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
Bleher, P M
2005-01-01
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...
Jenkins, Elizabeth E; Trott, Michael
2013-01-01
We calculate the order \\lambda, \\lambda^2 and \\lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \\lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.
A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study
International Nuclear Information System (INIS)
Angelo, P.M.; Riela, G.
1981-01-01
We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
The Schroedinger-Newton equation as model of self-gravitating quantum systems
International Nuclear Information System (INIS)
Grossardt, Andre
2013-01-01
The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem
Equation-of-State Modeling of Phase Equilibria in Petroleum Fluids
DEFF Research Database (Denmark)
Jørgensen, Marianne
1996-01-01
The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters. A comphr......The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters....... A comphrensive study of pseudoization procedures is presented. It is concluded that the compared methods exhibit results of comparable accuracy, and that six to eight pseudocomponents are needed for optimal representation of petroleum fluids.Finally, it is investigated how well the EOS can represent the VLLE...
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Consistent three-equation model for thin films
Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul
2017-11-01
Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.
Random matrices and the six-vertex model
Bleher, Pavel
2013-01-01
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wa...
Mathematical modeling and the two-phase constitutive equations
International Nuclear Information System (INIS)
Boure, J.A.
1975-01-01
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr
Nusdwinuringtyas, Nury; Widjajalaksmi; Yunus, Faisal; Alwi, Idrus
2014-04-01
to develop a reference equation for prediction of the total distance walk using Indonesian anthropometrics of sedentary healthy subjects. Subsequently, the prediction obtained was compared to those calculated by the Caucasian-based Enright prediction equation. the cross-sectional study was conducted among 123 healthy Indonesian adults with sedentary life style (58 male and 65 female subjects in an age range between 18 and 50 years). Heart rate was recorded using Polar with expectation in the sub-maximal zone (120-170 beats per minute). The subjects performed two six-minute walk tests, the first one on a 15-meter track according to the protocol developed by the investigator. The second walk was carried out on Biodex®gait trainer as gold standard. an average total distance of 547±54.24 m was found, not significantly different from the gold standard of 544.72±54.11 m (p>0.05). Multiple regression analysis was performed to develop the new equation. the reference equation for prediction of the total distance using Indonesian anthropometrics is more applicable in Indonesia.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Six Sigma Driven Enterprise Model Transformation
Directory of Open Access Journals (Sweden)
Raymond Vella
2009-10-01
Full Text Available Enterprise architecture methods provide a structured system to understand enterprise activities. However, existing enterprise modelling methodologies take static views of the enterprise and do not naturally lead to a path of improvement during enterprise model transformation. This paper discusses the need for a methodology to facilitate changes for improvement in an enterprise. The six sigma methodology is proposed as the tool to facilitate progressive and continual Enterprise Model Transformation to allow businesses to adapt to meet increased customer expectation and global competition. An alignment of six sigma with phases of GERAM life cycle is described with inclusion of Critical-To-Satisfaction (CTS requirements. The synergies of combining the two methodologies are presented in an effort to provide a more culturally embedded framework for Enterprise Model Transformation that builds on the success of six sigma.
Differential Equations Models to Study Quorum Sensing.
Pérez-Velázquez, Judith; Hense, Burkhard A
2018-01-01
Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.
Structural equation modeling methods and applications
Wang, Jichuan
2012-01-01
A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a
Mazaheri, Mehrdad; Theuns, Peter
2009-01-01
The current study evaluates three hypothesized models on subjective well-being, comprising life domain ratings (LDR), overall satisfaction with life (OSWL), and overall dissatisfaction with life (ODWL), using structural equation modeling (SEM). A sample of 1,310 volunteering students, randomly assigned to six conditions, rated their overall life…
Development of a system dynamics model based on Six Sigma methodology
Directory of Open Access Journals (Sweden)
José Jovani Cardiel Ortega
2017-01-01
Full Text Available A dynamic model to analyze the complexity associated with the manufacturing systems and to improve the performance of the process through the Six Sigma philosophy is proposed. The research focuses on the implementation of the system dynamics tool to comply with each of the phases of the DMAIC methodology. In the first phase, define, the problem is articulated, collecting data, selecting the variables, and representing them in a mental map that helps build the dynamic hypothesis. In the second phase, measure, model is formulated, equations are developed, and Forrester diagram is developed to carry out the simulation. In the third phase, analyze, the simulation results are studied. For the fourth phase, improving, the model is validated through a sensitivity analysis. Finally, in control phase, operation policies are proposed. This paper presents the development of a dynamic model of the system of knitted textile production knitted developed; the implementation was done in a textile company in southern Guanajuato. The results show an improvement in the process performance by increasing the level of sigma allowing the validation of the proposed approach.
Meta-analysis a structural equation modeling approach
Cheung, Mike W-L
2015-01-01
Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo
Energy Technology Data Exchange (ETDEWEB)
Gregoire, O
2008-07-01
In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)
Dietzel, Anne; Rahn, Eric; Stamm, Christian
2014-05-01
Swiss agriculture is legally committed to fulfill several, partially conflicting goals such as agricultural production on the one hand and the conservation of natural resources on the other hand. In the context of the research project AProWa ("Agricultural Production and Water"), the relationships between the production aspect and the conservation of aquatic ecosystems is analyzed with a holistic approach. Agricultural production and the protection of water resources have high potential for conflicts: Farmers use ground and surface water to irrigate their fields. On the other hand, drainage systems enable the production on otherwise unfavorably wet soils. These in turn often affect ground water recharge and divert precipitation directly into surface waters, which changes their hydrological regime. Typically, drainage systems also elevate the input of nutrients and pesticides into the water bodies. In general, applied fertilizers, plant protection products, veterinary drugs and phytohormones of cultivated plants are introduced into the ground and surface waters through different processes such as drift, leaching, runoff, preferential flow or erosion. They influence the nutrient cycles and ecological health of aquatic systems. The nutrient and pesticide loss processes themselves can be altered by tillage operations and other agricultural practices. Furthermore, the competition for space can lead to additional conflicts between agriculture and the protection of aquatic ecosystems. For example, channelized or otherwise morphologically changed rivers do not have a natural discharge pattern and are often not suitable for the local flora and fauna; but naturally meandering rivers need space that cannot be used for agriculture. In a highly industrialized and densely populated country like Switzerland, all these potential conflicts are of importance. Although it is typically seen as a water-rich country, local and seasonal overexploitation of rivers through water extraction
Hong, Sehee; Kim, Soyoung
2018-01-01
There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.
A first course in structural equation modeling
Raykov, Tenko
2012-01-01
In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation
Directory of Open Access Journals (Sweden)
Huei Chu Weng
2013-09-01
Full Text Available Despite a long research history, theoretical predictions for the material properties as well as the flow fields and characteristics of magnetic fluids were not well consistent with the experimental data. The lack of a universally accepted magnetization equation for accurately modeling hydrodynamics of magnetic fluids/nanofluids is particularly a major issue. In this paper, we give an overview on the continuum theory and test the six well-known models via comparisons with magnetoviscosity measurements to make clear the magnetization relaxation due to the rotation of magnetic particles and see how well they make predictions on the basis of numerical calculations. Results reveal that the ML model leads to unexplainable behavior. Moreover, the WC model with a ‘relaxation rate’ modification is found to reproduce the predictions of the MRSh model, which agree well with experimental data. The revised WC model (WCC should therefore be preferred.
Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling
Hesan, R.; Ghorbani, A.; Dignum, M.V.
2014-01-01
In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we
About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models
De La Sen, M.
2008-01-01
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called ...
Cheung, Mike W.-L.; Cheung, Shu Fai
2016-01-01
Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…
Macroscopic balance equations for two-phase flow models
International Nuclear Information System (INIS)
Hughes, E.D.
1979-01-01
The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)
Introduction to computation and modeling for differential equations
Edsberg, Lennart
2008-01-01
An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h
Differential equation models for sharp threshold dynamics.
Schramm, Harrison C; Dimitrov, Nedialko B
2014-01-01
We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.
Fitting ARMA Time Series by Structural Equation Models.
van Buuren, Stef
1997-01-01
This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)
The reservoir model: a differential equation model of psychological regulation.
Deboeck, Pascal R; Bergeman, C S
2013-06-01
Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).
Six-vertex model and Schramm-Loewner evolution
Kenyon, Richard; Miller, Jason; Sheffield, Scott; Wilson, David B.
2017-05-01
Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SL E κ, Schramm-Loewner evolution with parameter κ , where 4 <κ ≤12 +8 √{2 } . For square ice, κ =12 . At the "free-fermion point" of the six-vertex model, κ =8 +4 √{3 } . These unusual values lie outside the classical interval 2 ≤κ ≤8 .
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...
Partial Differential Equations Modeling and Numerical Simulation
Glowinski, Roland
2008-01-01
This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...
A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID
Energy Technology Data Exchange (ETDEWEB)
Feng, Xueshang; Zhang, Man; Zhou, Yufen, E-mail: fengx@spaceweather.ac.cn [SIGMA Weather Group, State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)
2014-09-01
In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.
DEFF Research Database (Denmark)
Andersen, Henrik; Ritter, Thomas
Ever seen a growth strategies fail because it was not connect ed to the firm’s customer base? Or a customer relationship strategy falters just because it was the wrong thing to do with that given customer? This article presents the six pack model, a tool that makes growth profitable and predictable....... Not all customers can and should grow – thus a firm needs to classify its customers in order to implement the right customer strategy....
Study of a Model Equation in Detonation Theory
Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.
2014-01-01
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation
Generalized latent variable modeling multilevel, longitudinal, and structural equation models
Skrondal, Anders; Rabe-Hesketh, Sophia
2004-01-01
This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.
Nurfaizal, Yusmedi
2015-01-01
Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...
A discrete model of a modified Burgers' partial differential equation
Mickens, R. E.; Shoosmith, J. N.
1990-01-01
A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Directory of Open Access Journals (Sweden)
Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
Lattice Boltzmann model for high-order nonlinear partial differential equations.
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Lattice Boltzmann model for high-order nonlinear partial differential equations
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Dynamic data analysis modeling data with differential equations
Ramsay, James
2017-01-01
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Directory of Open Access Journals (Sweden)
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
Energy Technology Data Exchange (ETDEWEB)
Smith, H.L. (Arizona State Univ., Tempe (United States))
1993-01-01
It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Energy Technology Data Exchange (ETDEWEB)
Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
The dispersionless Lax equations and topological minimal models
International Nuclear Information System (INIS)
Krichever, I.
1992-01-01
It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)
International Nuclear Information System (INIS)
Sanchez-Castro, C.R.
1988-01-01
This dissertation is divided in six chapters. Chapter 1 is an introduction to the rest of the dissertation. In it, the author presents the different models for the magnetic equation state of liquid 3 He, a derivation of the induced interaction equations for a one component Fermi liquid, and discuss the basic hamiltonian describing the heavy fermion compounds. In Chapter 2 and Chapter 3, he presents a complete discussion of the thermodynamics and Landau theory of a spin polarized Fermi liquid. A phenomenological model is then developed to predict the polarization dependence of the longitudinal Landau parameters in liquid 3 He. This model predicts a new magnetic equation of state and the possibility of liquid 3 He being 'nearly metamagnetic' at high pressures. Chapter 4 contains a microscopic calculation of the magnetic field dependence of the Landau parameters in a strongly correlated Fermi system using the induced interaction model. The system he studied consists of a single component Fermi liquid with parabolic energy bands, and a large on-site repulsive interaction. In Chapter 5, he presents a complete discussion of the Landau theory of a two component Fermi liquid. Then, he generalizes the induced interaction equations to calculate Landau parameters and scattering amplitudes for an arbitrary, spin polarized, two component Fermi liquid. The resulting equations are used to study a model for the heavy fermion Fermi liquid state: a two band electronic system with an antiferromagnetic interaction between the two bands. Chapter 6 contains the concluding remarks of the dissertation
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
Bogomolny equations in certain generalized baby BPS Skyrme models
Stępień, Ł. T.
2018-01-01
By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi-Prasad-Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model: the nonminimal coupling to the gauge field and the k-deformed ungauged model. In particular, we study how the Bogomolny equations and the equation for the potential reflect these two modifications. In both examples, the CSNC method appears to be a very useful tool. We also find certain localized solutions of these Bogomolny equations.
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Korff, C
2003-01-01
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U sub q (s-tilde l-tilde sub 2) at q sup N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra pa...
Multi-Agent Modeling in Managing Six Sigma Projects
Directory of Open Access Journals (Sweden)
K. Y. Chau
2009-10-01
Full Text Available In this paper, a multi-agent model is proposed for considering the human resources factor in decision making in relation to the six sigma project. The proposed multi-agent system is expected to increase the acccuracy of project prioritization and to stabilize the human resources service level. A simulation of the proposed multiagent model is conducted. The results show that a multi-agent model which takes into consideration human resources when making decisions about project selection and project team formation is important in enabling efficient and effective project management. The multi-agent modeling approach provides an alternative approach for improving communication and the autonomy of six sigma projects in business organizations.
Revised predictive equations for salt intrusion modelling in estuaries
Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.
2015-01-01
For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Multiplicity Control in Structural Equation Modeling
Cribbie, Robert A.
2007-01-01
Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…
Parameter Estimates in Differential Equation Models for Chemical Kinetics
Winkel, Brian
2011-01-01
We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…
Structural Equation Modeling of Multivariate Time Series
du Toit, Stephen H. C.; Browne, Michael W.
2007-01-01
The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…
Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory
CERN. Geneva
2015-01-01
The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.
Non-Equilibrium Turbulence and Two-Equation Modeling
Rubinstein, Robert
2011-01-01
Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.
Eight equation model for arbitrary shaped pipe conveying fluid
International Nuclear Information System (INIS)
Gale, J.; Tiselj, I.
2006-01-01
Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models
Directory of Open Access Journals (Sweden)
M. De La Sen
2008-01-01
Full Text Available This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability, the degree of sympathy of the species with the habitat (described by a so-called environment carrying capacity, a penalty term to deal with overpopulation levels, the harvesting (fishing or hunting regulatory quota, or related to use of pesticides when fighting damaging plagues, and the independent consumption which basically quantifies predation. The independent consumption is considered as a part of a more general additive disturbance which also potentially includes another extra additive disturbance term which might be attributed to net migration from or to the habitat or modeling measuring errors. Both potential contributions are included for generalization purposes in the proposed modified generalized Beverton-Holt equation. The properties of stability and boundedness of the solution sequences, equilibrium points of the stationary model, and the existence of oscillatory solution sequences are investigated. A numerical example for a population of aphids is investigated with the theoretical tools developed in the paper.
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Relations between the kinetic equation and the Langevin models in two-phase flow modelling
International Nuclear Information System (INIS)
Minier, J.P.; Pozorski, J.
1997-05-01
The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)
Stochastic higher spin six vertex model and Macdonald measures
Borodin, Alexei
2018-02-01
We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.
International Nuclear Information System (INIS)
Esmail, S.F.H.
2006-01-01
the mathematical formulation of numerous physical problems results in differential equations actually non-linear differential equations . in our study we are interested in solutions of differential equations which describe the structure of neutron star in non-relativistic and relativistic cases. the aim of this work is to determine the mass and the radius of a neutron star, by solving the tolmann-oppenheimer-volkoff (TOV) differential equation using different models of the nuclear equation of state (EOS). analytically solutions are obtained for a simple form of the nuclear equation of state of Clayton model and poly trope model. for a more realistic equation of state the TOV differential equation is solved numerically using rung -Kutta method
Factors influencing creep model equation selection
International Nuclear Information System (INIS)
Holdsworth, S.R.; Askins, M.; Baker, A.; Gariboldi, E.; Holmstroem, S.; Klenk, A.; Ringel, M.; Merckling, G.; Sandstrom, R.; Schwienheer, M.; Spigarelli, S.
2008-01-01
During the course of the EU-funded Advanced-Creep Thematic Network, ECCC-WG1 reviewed the applicability and effectiveness of a range of model equations to represent the accumulation of creep strain in various engineering alloys. In addition to considering the experience of network members, the ability of several models to describe the deformation characteristics of large single and multi-cast collations of ε(t,T,σ) creep curves have been evaluated in an intensive assessment inter-comparison activity involving three steels, 21/4 CrMo (P22), 9CrMoVNb (Steel-91) and 18Cr13NiMo (Type-316). The choice of the most appropriate creep model equation for a given application depends not only on the high-temperature deformation characteristics of the material under consideration, but also on the characteristics of the dataset, the number of casts for which creep curves are available and on the strain regime for which an analytical representation is required. The paper focuses on the factors which can influence creep model selection and model-fitting approach for multi-source, multi-cast datasets
Nonlinear integral equations for the sausage model
Ahn, Changrim; Balog, Janos; Ravanini, Francesco
2017-08-01
The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.
On the Use of Structural Equation Models in Marketing Modeling
Steenkamp, J.E.B.M.; Baumgartner, H.
2000-01-01
We reflect on the role of structural equation modeling (SEM) in marketing modeling and managerial decision making. We discuss some benefits provided by SEM and alert marketing modelers to several recent developments in SEM in three areas: measurement analysis, analysis of cross-sectional data, and
Is the Langevin phase equation an efficient model for oscillating neurons?
Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru
2009-12-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Is the Langevin phase equation an efficient model for oscillating neurons?
International Nuclear Information System (INIS)
Ota, Keisuke; Tsunoda, Takamasa; Aonishi, Toru; Omori, Toshiaki; Okada, Masato; Watanabe, Shigeo; Miyakawa, Hiroyoshi
2009-01-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Pepe, Daniele; Do, Jin Hwan
2015-12-16
Increasing evidence indicates that different morphological types of cell death coexist in the brain of patients with Parkinson's disease (PD), but the molecular explanation for this is still under investigation. In this study, we identified perturbed pathways in two different cell models for PD through the following procedures: (1) enrichment pathway analysis with differentially expressed genes and the Reactome pathway database, and (2) construction of the shortest path model for the enriched pathway and detection of significant shortest path model with fitting time-course microarray data of each PD cell model to structural equation model. Two PD cell models constructed by the same neurotoxin showed different perturbed pathways. That is, one showed perturbation of three Reactome pathways, including cellular senescence, chromatin modifying enzymes, and chromatin organization, while six modules within metabolism pathway represented perturbation in the other. This suggests that the activation of common upstream cell death pathways in PD may result in various down-stream processes, which might be associated with different morphological types of cell death. In addition, our results might provide molecular clues for coexistence of different morphological types of cell death in PD patients.
Partial differential equations methods, applications and theories
Hattori, Harumi
2013-01-01
This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...
Optimal harvesting for a predator-prey agent-based model using difference equations.
Oremland, Matthew; Laubenbacher, Reinhard
2015-03-01
In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.
Nonaligned shocks for discrete velocity models of the Boltzmann equation
Directory of Open Access Journals (Sweden)
J. M. Greenberg
1991-05-01
Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.
Half-trek criterion for generic identifiability of linear structural equation models
Foygel, R.; Draisma, J.; Drton, M.
2012-01-01
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations
Half-trek criterion for generic identifiability of linear structural equation models
Foygel, R.; Draisma, J.; Drton, M.
2011-01-01
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations
Comparison of six different models describing survival of mammalian cells after irradiation
International Nuclear Information System (INIS)
Sontag, W.
1990-01-01
Six different cell-survival models have been compared. All models are based on the similar assumption that irradiated cells are able to exist in one of three states. S A is the state of a totally repaired cell, in state S C the cell contains lethal lesions and in state S b the cell contains potentially lethal lesions i.e. those which either can be repaired or converted into lethal lesions. The differences between the six models lie in the different mathematical relationships between the three states. To test the six models, six different sets of experimental data were used which describe cell survival at different repair times after irradiation with sparsely ionizing irradiation. In order to compare the models, a goodness-of-fit function was used. The differences between the six models were tested by use of the nonparametric Mann-Whitney two sample test. Based on the 95% confidence limit, this required separation into three groups. (orig.)
Structural equation modeling and natural systems
Grace, James B.
2006-01-01
This book, first published in 2006, presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems.
Equation-free modeling unravels the behavior of complex ecological systems
DeAngelis, Donald L.; Yurek, Simeon
2015-01-01
Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.
International Nuclear Information System (INIS)
Perfetti, E.
2006-11-01
Modelling fluid-rock interactions as well as mixing and unmixing phenomena in geological processes requires robust equations of state (EOS) which must be applicable to systems containing water, gases over a broad range of temperatures and pressures. Cubic equations of state based on the Van der Waals theory (e. g. Soave-Redlich-Kwong or Peng-Robinson) allow simple modelling from the critical parameters of the studied fluid components. However, the accuracy of such equations becomes poor when water is a major component of the fluid since neither association trough hydrogen bonding nor dipolar interactions are accounted for. The Helmholtz energy of a fluid may be written as the sum of different energetic contributions by factorization of partition function. The model developed in this thesis for the pure H 2 O and H 2 S considers three contributions. The first contribution represents the reference Van der Waals fluid which is modelled by the SRK cubic EOS. The second contribution accounts for association through hydrogen bonding and is modelled by a term derived from Cubic Plus Association (CPA) theory. The third contribution corresponds to the dipolar interactions and is modelled by the Mean Spherical Approximation (MSA) theory. The resulting CPAMSA equation has six adjustable parameters, which three represent physical terms whose values are close to their experimental counterpart. This equation results in a better reproduction of the thermodynamic properties of pure water than obtained using the classical CPA equation along the vapour-liquid equilibrium. In addition, extrapolation to higher temperatures and pressure is satisfactory. Similarly, taking into account dipolar interactions together with the SRK cubic equation of state for calculating molar volume of H 2 S as a function of pressure and temperature results in a significant improvement compared to the SRK equation alone. Simple mixing rules between dipolar molecules are proposed to model the H 2 O-H 2 S
Illness-death model: statistical perspective and differential equations.
Brinks, Ralph; Hoyer, Annika
2018-01-27
The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.
Generalized Ordinary Differential Equation Models.
Miao, Hongyu; Wu, Hulin; Xue, Hongqi
2014-10-01
Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.
Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research
Cheung, Mike W.-L.; Au, Kevin
2005-01-01
Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…
Equations of motion for a (non-linear) scalar field model as derived from the field equations
International Nuclear Information System (INIS)
Kaniel, S.; Itin, Y.
2006-01-01
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Model identification using stochastic differential equation grey-box models in diabetes.
Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik
2013-03-01
The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.
The issue of statistical power for overall model fit in evaluating structural equation models
Directory of Open Access Journals (Sweden)
Richard HERMIDA
2015-06-01
Full Text Available Statistical power is an important concept for psychological research. However, examining the power of a structural equation model (SEM is rare in practice. This article provides an accessible review of the concept of statistical power for the Root Mean Square Error of Approximation (RMSEA index of overall model fit in structural equation modeling. By way of example, we examine the current state of power in the literature by reviewing studies in top Industrial-Organizational (I/O Psychology journals using SEMs. Results indicate that in many studies, power is very low, which implies acceptance of invalid models. Additionally, we examined methodological situations which may have an influence on statistical power of SEMs. Results showed that power varies significantly as a function of model type and whether or not the model is the main model for the study. Finally, results indicated that power is significantly related to model fit statistics used in evaluating SEMs. The results from this quantitative review imply that researchers should be more vigilant with respect to power in structural equation modeling. We therefore conclude by offering methodological best practices to increase confidence in the interpretation of structural equation modeling results with respect to statistical power issues.
International Nuclear Information System (INIS)
Korff, Christian
2003-01-01
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U q (s-tilde l-tilde 2 ) at q N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged centre Z of the algebra U q (s-tilde l-tilde 2 ) at q N = 1. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a hypersurface Spec Z subset of C 4 which remains invariant under the action of an infinite-dimensional group G of analytic transformations, called the quantum coadjoint action
Energy Technology Data Exchange (ETDEWEB)
Baldessar, Fabio; Negrao, Cezar O. Ribeiro; Palu, Claudia [Centro Federal de Educacao Tecnologica do Parana (CEFET-PR), Curitiba, PR (Brazil)
2004-07-01
The current work presents a mathematical model of an ascendant flow vertical reactor (riser) of a Fluid Catalytic Cracking Unit. The two-phase flow (gas-solid) and the cracking reactions are admitted one-dimensional and steady state. Mass, momentum and energy conservation equations are considered for each phase (solid and gas). A six-lump kinetic model is employed to evaluate gasoil, gasoline, GLP, fuel gas, light cycle oil and coke fractions. The model results are compared to experimental values from a pilot plant and to another model found in the literature. The results are in good agreement, showing the model has great potential. (author)
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
The lattice Boltzmann model for the second-order Benjamin–Ono equations
International Nuclear Information System (INIS)
Lai, Huilin; Ma, Changfeng
2010-01-01
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations
Katharaki, Maria; Daskalakis, Stelios; Mantas, John
2010-01-01
The objective of this paper is to assess the future adaptability of e-Learning platforms within postgraduate modules. An ongoing empirical assessment was conducted amongst postgraduate students, based on the Technology Acceptance Model (TAM). The current paper presents the outcomes from the second phase of a survey, involving fifty six participants. Data analysis was performed using a structural equation model, based on partial least squares. Results highlighted the very strong effect of perceived usefulness and perceived ease of use to attitude towards using e-Learning platforms. Consequently, attitude towards use proved to be a very strong predictor of behavioral intention. Perceived usefulness, on the contrary, did not prove to have an effect to behavioral intention. Implications on the potential of using e-Learning platforms are discussed along with limitations and future directions of the study.
Dynamic Model of Platform Manipulator with Six Degrees of Freedom
Directory of Open Access Journals (Sweden)
A. L. Lapikov
2015-01-01
Full Text Available The paper considers a solution of the relevant tasks related to deriving dynamic equations for the platform manipulators with 6 degrees of freedom. It presents a detailed analysis of the subject area, describes key problems arising in the course of research, and suggests their solution methods. The equations describing dynamics of the mechanical system under discussion were derived using Lagrange equation of the second kind. For this purpose Cartesian coordinates and three Euler angles (angles of precession, nutation and intrinsic rotation describing the orientation of moving frame of reference connected with the platform towards the base were chosen as generalized coordinates of the model. Such choice allowed us to simplify the derivation of the model considerably, because it was possible to represent a dependence of kinetic energy of the mechanical system on the generalized coordinates in an explicit form. In addition, formulation of kinetic energy was supplemented with correlations describing kinetic energy of the mechanism legs. During the derivation of equations for the legs velocities the part of the component defining a rotation movement of the leg against the joint of the base was ignored because of it was small in comparison with the component of linear separation. Besides, during the derivation of equations for kinetic energy of the legs, modified correlations for kinematics of platform manipulators with 6 degrees of freedom suggested in the previous papers of the authors were used.he paper examines a numerical example to solve a reverse dynamic problem in the case of equal harmonic changes of controlling forces. It was found out that under controlling forces described above the platform carries out harmonic advancing movements along the vertical axis.Further planning research concerns the extended capabilities of the model to consider the influence of the working load and to create algorithms for deriving dynamic models of a
Modeling High Frequency Semiconductor Devices Using Maxwell's Equations
National Research Council Canada - National Science Library
El-Ghazaly, Samier
1999-01-01
.... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...
Testing strong factorial invariance using three-level structural equation modeling
Directory of Open Access Journals (Sweden)
Suzanne eJak
2014-07-01
Full Text Available Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak, Oort and Dolan (2013 showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.
Mathematical analysis of partial differential equations modeling electrostatic MEMS
Esposito, Pierpaolo; Guo, Yujin
2010-01-01
Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed
International Nuclear Information System (INIS)
Miettinen, Jaakko; Hamalainen, Anitta; Pekkarinen, Esko
2002-01-01
Thermal hydraulic simulation capability for accident conditions is needed at present in VTT in several programs. Traditional thermal hydraulic models are too heavy for simulation in the analysis tasks, where the main emphasis is the rapid neutron dynamics or the core melting. The GENFLO thermal hydraulic model has been developed at VTT for special applications in the combined codes. The basic field equations in GENFLO are for the phase mass, the mixture momentum and phase energy conservation equations. The phase separation is solved with the drift flux model. The basic variables to be solved are the pressure, void fraction, mixture velocity, gas enthalpy, liquid enthalpy, and concentration of non-condensable gas fractions. The validation of the thermohydraulic solution alone includes large break LOCA reflooding experiments and in specific for the severe accident conditions QUENCH tests. In the recriticality analysis the core neutronics is simulated with a two-dimensional transient neutronics code TWODIM. The recriticality with one rapid prompt peak is expected during a severe accident scenario, where the control rods have been melted and ECCS reflooding is started after the depressurization. The GENFLO module simulates the BWR thermohydraulics in this application. The core melting module has been developed for the real time operator training by using the APROS engineering simulators. The core heatup, oxidation, metal and fuel pellet relocation and corium pool formation into the lower plenum are calculated. In this application the GENFLO model simulates the PWR vessel thermohydraulics. In the fuel performance analysis the fuel rod transient behavior is simulated with the FRAPTRAN code. GENFLO simulates the subchannel around a single fuel rod and delivers the heat transfer on the cladding surface for the FRAPTRAN. The transient boundary conditions for the subchannel are transmitted from the system code for operational transient, loss of coolant accidents and
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
On a Paneitz type equation in six dimensional domains
International Nuclear Information System (INIS)
Chtioui, Hichem; El Mehdi, Khalil
2003-09-01
In this paper, we consider the equation Δ 2 u = Ku 5 , u > 0 in Ω, u = Δu = 0 on ∂Ω, where K is a positive function and Ω is a bounded and smooth domain in R 6 . Using the theory of critical points at infinity, we give some topological conditions on K to ensure some existence results. (author)
A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency
Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake
2014-01-01
This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…
Taper and volume equations for selected Appalachian hardwood species
A. Jeff Martin
1981-01-01
Coefficients for five taper/volume models are developed for 18 Appalachian hardwood species. Each model can be used to estimate diameter at any point on the bole, height to any preselected diameter, and cubic-foot volume between any two points on the bole. The resulting equations were tested on six sets of independent data and an evaluation of these tests is included,...
The discretized Schroedinger equation and simple models for semiconductor quantum wells
International Nuclear Information System (INIS)
Boykin, Timothy B; Klimeck, Gerhard
2004-01-01
The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one
Equations for the kinetic modeling of supersonically flowing electrically excited lasers
International Nuclear Information System (INIS)
Lind, R.C.
1973-01-01
The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed
Prediction equations for spirometry in four- to six-year-old children.
França, Danielle Corrêa; Camargos, Paulo Augusto Moreira; Jones, Marcus Herbert; Martins, Jocimar Avelar; Vieira, Bruna da Silva Pinto Pinheiro; Colosimo, Enrico Antônio; de Mendonça, Karla Morganna Pereira Pinto; Borja, Raíssa de Oliveira; Britto, Raquel Rodrigues; Parreira, Verônica Franco
2016-01-01
To generate prediction equations for spirometry in 4- to 6-year-old children. Forced vital capacity, forced expiratory volume in 0.5s, forced expiratory volume in one second, peak expiratory flow, and forced expiratory flow at 25-75% of the forced vital capacity were assessed in 195 healthy children residing in the town of Sete Lagoas, state of Minas Gerais, Southeastern Brazil. The least mean squares method was used to derive the prediction equations. The level of significance was established as p<0.05. Overall, 85% of the children succeeded in performing the spirometric maneuvers. In the prediction equation, height was the single predictor of the spirometric variables as follows: forced vital capacity=exponential [(-2.255)+(0.022×height)], forced expiratory volume in 0.5s=exponential [(-2.288)+(0.019×height)], forced expiratory volume in one second=exponential [(-2.767)+(0.026×height)], peak expiratory flow=exponential [(-2.908)+(0.019×height)], and forced expiratory flow at 25-75% of the forced vital capacity=exponential [(-1.404)+(0.016×height)]. Neither age nor weight influenced the regression equations. No significant differences in the predicted values for boys and girls were observed. The predicted values obtained in the present study are comparable to those reported for preschoolers from both Brazil and other countries. Copyright © 2016 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.
Dynamic modeling of interfacial structures via interfacial area transport equation
International Nuclear Information System (INIS)
Seungjin, Kim; Mamoru, Ishii
2005-01-01
The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Directory of Open Access Journals (Sweden)
Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Dynamic modeling of interfacial structures via interfacial area transport equation
International Nuclear Information System (INIS)
Seungjin, Kim; Mamoru, Ishii
2004-01-01
Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap
Continuous Time Structural Equation Modeling with R Package ctsem
Directory of Open Access Journals (Sweden)
Charles C. Driver
2017-04-01
Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.
Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping
2018-06-01
As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.
TBA equations for excited states in the sine-Gordon model
International Nuclear Information System (INIS)
Balog, Janos; Hegedus, Arpad
2004-01-01
We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found
Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation
International Nuclear Information System (INIS)
Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul
2009-01-01
We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations
On a Paneitz type equation in six dimensional domains
Energy Technology Data Exchange (ETDEWEB)
Chtioui, Hichem [Departement de Mathematiques, Faculte des Sciences de Sfax, Route Soukra, Sfax (Tunisia); El Mehdi, Khalil [Faculte des Sciences et Techniques, Universite de Nouakchott, Nouakchott (Morocco); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: khalil@univ-nkc.mr; it, elmehdik@ictp trieste
2003-09-01
In this paper, we consider the equation {delta}{sup 2}u = Ku{sup 5}, u > 0 in {omega}, u = {delta}u = 0 on {partial_derivative}{omega}, where K is a positive function and {omega} is a bounded and smooth domain in R{sup 6}. Using the theory of critical points at infinity, we give some topological conditions on K to ensure some existence results. (author)
Excited TBA equations I: Massive tricritical Ising model
International Nuclear Information System (INIS)
Pearce, Paul A.; Chim, Leung; Ahn, Changrim
2001-01-01
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II
On the Schroedinger equation for the minisuperspace models
International Nuclear Information System (INIS)
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
2000-01-01
We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator
A Comparison of Methods of Vertical Equating.
Loyd, Brenda H.; Hoover, H. D.
Rasch model vertical equating procedures were applied to three mathematics computation tests for grades six, seven, and eight. Each level of the test was composed of 45 items in three sets of 15 items, arranged in such a way that tests for adjacent grades had two sets (30 items) in common, and the sixth and eighth grades had 15 items in common. In…
Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation
Hofstrand, A.; Moloney, J. V.
2018-03-01
In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.
A four-equation friction model for water hammer calculation in quasi-rigid pipelines
International Nuclear Information System (INIS)
Ghodhbani, Abdelaziz; Haj Taïeb, Ezzeddine
2017-01-01
Friction coupling affects water hammer evolution in pipelines according to the initial flow regime. Unsteady friction models are only validated with uncoupled formulation. On the other hand, coupled models such as four-equation model, provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. This paper deals with the creation of the “four-equation friction model” which is based on the incorporation of the unsteady head loss given by an unsteady friction model into the four-equation model. For transient laminar flow cases, the Zielke model is considered. The proposed model is applied to a quasi-rigid pipe with axial moving valve, and then calculated by the method of characteristics (MOC). Damping and shape of the numerical solution are in good agreement with experimental data. Thus, the proposed model can be incorporated into a new computer code. - Highlights: • Both Zielke model and four-equation model are insufficient to predict water hammer. • The four-equation friction model proposed is obtained by incorporating the unsteady head loss in the four-equation model. • The solution obtained by the proposed model is in good agreement with experimental data. • The wave-speed adjustment scheme is more efficient than interpolations schemes.
equateIRT: An R Package for IRT Test Equating
Directory of Open Access Journals (Sweden)
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
Modified two-fluid model for the two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.
2003-01-01
This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
QCD corrections to neutron electric dipole moment from dimension-six four-quark operators
Energy Technology Data Exchange (ETDEWEB)
Hisano, Junji, E-mail: hisano@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); IPMU, TODIAS, University of Tokyo, Kashiwa 277-8568 (Japan); Tsumura, Koji, E-mail: ko2@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China); Yang, Masaki J.S., E-mail: yang@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)
2012-07-18
In this Letter, the renormalization-group equations for the (flavor-conserving) CP-violating interaction are derived up to the dimension six, including all the four-quark operators, at one-loop level. We apply them to the models with the neutral scalar boson or the color-octet scalar boson which have CP-violating Yukawa interactions with quarks, and discuss the neutron electric dipole moment in these models.
Calculus for cognitive scientists partial differential equation models
Peterson, James K
2016-01-01
This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.
String beta function equations from c=1 matrix model
Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R
1995-01-01
We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.
Differential equations and integrable models: the SU(3) case
International Nuclear Information System (INIS)
Dorey, Patrick; Tateo, Roberto
2000-01-01
We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz
Modeling biological gradient formation: combining partial differential equations and Petri nets.
Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J
2016-01-01
Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
Modelling equation of knee force during instep kicking using ...
African Journals Online (AJOL)
This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.
Empiric model for mean generation time adjustment factor for classic point kinetics equations
Energy Technology Data Exchange (ETDEWEB)
Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C., E-mail: david.goes@poli.ufrj.br, E-mail: aquilino@lmp.ufrj.br, E-mail: alessandro@con.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Departamento de Engenharia Nuclear
2017-11-01
Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)
Empiric model for mean generation time adjustment factor for classic point kinetics equations
International Nuclear Information System (INIS)
Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C.
2017-01-01
Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)
Structural Equation Modeling with the Smartpls
Directory of Open Access Journals (Sweden)
Christian M. Ringle
2014-05-01
Full Text Available The objective of this article is to present a didactic example of Structural Equation Modeling using the software SmartPLS 2.0 M3. The program mentioned uses the method of Partial Least Squares and seeks to address the following situations frequently observed in marketing research: Absence of symmetric distributions of variables measured by a theory still in its beginning phase or with little “consolidation”, formative models, and/or a limited amount of data. The growing use of SmartPLS has demonstrated its robustness and the applicability of the model in the areas that are being studied.
THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE
Directory of Open Access Journals (Sweden)
K. O. Soroka
2015-06-01
Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods
Yang, Xuguang; Shi, Baochang; Chai, Zhenhua
2014-07-01
In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).
Inflating baby-Skyrme branes in six dimensions
International Nuclear Information System (INIS)
Brihaye, Yves; Delsate, Terence; Kodama, Yuta; Sawado, Nobuyuki
2010-01-01
We consider a six-dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. The branes have a cosmological constant modeled by inflating four-dimensional slices, and we further consider a bulk cosmological constant. We construct solutions numerically and present evidence that the solutions cease to exist for large values of the brane cosmological constant in some particular case. Then we study the stability of the model by considering perturbation of the gravitational part (resp. baby Skyrmion) with fixed matter fields (resp. gravitational background). Our results indicate that the perturbation equations do not admit localized solutions for certain type of perturbation. The stability analysis can be alternatively seen as leading to a particle spectrum; we give mass estimations for the baby-Skyrme perturbation and for the graviton.
Ginzburg-Landau equation as a heuristic model for generating rogue waves
Lechuga, Antonio
2016-04-01
Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.
On the viability of rank-six superstring models
International Nuclear Information System (INIS)
Campbell, B.A.; Olive, K.A.; Reiss, D.B.
1988-01-01
We consider the possibility of breaking a rank-six superstring model to the rank-four standard model. In particular, we point out the difficulties in generating two vacuum expectation values for the two standard model singlets contained in the 27 of E 6 . Although one expectation value is compatible with low energy phenomenology, a vev for ν c is problematic because of the absence of large neutrino masses and/or flavor changing neutral currents. We show that even simple models containing extra fields from incomplete multiplets or E 6 singlets do not resolve these problems. (orig.)
Chaotic attractors in tumor growth and decay: a differential equation model.
Harney, Michael; Yim, Wen-sau
2015-01-01
Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions
Wideband Small-Signal Input dq Admittance Modeling of Six-Pulse Diode Rectifiers
DEFF Research Database (Denmark)
Yue, Xiaolong; Wang, Xiongfei; Blaabjerg, Frede
2018-01-01
This paper studies the wideband small-signal input dq admittance of six-pulse diode rectifiers. Considering the frequency coupling introduced by ripple frequency harmonics of d-and q-channel switching function, the proposed model successfully predicts the small-signal input dq admittance of six......-pulse diode rectifiers in high frequency regions that existing models fail to explain. Simulation and experimental results verify the accuracy of the proposed model....
Quirk, Meghan E.; Schmotzer, Brian J.; Schmotzer, Brian J.; Singh, Rani H.
2010-01-01
Resting energy expenditure (REE) is often used to estimate total energy needs. The Schofield equation based on weight and height has been reported to underestimate REE in female children with phenylketonuria (PKU). The objective of this observational, cross-sectional study was to evaluate the agreement of measured REE with predicted REE for female adolescents with PKU. A total of 36 females (aged 11.5-18.7 years) with PKU attending Emory University’s Metabolic Camp (June 2002 – June 2008) underwent indirect calorimetry. Measured REE was compared to six predictive equations using paired Student’s t-tests, regression-based analysis, and assessment of clinical accuracy. The differences between measured and predicted REE were modeled against clinical parameters to determine to if a relationship existed. All six selected equations significantly under predicted measured REE (P< 0.005). The Schofield equation based on weight had the greatest level of agreement, with the lowest mean prediction bias (144 kcal) and highest concordance correlation coefficient (0.626). However, the Schofield equation based on weight lacked clinical accuracy, predicting measured REE within ±10% in only 14 of 36 participants. Clinical parameters were not associated with bias for any of the equations. Predictive equations underestimated measured REE in this group of female adolescents with PKU. Currently, there is no accurate and precise alternative for indirect calorimetry in this population. PMID:20497783
A review of Lean Six Sigma deployment and maturity models
Lameijer, B.A.; de Mast, J.; Does, R.J.M.M.
2017-01-01
For guidance in implementing Lean Six Sigma (LSS), both the academic and the practitioners’ literature offer deployment models and models for assessing the implementation’s maturity. This paper makes a critical appraisal of the quality and usefulness of a sample of 19 such models. The appraisal
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N
2012-12-01
Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.
Informed Conjecturing of Solutions for Differential Equations in a Modeling Context
Winkel, Brian
2015-01-01
We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…
Model reduction of multiscale chemical langevin equations: a numerical case study.
Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N
2009-01-01
Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.
A Structural Equation Approach to Models with Spatial Dependence
Oud, Johan H. L.; Folmer, Henk
We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it
A structural equation approach to models with spatial dependence
Oud, J.H.L.; Folmer, H.
2008-01-01
We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it
A Structural Equation Approach to Models with Spatial Dependence
Oud, J.H.L.; Folmer, H.
2008-01-01
We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it
Integral equation models for image restoration: high accuracy methods and fast algorithms
International Nuclear Information System (INIS)
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2010-01-01
Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of true physical (continuous) models, and hence, inevitably impose bottleneck model errors. We propose to work directly with continuous models for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in this paper for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images
Ising models and soliton equations
International Nuclear Information System (INIS)
Perk, J.H.H.; Au-Yang, H.
1985-01-01
Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained
Modeling imperfectly repaired system data via grey differential equations with unequal-gapped times
International Nuclear Information System (INIS)
Guo Renkuan
2007-01-01
In this paper, we argue that grey differential equation models are useful in repairable system modeling. The arguments starts with the review on GM(1,1) model with equal- and unequal-spaced stopping time sequence. In terms of two-stage GM(1,1) filtering, system stopping time can be partitioned into system intrinsic function and repair effect. Furthermore, we propose an approach to use grey differential equation to specify a semi-statistical membership function for system intrinsic function times. Also, we engage an effort to use GM(1,N) model to model system stopping times and the associated operating covariates and propose an unequal-gapped GM(1,N) model for such analysis. Finally, we investigate the GM(1,1)-embed systematic grey equation system modeling of imperfectly repaired system operating data. Practical examples are given in step-by-step manner to illustrate the grey differential equation modeling of repairable system data
Loop equations for multi-cut matrix models
International Nuclear Information System (INIS)
Akemann, G.
1995-03-01
The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots
Yuan, Ke-Hai; Hayashi, Kentaro
2010-01-01
This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…
Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations
International Nuclear Information System (INIS)
Arkhincheev, V.E.
2001-04-01
To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)
Localizing gravity on Maxwell gauged CP1 model in six dimensions
International Nuclear Information System (INIS)
Kodama, Yuta; Kokubu, Kento; Sawado, Nobuyuki
2008-01-01
We shall consider a 3-brane embedded in six-dimensional space-time with a negative bulk cosmological constant. The 3-brane is constructed by a topological soliton solution living in two-dimensional axially symmetric transverse subspace. Similar to most previous works of six-dimensional soliton models, our Maxwell gauged CP 1 brane model can also achieve localizing gravity around the 3-brane. The CP 1 field is described by a scalar doublet and derived from the O(3) sigma model by projecting it onto two-dimensional complex space. In that sense, our framework is more effective than other solitonic brane models concerning gauge theory. We shall also discuss the linear stability analysis for our new model by fluctuating all fields.
Study of a Model Equation in Detonation Theory
Faria, Luiz
2014-04-24
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.
Annotated bibliography of structural equation modelling: technical work.
Austin, J T; Wolfle, L M
1991-05-01
Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...
Continuum model of the two-component Becker-Döring equations
Directory of Open Access Journals (Sweden)
Ali Reza Soheili
2004-01-01
Full Text Available The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.
Nestler, Steffen
2014-05-01
Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.
A New Six-Parameter Model Based on Chebyshev Polynomials for Solar Cells
Directory of Open Access Journals (Sweden)
Shu-xian Lun
2015-01-01
Full Text Available This paper presents a new current-voltage (I-V model for solar cells. It has been proved that series resistance of a solar cell is related to temperature. However, the existing five-parameter model ignores the temperature dependence of series resistance and then only accurately predicts the performance of monocrystalline silicon solar cells. Therefore, this paper uses Chebyshev polynomials to describe the relationship between series resistance and temperature. This makes a new parameter called temperature coefficient for series resistance introduced into the single-diode model. Then, a new six-parameter model for solar cells is established in this paper. This new model can improve the accuracy of the traditional single-diode model and reflect the temperature dependence of series resistance. To validate the accuracy of the six-parameter model in this paper, five kinds of silicon solar cells with different technology types, that is, monocrystalline silicon, polycrystalline silicon, thin film silicon, and tripe-junction amorphous silicon, are tested at different irradiance and temperature conditions. Experiment results show that the six-parameter model proposed in this paper is an I-V model with moderate computational complexity and high precision.
Directory of Open Access Journals (Sweden)
Enrique Álvarez
Full Text Available Poliovirus protease 2A (2A(pro obstructs host gene expression by reprogramming transcriptional and post-transcriptional regulatory events during infection. Here we demonstrate that expression of 2A(pro induces a selective nucleo-cytoplasm translocation of several important RNA binding proteins and splicing factors. Subcellular fractionation studies, together with immunofluorescence microscopy revealed an asymmetric distribution of HuR and TIA1/TIAR in 2A(pro expressing cells, which modulates splicing of the human Fas exon 6. Consistent with this result, knockdown of HuR or overexpression of TIA1/TIAR, leads to Fas exon 6 inclusion in 2A(pro-expressing cells. Therefore, poliovirus 2A(pro can target alternative pre-mRNA splicing by regulating protein shuttling between the nucleus and the cytoplasm.
Reduction of static field equation of Faddeev model to first order PDE
International Nuclear Information System (INIS)
Hirayama, Minoru; Shi Changguang
2007-01-01
A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations
Stochastic modeling of stock price process induced from the conjugate heat equation
Paeng, Seong-Hun
2015-02-01
Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.
River water quality model no. 1 (RWQM1): II. Biochemical process equations
DEFF Research Database (Denmark)
Reichert, P.; Borchardt, D.; Henze, Mogens
2001-01-01
In this paper, biochemical process equations are presented as a basis for water quality modelling in rivers under aerobic and anoxic conditions. These equations are not new, but they summarise parts of the development over the past 75 years. The primary goals of the presentation are to stimulate...... transformation processes. This paper is part of a series of three papers. In the first paper, the general modelling approach is described; in the present paper, the biochemical process equations of a complex model are presented; and in the third paper, recommendations are given for the selection of a reasonable...
On singularity formation of a 3D model for incompressible Navier–Stokes equations
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu
2012-01-01
We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...
Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.
Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J
2017-03-01
Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.
Testing strong factorial invariance using three-level structural equation modeling
Jak, Suzanne
Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is
Parameter Estimates in Differential Equation Models for Population Growth
Winkel, Brian J.
2011-01-01
We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…
Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.
2009-01-01
This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…
A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling
DEFF Research Database (Denmark)
Banijamali, Babak
model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...
Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation
Energy Technology Data Exchange (ETDEWEB)
Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp
2017-02-01
The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.
Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian
Directory of Open Access Journals (Sweden)
A. Zabrodin
2018-02-01
Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.
A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers
Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.
2016-10-01
Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.
Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics
Directory of Open Access Journals (Sweden)
Weam Alharbi
2018-04-01
Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.
Application of Fokker-Planck equation in positron diffusion trapping model
International Nuclear Information System (INIS)
Bartosova, I.; Ballo, P.
2015-01-01
This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)
Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem
Kovacs, Zoltan
2010-01-01
The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…
Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.
2013-01-01
Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077
Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations
International Nuclear Information System (INIS)
Yotsuji, K.; Tachi, Y.; Nishimaki, Y.
2012-01-01
Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3
A quantum relativistic integrable model as the continuous limit of the six-vertex model
International Nuclear Information System (INIS)
Zhou, Y.K.
1992-01-01
The six-vertex model in two-dimensional statistical mechanics is used to construct the L-matrix of a one-dimensional quantum relativistic integrable model through a continuous limit. This is the first step to extend the method used earlier by the author to construct quantum completely integrable systems from other well-known two-dimensional vertex models. (orig.)
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Parametric reduced models for the nonlinear Schrödinger equation.
Harlim, John; Li, Xiantao
2015-05-01
Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.
Meta-analytic structural equation modelling
Jak, Suzanne
2015-01-01
This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.
Kinar, N. J.
2017-05-01
An equation was proposed to model the height of blowing snow accumulation downwind of an obstacle such as vegetation, a snow fence, a building, or a topographic feature. The equation does not require aerodynamic flow condition parameters such as wind speed, allowing for the spatial distribution of snow to be determined at locations where meteorological data is not available. However, snow particle diffusion, drift, and erosion coefficients must be estimated for application of the equation. These coefficients can be used to provide insight into the relative magnitude of blowing snow processes at a field location. Further research is required to determine efficient methods for coefficient estimation. The equation could be used with other models of wind-transported snow to predict snow accumulation downwind of an obstacle without the need for wind speed adjustments or correction equations. Applications for this equation include the design of snow fences, and the use of this equation with other hydrological models to predict snow distribution, climate change, drought, flooding, and avalanches.
Homogeneous axisymmetric model with a limitting stiff equation of state
International Nuclear Information System (INIS)
Korkina, M.P.; Martynenko, V.G.
1976-01-01
A solution is obtained for Einstein's equations in which all metric coefficients are time functions for a limiting stiff equation of the substance state. Thr solution describes a homogeneous cosmological model with cylindrical symmetry. It is shown that the same metrics can be induced by a massless scalar only time-dependent field. Analysis of this solution is presented
Structural-equation models of migration: an example from the Upper Midwest USA.
Cadwallader, M
1985-01-01
"To date, most migration models have been specified in terms of a single equation, whereby a set of regional characteristics are used to predict migration rates for various kinds of spatial units. These models are inadequate in at least two respects. First, they omit any causal links between the explanatory variables, thus ignoring indirect effects between these variables and migration. Second, they ignore the possibility of reciprocal causation, or feedback effects, between migration and the explanatory variables...." The author uses data for State Economic Areas to construct a path model and simultaneous-equation model to identify both indirect and feedback effects on migration in the Upper Midwestern United States. "On the basis of the path model, it is suggested that the direct effects of many variables on migration are at least partially offset by the indirect effects, whereas the simultaneous-equation model emphasizes the reciprocal relationship between income and migration." excerpt
Virulence of six capsular serotypes of Porphyromonas gingivalis in a mouse model
Laine, ML; van Winkelhoff, AJ
1998-01-01
Capsular structures of Porphyromonas gingivalis have been correlated to the pathogenicity in animal models. Six polysaccharide capsular serotypes have recently been described in P. gingivalis. In the present study, virulence of the P. gingivalis strains of the six capsular serotypes was compared
Tao, Youshan; Guo, Qian; Aihara, Kazuyuki
2014-10-01
Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.
Ordinary Differential Equation Models for Adoptive Immunotherapy.
Talkington, Anne; Dantoin, Claudia; Durrett, Rick
2018-05-01
Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.
International Nuclear Information System (INIS)
Foroutan, A.
1992-05-01
The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)
Multiloop soliton and multibreather solutions of the short pulse model equation
International Nuclear Information System (INIS)
Matsuno, Yoshimasa
2007-01-01
We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear medica. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre. (author)
Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model
Directory of Open Access Journals (Sweden)
Xiao-Wei Guan
2018-01-01
Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.
On petroleum fluid characterization with the PC-SAFT equation of state
DEFF Research Database (Denmark)
Liang, Xiaodong; Yan, Wei; Thomsen, Kaj
2014-01-01
The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has shown promising results for describing complex phase behaviors and high pressure properties of various systems. It has been proposed as an alternative to the classical cubic equations of state in the petroleum...... industry. It is, however, far from a simple task to develop a sophisticated oil characterization method for the PC-SAFT EOS. In this work, in order to answer some fundamental questions of developing new characterization methods for PC-SAFT, six methods are proposed to estimate the model parameters...
Advanced structural equation modeling issues and techniques
Marcoulides, George A
2013-01-01
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
DEFF Research Database (Denmark)
Salarzadeh Jenatabadi, Hashem; Babashamsi, Peyman; Khajeheian, Datis
2016-01-01
There are many factors which could inﬂuence the sustainability of airlines. The main purpose of this study is to introduce a framework for a financial sustainability index and model it based on structural equation modeling (SEM) with maximum likelihood and Bayesian predictors. The introduced...
A Structural Equation Model of Expertise in College Physics
Taasoobshirazi, Gita; Carr, Martha
2009-01-01
A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…
A Structural Equation Model of Conceptual Change in Physics
Taasoobshirazi, Gita; Sinatra, Gale M.
2011-01-01
A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…
Principles and practice of structural equation modeling
Kline, Rex B
2015-01-01
Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex
Caglar, Mehmet Umut; Pal, Ranadip
2011-03-01
Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices
Deboeck, Pascal R.; Boker, Steven M.
2010-01-01
Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…
Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces
Wang, Chi R.
2005-01-01
This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation
Computer models for kinetic equations of magnetically confined plasmas
International Nuclear Information System (INIS)
Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.
1987-01-01
This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method
Modeling Inflation Using a Non-Equilibrium Equation of Exchange
Chamberlain, Robert G.
2013-01-01
Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project
Validation of an employee satisfaction model: A structural equation model approach
Ophillia Ledimo; Nico Martins
2015-01-01
The purpose of this study was to validate an employee satisfaction model and to determine the relationships between the different dimensions of the concept, using the structural equation modelling approach (SEM). A cross-sectional quantitative survey design was used to collect data from a random sample of (n=759) permanent employees of a parastatal organisation. Data was collected using the Employee Satisfaction Survey (ESS) to measure employee satisfaction dimensions. Following the steps of ...
Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory
International Nuclear Information System (INIS)
Sanchez, N.; Whiting, B.
1986-01-01
The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers
Introduction to inverse problems for differential equations
Hasanov Hasanoğlu, Alemdar
2017-01-01
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here a...
Umut Caglar, Mehmet; Pal, Ranadip
2010-10-01
The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology
Application of flexible model in neutron dynamics equations
International Nuclear Information System (INIS)
Liu Cheng; Zhao Fuyu; Fu Xiangang
2009-01-01
Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)
Generalised and Fractional Langevin Equations-Implications for Energy Balance Models
Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.
2017-12-01
Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).
Nonsingular 4d-flat branes in six-dimensional supergravities
International Nuclear Information System (INIS)
Nair, V.P.; Randjbar-Daemi, S.
2005-01-01
We show that six-dimensional supergravity models admit nonsingular solutions in the presence of flat three-brane sources with positive tensions. The models studied in this paper involve nonlinear sigma model scalar fields targeted on noncompact manifolds. For the particular solutions of the scalar field equations which we consider, only two brane sources are possible which are positioned at those points where the scalar field densities diverge, without creating a divergence in the Ricci scalar or the total energy. These solutions are invariant under 1/2 of D=6 supersymmetries far away from the branes, which, however, do not integrate to global Killing spinors. Other branes can be introduced by hand by allowing for local deficit angles in the transverse space without generating any kind of curvature singularities. (author)
Thielmann, Isabel; Hilbig, Benjamin E; Zettler, Ingo; Moshagen, Morten
2017-12-01
Recent developments in personality research led to the proposition of two alternative six-factor trait models, the HEXACO model and the Big Six model. However, given the lack of direct comparisons, it is unclear whether the HEXACO and Big Six factors are distinct or essentially equivalent, that is, whether corresponding inventories measure similar or distinct personality traits. Using Structural Equation Modeling (Study 1), we found substantial differences between the traits as measured via the HEXACO-60 and the 30-item Questionnaire Big Six (30QB6), particularly for Honesty-Humility and Honesty-Propriety (both model's critical difference to the Big Five approach). This distinction was further supported by Study 2, showing differential capabilities of the HEXACO-60 and the 30QB6 to account for several criteria representing the theoretical core of Honesty-Humility and/or Honesty-Propriety. Specifically, unlike the indicator of Honesty-Humility, the indicator of Honesty-Propriety showed low predictive power for some conceptually relevant criteria, suggesting a limited validity of the 30QB6.
Partial differential equation models in the socio-economic sciences
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.
2014-01-01
Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences
Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.
2017-07-01
Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.
Climate Modeling in the Calculus and Differential Equations Classroom
Kose, Emek; Kunze, Jennifer
2013-01-01
Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…
Modeling of superconductors based on the timedependent Ginsburg-Landau equations
Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.
2009-11-01
Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.
Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul
2018-03-01
In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.
Chow, Sy-Miin; Ou, Lu; Ciptadi, Arridhana; Prince, Emily B; You, Dongjun; Hunter, Michael D; Rehg, James M; Rozga, Agata; Messinger, Daniel S
2018-06-01
A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of [Formula: see text] mother-infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children's tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.
Algebraic models for the hierarchy structure of evolution equations at small x
International Nuclear Information System (INIS)
Rembiesa, P.; Stasto, A.M.
2005-01-01
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit
MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model
International Nuclear Information System (INIS)
Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio
1991-05-01
MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)
Alternans promotion in cardiac electrophysiology models by delay differential equations.
Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M
2017-09-01
Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.
Alternans promotion in cardiac electrophysiology models by delay differential equations
Gomes, Johnny M.; dos Santos, Rodrigo Weber; Cherry, Elizabeth M.
2017-09-01
Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.
Convergence of the Stochastic Six-Vertex Model to the ASEP
Energy Technology Data Exchange (ETDEWEB)
Aggarwal, Amol, E-mail: amolaggarwal@g.harvard.edu [Harvard University Cambridge (United States)
2017-06-15
In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.
Guidelines for a graph-theoretic implementation of structural equation modeling
Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William
2012-01-01
Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for
A modified two-fluid model for the application of two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun, X.; Ishii, M.; Kelly, J.
2003-01-01
This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
A one-step method for modelling longitudinal data with differential equations.
Hu, Yueqin; Treinen, Raymond
2018-04-06
Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.
Hidden physics models: Machine learning of nonlinear partial differential equations
Raissi, Maziar; Karniadakis, George Em
2018-03-01
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.
Neutron star models with realistic high-density equations of state
International Nuclear Information System (INIS)
Malone, R.C.; Johnson, M.B.; Bethe, H.A.
1975-01-01
We calculate neutron star models using four realistic high-density models of the equation of state. We conclude that the maximum mass of a neutron star is unlikely to exceed 2 M/sub sun/. All of the realistic models are consistent with current estimates of the moment of inertia of the Crab pulsar
International Nuclear Information System (INIS)
Fujii, Akira; Kluemper, Andreas
1999-01-01
We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation
Modelling the heat dynamics of a building using stochastic differential equations
DEFF Research Database (Denmark)
Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik
2000-01-01
estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
A modelling of robot manipulator dynamics based on Newton-Euler's equations
International Nuclear Information System (INIS)
Sasaki, Shinobu
1990-09-01
In this paper is presented an algorithm for solving the inverse dynamics of robot manipulators. In comparison with the dynamical equations derived from the Lagrange's mechanics, the relations to be treated are of simple forms due to recursive expressions of relative link motions. A computer simulation for applying the algorithm to a six-link manipulator indicated that the present method might be most appropriate among the existing approaches from the viewpoint of computational efficiency. In particular, it is noted that the increase of the number of links has hardly great effect on the intricacy of calculation. (author)
Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.
Saveliev, V L; Gorokhovski, M A
2005-07-01
On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.
Newtonian nudging for a Richards equation-based distributed hydrological model
Paniconi, Claudio; Marrocu, Marino; Putti, Mario; Verbunt, Mark
The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model's behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation
Role of secondary instability theory and parabolized stability equations in transition modeling
El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.
1993-01-01
In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.
DEFF Research Database (Denmark)
Mikkelsen, Frederik Vissing
eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...
Equation-based model for the stock market.
Xavier, Paloma O C; Atman, A P F; de Magalhães, A R Bosco
2017-09-01
We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.
Equation-based model for the stock market
Xavier, Paloma O. C.; Atman, A. P. F.; de Magalhães, A. R. Bosco
2017-09-01
We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.
Partial differential equation models in macroeconomics.
Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin
2014-11-13
The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
A single model procedure for estimating tank calibration equations
International Nuclear Information System (INIS)
Liebetrau, A.M.
1997-10-01
A fundamental component of any accountability system for nuclear materials is a tank calibration equation that relates the height of liquid in a tank to its volume. Tank volume calibration equations are typically determined from pairs of height and volume measurements taken in a series of calibration runs. After raw calibration data are standardized to a fixed set of reference conditions, the calibration equation is typically fit by dividing the data into several segments--corresponding to regions in the tank--and independently fitting the data for each segment. The estimates obtained for individual segments must then be combined to obtain an estimate of the entire calibration function. This process is tedious and time-consuming. Moreover, uncertainty estimates may be misleading because it is difficult to properly model run-to-run variability and between-segment correlation. In this paper, the authors describe a model whose parameters can be estimated simultaneously for all segments of the calibration data, thereby eliminating the need for segment-by-segment estimation. The essence of the proposed model is to define a suitable polynomial to fit to each segment and then extend its definition to the domain of the entire calibration function, so that it (the entire calibration function) can be expressed as the sum of these extended polynomials. The model provides defensible estimates of between-run variability and yields a proper treatment of between-segment correlations. A portable software package, called TANCS, has been developed to facilitate the acquisition, standardization, and analysis of tank calibration data. The TANCS package was used for the calculations in an example presented to illustrate the unified modeling approach described in this paper. With TANCS, a trial calibration function can be estimated and evaluated in a matter of minutes
Phenomenological neutron star equations of state. 3-window modeling of QCD matter
Energy Technology Data Exchange (ETDEWEB)
Kojo, Toru [University of Illinois at Urbana-Champaign, Department of Physics, Urbana, Illinois (United States)
2016-03-15
We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n{sub B}
Working covariance model selection for generalized estimating equations.
Carey, Vincent J; Wang, You-Gan
2011-11-20
We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.
A single-equation study of US petroleum consumption: The role of model specificiation
International Nuclear Information System (INIS)
Jones, C.T.
1993-01-01
The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas ampersand electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns
Continuum model of the two-component Becker-Döring equations
Soheili, Ali Reza
2004-01-01
The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum m...
FEQinput—An editor for the full equations (FEQ) hydraulic modeling system
Ancalle, David S.; Ancalle, Pablo J.; Domanski, Marian M.
2017-10-30
IntroductionThe Full Equations Model (FEQ) is a computer program that solves the full, dynamic equations of motion for one-dimensional unsteady hydraulic flow in open channels and through control structures. As a result, hydrologists have used FEQ to design and operate flood-control structures, delineate inundation maps, and analyze peak-flow impacts. To aid in fighting floods, hydrologists are using the software to develop a system that uses flood-plain models to simulate real-time streamflow.Input files for FEQ are composed of text files that contain large amounts of parameters, data, and instructions that are written in a format exclusive to FEQ. Although documentation exists that can aid in the creation and editing of these input files, new users face a steep learning curve in order to understand the specific format and language of the files.FEQinput provides a set of tools to help a new user overcome the steep learning curve associated with creating and modifying input files for the FEQ hydraulic model and the related utility tool, Full Equations Utilities (FEQUTL).
Notes on TQFT wire models and coherence equations for SU(3) triangular cells
Coquereaux, R.; Schieber, G.
2010-01-01
After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.
A simplified model for computing equation of state of argon plasma
International Nuclear Information System (INIS)
Wang Caixia; Tian Yangmeng
2006-01-01
The paper present a simplified new model of computing equation of state and ionization degree of Argon plasma, which based on Thomas-Fermi (TF) statistical model: the authors fitted the numerical results of the ionization potential calculated by Thomas-Fermi statistical model and gained the analytical function of the potential versus the degree of ionization, then calculated the ionization potential and the average degree of ionization for Argon versus temperature and density in local thermal equilibrium case at 10-1000 eV. The results calculated of this simplified model are basically in agreement with several sets of theory data and experimental data. This simplified model can be used to calculation of the equation of state of plasmas mixture and is expected to have a more wide use in the field of EML technology involving the strongly ionized plasmas. (authors)
Modeling Blazar Spectra by Solving an Electron Transport Equation
Lewis, Tiffany; Finke, Justin; Becker, Peter A.
2018-01-01
Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.
International Nuclear Information System (INIS)
Lin-Jie, Chen; Chang-Feng, Ma
2010-01-01
This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)
Exploratory structural equation modeling of personality data.
Booth, Tom; Hughes, David J
2014-06-01
The current article compares the use of exploratory structural equation modeling (ESEM) as an alternative to confirmatory factor analytic (CFA) models in personality research. We compare model fit, factor distinctiveness, and criterion associations of factors derived from ESEM and CFA models. In Sample 1 (n = 336) participants completed the NEO-FFI, the Trait Emotional Intelligence Questionnaire-Short Form, and the Creative Domains Questionnaire. In Sample 2 (n = 425) participants completed the Big Five Inventory and the depression and anxiety scales of the General Health Questionnaire. ESEM models provided better fit than CFA models, but ESEM solutions did not uniformly meet cutoff criteria for model fit. Factor scores derived from ESEM and CFA models correlated highly (.91 to .99), suggesting the additional factor loadings within the ESEM model add little in defining latent factor content. Lastly, criterion associations of each personality factor in CFA and ESEM models were near identical in both inventories. We provide an example of how ESEM and CFA might be used together in improving personality assessment. © The Author(s) 2014.
Ramlall, Indranarain
2016-01-01
This book explains in a rigorous, concise and practical manner all the vital components embedded in structural equation modelling. Focusing on R and stata to implement and perform various structural equation models.
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
Potsepaev, R.
2010-09-06
Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.
Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Ito, Katsushi; Satoh, Yuji; Suzuki, Junji
2014-06-01
We study the six-point gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling based on the twisted Z 4 -symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model.
Where are the roots of the Bethe Ansatz equations?
Energy Technology Data Exchange (ETDEWEB)
Vieira, R.S., E-mail: rsvieira@df.ufscar.br; Lima-Santos, A., E-mail: dals@df.ufscar.br
2015-10-02
Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and the BAE arising from the Coordinate Bethe Ansatz (CBA). For two magnon states this polynomial system could be decoupled and the solutions given in terms of the roots of some self-inversive polynomials. From theorems concerning the distribution of the roots of self-inversive polynomials we made a thorough analysis of the two magnon states, which allowed us to find the location and multiplicity of the Bethe roots in the complex plane, to discuss the completeness and singularities of Bethe's equations, the ill-founded string-hypothesis concerning the location of their roots, as well as to find an interesting connection between the BAE with Salem’s polynomials.
A delay differential equation model of follicle waves in women.
Panza, Nicole M; Wright, Andrew A; Selgrade, James F
2016-01-01
This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.
Integrable discretizations for the short-wave model of the Camassa-Holm equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.
Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity
International Nuclear Information System (INIS)
Yepez, Jeffrey
2006-01-01
Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory
Mathematical modelling of tissue formation on the basis of ordinary differential equations
Directory of Open Access Journals (Sweden)
Maxim N. Nazarov
2017-10-01
Full Text Available A mathematical model is proposed for describing the population dynamics of cellular clusters on the basis of systems of the first-order ordinary differential equations. The main requirement for the construction of model equations was to obtain a formal biological justification for their derivation, as well as proof of their correctness. In addition, for all the parameters involved in the model equations, the presence of biological meaning was guaranteed, as well as the possibility of evaluating them either during the experiment or by using models of intracellular biochemistry. In the desired model the intercellular exchange of a special signal molecules was chosen as the main mechanism for coordination of the tissue growth and new types selection during cell division. For simplicity, all signalling molecules that can create cells of the same type were not considered separately in the model, but were instead combined in a single complex of molecules: a ‘generalized signal’. Such an approach allows us to eventually assign signals as a functions of cell types and introduce their effects in the form of matrices in the models, where the rows are responsible for the types of cells receiving the signals, and the columns for the types of cells emitting signals.
Analytic solution of boundary-value problems for nonstationary model kinetic equations
International Nuclear Information System (INIS)
Latyshev, A.V.; Yushkanov, A.A.
1993-01-01
A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann
2003-01-01
The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth...... by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...
Padrino, Juan C.; Sprittles, James; Lockerby, Duncan
2017-11-01
Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).
Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas
International Nuclear Information System (INIS)
Eliezer, S.; Falquina, R.; Minguez, E.
1994-01-01
Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution
Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation
Wang, D.
2017-12-01
The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.
Six Conductivity Values to Use in the Bidomain Model of Cardiac Tissue.
Johnston, Barbara M
2016-07-01
The aim of this work is to produce a consistent set of six conductivity values for use in the bidomain model of cardiac tissue. Studies in 2007 by Hooks et al. and in 2009 by Caldwell et al. have found that, in the directions longitudinal:transverse:normal (l:t:n) to the cardiac fibers, ratios of bulk conductivities and conduction velocities are each approximately in the ratio 4:2:1. These results are used here as the basis for a method that can find sets of six normalized bidomain conductivity values. It is found that the ratios involving transverse and normal conductivities are quite consistent, allowing new light to be shed on conductivity in the normal direction. For example, it is found that the ratio of transverse to normal conductivity is much greater in the intracellular (i) than the extracellular (e) domain. Using parameter values from experimental studies leads to the proposal of a new nominal six conductivity dataset: gil=2.4, gel=2.4, git=0.35, get=2.0, gin=0.08, and gen=1.1 (all in mS/cm). When it is used to model partial thickness ischaemia, this dataset produces epicardial potential distributions in accord with experimental studies in an animal model. It is, therefore, suggested that the dataset is suitable for use in numerical simulations. Since the bidomain approach is the most commonly used method for modeling cardiac electrophysiological phenomena, new information about conductivity in the normal direction, as well as a consistent set of six conductivity values, is valuable for researchers who perform simulation studies.
Practice and philosophy of climate model tuning across six US modeling centers
Directory of Open Access Journals (Sweden)
G. A. Schmidt
2017-09-01
Full Text Available Model calibration (or tuning is a necessary part of developing and testing coupled ocean–atmosphere climate models regardless of their main scientific purpose. There is an increasing recognition that this process needs to become more transparent for both users of climate model output and other developers. Knowing how and why climate models are tuned and which targets are used is essential to avoiding possible misattributions of skillful predictions to data accommodation and vice versa. This paper describes the approach and practice of model tuning for the six major US climate modeling centers. While details differ among groups in terms of scientific missions, tuning targets, and tunable parameters, there is a core commonality of approaches. However, practices differ significantly on some key aspects, in particular, in the use of initialized forecast analyses as a tool, the explicit use of the historical transient record, and the use of the present-day radiative imbalance vs. the implied balance in the preindustrial era as a target.
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Interactive differential equations modeling program
International Nuclear Information System (INIS)
Rust, B.W.; Mankin, J.B.
1976-01-01
Due to the recent emphasis on mathematical modeling, many ecologists are using mathematics and computers more than ever, and engineers, mathematicians and physical scientists are now included in ecological projects. However, the individual ecologist, with intuitive knowledge of the system, still requires the means to critically examine and adjust system models. An interactive program was developed with the primary goal of allowing an ecologist with minimal experience in either mathematics or computers to develop a system model. It has also been used successfully by systems ecologists, engineers, and mathematicians. This program was written in FORTRAN for the DEC PDP-10, a remote terminal system at Oak Ridge National Laboratory. However, with relatively minor modifications, it can be implemented on any remote terminal system with a FORTRAN IV compiler, or equivalent. This program may be used to simulate any phenomenon which can be described as a system of ordinary differential equations. The program allows the user to interactively change system parameters and/or initial conditions, to interactively select a set of variables to be plotted, and to model discontinuities in the state variables and/or their derivatives. One of the most useful features to the non-computer specialist is the ability to interactively address the system parameters by name and to interactively adjust their values between simulations. These and other features are described in greater detail
Quintom models with an equation of state crossing -1
International Nuclear Information System (INIS)
Zhao Wen; Zhang Yang
2006-01-01
In this paper, we investigate a kind of special quintom model, which is made of a quintessence field φ 1 and a phantom field φ 2 , and the potential function has the form of V(φ 1 2 -φ 2 2 ). This kind of quintom field can be separated into two kinds: the hessence model, which has the state of φ 1 2 >φ 2 2 , and the hantom model with the state φ 1 2 2 2 . We discuss the evolution of these models in the ω-ω ' plane (ω is the state equation of the dark energy, and ω ' is its time derivative in units of Hubble time), and find that according to ω>-1 or ' plane can be divided into four parts. The late time attractor solution, if existing, is always quintessencelike or Λ-like for hessence field, so the big rip does not exist. But for hantom field, its late time attractor solution can be phantomlike or Λ-like, and sometimes, the big rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the ω-ω ' plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation-of-state function ω(z). We apply our method to five kinds of parametrizations of equation-of-state parameter, where ω crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom δ Q and the metric Φ are all finite even at the state of ω=-1 and ω ' ≠0
Discrete ellipsoidal statistical BGK model and Burnett equations
Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei
2018-06-01
A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.
Dissolution process analysis using model-free Noyes-Whitney integral equation.
Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto
2013-02-01
Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.
Estimating varying coefficients for partial differential equation models.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2017-09-01
Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.
Wang, Bo; Deveaux, Lynette; Lunn, Sonja; Dinaj-Koci, Veronica; Li, Xiaoming; Stanton, Bonita
2016-03-01
This study examined the relationships between youth and parental sensation-seeking, peer influence, parental monitoring and youth risk involvement in adolescence using structural equation modeling. Beginning in grade-six, longitudinal data were collected from 543 students over three years. Youth sensation-seeking in grade six contributed to risk involvement in early adolescence (grades six and seven) indirectly through increased peer risk influence and decreased parental monitoring but did not have a direct contribution. It contributed directly and indirectly to risk involvement in middle adolescence (grades eight and nine). Parent sensation-seeking at baseline was positively associated with peer risk influence and negatively associated with parental monitoring; it had no direct effect on adolescent risk involvement. Parental monitoring buffers negative peer influence on adolescent risk involvement. Results highlight the need for intervention efforts to provide normative feedback about adolescent risky behaviors and to vary among families in which parents and/or youth have high sensation-seeking propensities.
Wang, Bo; Deveaux, Lynette; Lunn, Sonja; Dinaj-Koci, Veronica; Li, Xiaoming; Stanton, Bonita
2014-01-01
This study examined the relationships between youth and parental sensation-seeking, peer influence, parental monitoring and youth risk involvement in adolescence using structural equation modeling. Beginning in grade-six, longitudinal data were collected from 543 students over three years. Youth sensation-seeking in grade six contributed to risk involvement in early adolescence (grades six and seven) indirectly through increased peer risk influence and decreased parental monitoring but did not have a direct contribution. It contributed directly and indirectly to risk involvement in middle adolescence (grades eight and nine). Parent sensation-seeking at baseline was positively associated with peer risk influence and negatively associated with parental monitoring; it had no direct effect on adolescent risk involvement. Parental monitoring buffers negative peer influence on adolescent risk involvement. Results highlight the need for intervention efforts to provide normative feedback about adolescent risky behaviors and to vary among families in which parents and/or youth have high sensation-seeking propensities. PMID:27030784
Prior Sensitivity Analysis in Default Bayesian Structural Equation Modeling.
van Erp, Sara; Mulder, Joris; Oberski, Daniel L
2017-11-27
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models and solve some of the issues often encountered in classical maximum likelihood estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of the unknown model parameters. Often, researchers rely on default priors, which are constructed in an automatic fashion without requiring substantive prior information. However, the prior can have a serious influence on the estimation of the model parameters, which affects the mean squared error, bias, coverage rates, and quantiles of the estimates. In this article, we investigate the performance of three different default priors: noninformative improper priors, vague proper priors, and empirical Bayes priors-with the latter being novel in the BSEM literature. Based on a simulation study, we find that these three default BSEM methods may perform very differently, especially with small samples. A careful prior sensitivity analysis is therefore needed when performing a default BSEM analysis. For this purpose, we provide a practical step-by-step guide for practitioners to conducting a prior sensitivity analysis in default BSEM. Our recommendations are illustrated using a well-known case study from the structural equation modeling literature, and all code for conducting the prior sensitivity analysis is available in the online supplemental materials. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Approximating a retarded-advanced differential equation that models human phonation
Teodoro, M. Filomena
2017-11-01
In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.
Rate equation modelling of the optically pumped spin-exchange source
International Nuclear Information System (INIS)
Stenger, J.; Rith, K.
1995-01-01
Sources for spin polarized hydrogen or deuterium, polarized via spin-exchange of a laser optically pumped alkali metal, can be modelled by rate equations. The rate equations for this type of source, operated either with hydrogen or deuterium, are given explicitly with the intention of providing a useful tool for further source optimization and understanding. Laser optical pumping of alkali metal, spin-exchange collisions of hydrogen or deuterium atoms with each other and with alkali metal atoms are included, as well as depolarization due to flow and wall collisions. (orig.)
Modeling tree crown dynamics with 3D partial differential equations.
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.
A Multi-Phase Equation of State and Strength Model for Tin
International Nuclear Information System (INIS)
Cox, G. A.
2006-01-01
This paper considers a multi-phase equation of state and a multi-phase strength model for tin in the β, γ and liquid phases. At a phase transition there are changes in volume, energy, and properties of a material that should be included in an accurate model. The strength model will also be affected by a solid-solid phase transition. For many materials there is a lack of experimental data for strength at high pressures making the derivation of strength parameters for some phases difficult. In the case of tin there are longitudinal sound speed data on the Hugoniot available that have been used here in conjunction with a multi-phase equation of state to derive strength parameters for the γ phase, a phase which does not exist at room temperature and pressure
The solution space of the unitary matrix model string equation and the Sato Grassmannian
International Nuclear Information System (INIS)
Anagnostopoulos, K.N.; Bowick, M.J.; Schwarz, A.
1992-01-01
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equations is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P, 2 - ]=1, with P and 2 - 2x2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n≥0), where L n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model. (orig.)
Directory of Open Access Journals (Sweden)
Wang Woei-Fuh
2008-03-01
Full Text Available Abstract Background With the abundant information produced by microarray technology, various approaches have been proposed to infer transcriptional regulatory networks. However, few approaches have studied subtle and indirect interaction such as genetic compensation, the existence of which is widely recognized although its mechanism has yet to be clarified. Furthermore, when inferring gene networks most models include only observed variables whereas latent factors, such as proteins and mRNA degradation that are not measured by microarrays, do participate in networks in reality. Results Motivated by inferring transcriptional compensation (TC interactions in yeast, a stepwise structural equation modeling algorithm (SSEM is developed. In addition to observed variables, SSEM also incorporates hidden variables to capture interactions (or regulations from latent factors. Simulated gene networks are used to determine with which of six possible model selection criteria (MSC SSEM works best. SSEM with Bayesian information criterion (BIC results in the highest true positive rates, the largest percentage of correctly predicted interactions from all existing interactions, and the highest true negative (non-existing interactions rates. Next, we apply SSEM using real microarray data to infer TC interactions among (1 small groups of genes that are synthetic sick or lethal (SSL to SGS1, and (2 a group of SSL pairs of 51 yeast genes involved in DNA synthesis and repair that are of interest. For (1, SSEM with BIC is shown to outperform three Bayesian network algorithms and a multivariate autoregressive model, checked against the results of qRT-PCR experiments. The predictions for (2 are shown to coincide with several known pathways of Sgs1 and its partners that are involved in DNA replication, recombination and repair. In addition, experimentally testable interactions of Rad27 are predicted. Conclusion SSEM is a useful tool for inferring genetic networks, and the
Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard
2013-01-01
are uncorrelated and provides the possibility to pinpoint model deficiencies. METHODS: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters...... in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. CONCLUSION: This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained...... are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. RESULTS: We found that the transformation of the ODE model into an SDE-GB resulted...
DEFF Research Database (Denmark)
Amado, Cristina; Teräsvirta, Timo
-run and the short-run dynamic behaviour of the volatilities. The structure of the conditional correlation matrix is assumed to be either time independent or to vary over time. We apply our model to pairs of seven daily stock returns belonging to the S&P 500 composite index and traded at the New York Stock Exchange......In this paper we investigate the effects of careful modelling the long-run dynamics of the volatilities of stock market returns on the conditional correlation structure. To this end we allow the individual unconditional variances in Conditional Correlation GARCH models to change smoothly over time...... by incorporating a nonstationary component in the variance equations. The modelling technique to determine the parametric structure of this time-varying component is based on a sequence of specification Lagrange multiplier-type tests derived in Amado and Teräsvirta (2011). The variance equations combine the long...
Averaging of the Equations of the Standard Cosmological Model over Rapid Oscillations
Ignat'ev, Yu. G.; Samigullina, A. R.
2017-11-01
An averaging of the equations of the standard cosmological model (SCM) is carried out. It is shown that the main contribution to the macroscopic energy density of the scalar field comes from its microscopic oscillations with the Compton period. The effective macroscopic equation of state of the oscillations of the scalar field corresponds to the nonrelativistic limit.
Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations
Hou, Thomas Y.; Liu, Pengfei; Wang, Fei
2018-05-01
We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.
Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state
International Nuclear Information System (INIS)
Sharov, G.S.
2016-01-01
Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r s ( z d ). Among the considered models the best value of χ 2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.
Three-dimensional wave-induced current model equations and radiation stresses
Xia, Hua-yong
2017-08-01
After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.
The Cauchy problem for the Bogolyubov hierarchy of equations. The BCS model
International Nuclear Information System (INIS)
Vidybida, A.K.
1975-01-01
A chain of Bogolyubov's kinetic equations for an infinite quantum system of particles distributed in space with the mean density 1/V and interacting with the BCS model operator is considered as a single abstract equation in some countable normalized space bsup(v) of sequences of integral operators. In this case an unique solution of the Cauchy problem has been obtained at arbitrary initial conditions from bsup(v), stationary solutions of the equation have been derived, and the class of the initial conditions which approach to stationary ones is indicated
Generalized isothermal models with strange equation of state
Indian Academy of Sciences (India)
intention to study the Einstein–Maxwell system with a linear equation of state with ... It is our intention to model the interior of a dense realistic star with a general ... The definition m(r) = 1. 2. ∫ r. 0 ω2ρ(ω)dω. (14) represents the mass contained within a radius r which is a useful physical quantity. The mass function (14) has ...
2011-06-01
STRATEGIC IMPLICATIONS OF US FIGHTER FORCE REDUCTIONS: AIR-TO-AIR COMBAT MODELING USING LANCHESTER ...TO-AIR COMBAT MODELING USING LANCHESTER EQUATIONS GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...MODELING USING LANCHESTER EQUATIONS Ronald E. Gilbert, BS, MBA Major, USAF Approved
Radio wave propagation and parabolic equation modeling
Apaydin, Gokhan
2018-01-01
A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...
Estimating structural equation models with non-normal variables by using transformations
Montfort, van K.; Mooijaart, A.; Meijerink, F.
2009-01-01
We discuss structural equation models for non-normal variables. In this situation the maximum likelihood and the generalized least-squares estimates of the model parameters can give incorrect estimates of the standard errors and the associated goodness-of-fit chi-squared statistics. If the sample
Analysis of bilinear relation of a six-vertex model
International Nuclear Information System (INIS)
Korepin, V.E.
1982-01-01
A problem of calculating all matrices of T(μ) monodromy satisfying certain commutation relations for the six-vertex model matrix is considered. The paper presents full description of all accurate L-operators (all monodromy-matrices per one lattice step). It is noted that the a/d function has the simpliest form for L operators, and the corresponding A, B, C, D operators act transitively in rather narrow subspace of the constructed space
Jackson, E. Bruce; Madden, Michael M.; Shelton, Robert; Jackson, A. A.; Castro, Manuel P.; Noble, Deleena M.; Zimmerman, Curtis J.; Shidner, Jeremy D.; White, Joseph P.; Dutta, Doumyo;
2015-01-01
This follow-on paper describes the principal methods of implementing, and documents the results of exercising, a set of six-degree-of-freedom rigid-body equations of motion and planetary geodetic, gravitation and atmospheric models for simple vehicles in a variety of endo- and exo-atmospheric conditions with various NASA, and one popular open-source, engineering simulation tools. This effort is intended to provide an additional means of verification of flight simulations. The models used in this comparison, as well as the resulting time-history trajectory data, are available electronically for persons and organizations wishing to compare their flight simulation implementations of the same models.
Expressions of manipulator kinematic equations via symbolic computation
International Nuclear Information System (INIS)
Sasaki, Shinobu
1993-09-01
While it is simple in principle to determine the position and orientation of the manipulator hand, its computational process has been regarded as extremely laborious since trigonometric functions must be calculated many times in operations of revolute or rotation. Due to development of a general class of kinematic algorithm based on iterative methods, however, we have come to a satisfactory settlement of this problem. In the present article, we consider to construct symbolic kinematic equations in an automatic fashion making use of the algorithm. To this end, recursive expressions are applied to a symbolic computation system REDUCE. As a concrete result, a complete kinematic model for a six-jointed arm having all kinematic attributes is provided. Together with work space analysis, the computer-aided generation of kinematic equations in symbolic form will serve to liberate us from their cumbersome derivations. (author)
Equation-free model reduction for complex dynamical systems
International Nuclear Information System (INIS)
Le Maitre, O. P.; Mathelin, L.; Le Maitre, O. P.
2010-01-01
This paper presents a reduced model strategy for simulation of complex physical systems. A classical reduced basis is first constructed relying on proper orthogonal decomposition of the system. Then, unlike the alternative approaches, such as Galerkin projection schemes for instance, an equation-free reduced model is constructed. It consists in the determination of an explicit transformation, or mapping, for the evolution over a coarse time-step of the projection coefficients of the system state on the reduced basis. The mapping is expressed as an explicit polynomial transformation of the projection coefficients and is computed once and for all in a pre-processing stage using the detailed model equation of the system. The reduced system can then be advanced in time by successive applications of the mapping. The CPU cost of the method lies essentially in the mapping approximation which is performed offline, in a parallel fashion, and only once. Subsequent application of the mapping to perform a time-integration is carried out at a low cost thanks to its explicit character. Application of the method is considered for the 2-D flow around a circular cylinder. We investigate the effectiveness of the reduced model in rendering the dynamics for both asymptotic state and transient stages. It is shown that the method leads to a stable and accurate time-integration for only a fraction of the cost of a detailed simulation, provided that the mapping is properly approximated and the reduced basis remains relevant for the dynamics investigated. (authors)
Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L
2015-01-01
Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model
Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L
2015-01-01
There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.
Integral equation models for the inverse problem of biological ion channel distributions
International Nuclear Information System (INIS)
French, D A; Groetsch, C W
2007-01-01
Olfactory cilia are thin hair-like filaments that extend from olfactory receptor neurons into the nasal mucus. Transduction of an odor into an electrical signal is accomplished by a depolarizing influx of ions through cyclic-nucleotide-gated channels in the membrane that forms the lateral surface of the cilium. In an experimental procedure developed by S. Kleene, a cilium is detached at its base and drawn into a recording pipette. The cilium base is then immersed in a bath of a channel activating agent (cAMP) which is allowed to diffuse into the cilium interior, opening channels as it goes and initiating a transmembrane current. The total current is recorded as a function of time and serves as data for a nonlinear integral equation of the first kind modeling the spatial distribution of ion channels along the length of the cilium. We discuss some linear Fredholm integral equations that result from simplifications of this model. A numerical procedure is proposed for a class of integral equations suggested by this simplified model and numerical results using simulated and laboratory data are presented
Generalized structured component analysis a component-based approach to structural equation modeling
Hwang, Heungsun
2014-01-01
Winner of the 2015 Sugiyama Meiko Award (Publication Award) of the Behaviormetric Society of Japan Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner. Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling provides a detailed account of this novel statistical methodology and its various extensions. The authors present the theoretical underpinnings of generalized structured component analysis and demonstrate how it can be applied to various empirical examples. The book enables quantitative methodologists, applied researchers, and practitioners to grasp the basic concepts behind this new a...
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
International Nuclear Information System (INIS)
Yang Pei; Li Zhibin; Chen Yong
2010-01-01
In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)
Requirements on mechanistic NPP models used in CSS for diagnostics and predictions
International Nuclear Information System (INIS)
Juslin, K.
1996-01-01
Mechanistic models have for several years with good experience been used for operators' support in electric power dispatching centres. Some models of limited scope have already been in use at nuclear power plants. It is considered that also advanced mechanistic models in combination with present computer technology with preference could be used in Computerized Support Systems (CSS) for the assistance of Nuclear Power Plant (NPP) operators. Requirements with respect to accuracy, validity range, speed flexibility and level of detail on the models used for such purposes are discussed. Quality Assurance, Verification and Validation efforts are considered. A long term commitment in the field of mechanistic modelling and real time simulation is considered as the key to successful implementations. The Advanced PROcess Simulation (APROS) code system and simulation environment developed at the Technical Research Centre of Finland (VTT) is intended also for CSS applications in NPP control rooms. (author). 4 refs
q-deformed Weinberg-Salam model and q-deformed Maxwell equations
International Nuclear Information System (INIS)
Alavi, S.A.; Sarbishaei, M.; Mokhtari, A.
2000-01-01
We study the q-deformation of the gauge part of the Weinberg-Salam model and show that the q-deformed theory involves new interactions. We then obtain q-deformed Maxwell equations from which magnetic monopoles appear naturally. (author)
A model for the stochastic origins of Schrodinger's equation
Davidson, Mark P.
2001-01-01
A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.
DEFF Research Database (Denmark)
Costa, Rafael S.; Machado, Daniel; Rocha, Isabel
2010-01-01
, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action......The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters...
Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
International Nuclear Information System (INIS)
Steinacker, Harold
2009-01-01
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.
Structural Equation Modeling with Lisrel: An Initial Vision
Naresh K Malhotra; Evandro Luiz Lopes; Ricardo Teixeira Veiga
2014-01-01
LISREL is considered one of the most robust software packages for Structural Equation Modeling with covariance matrices, while it is also considered complex and difficult to use. In this special issue of the Brazilian Journal of Marketing, we aim to present the main functions of LISREL, its features and, through a didactic example, reduce the perceived difficulty of using it. We also provide helpful guidelines to properly using this technique.
Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.
2013-01-01
The gas holdup time (tM) is a dominant parameter in gas chromatographic retention models. The difference equation (DE) model proposed by Wu et al. (J. Chromatogr. A 2012, http://dx.doi.org/10.1016/j.chroma.2012.07.077) excluded tM. In the present paper, we propose that the relationship between the adjusted retention time tRZ′ and carbon number z of n-alkanes follows a quadratic equation (QE) when an accurate tM is obtained. This QE model is the same as or better than the DE model for an accurate expression of the retention behavior of n-alkanes and model applications. The QE model covers a larger range of n-alkanes with better curve fittings than the linear model. The accuracy of the QE model was approximately 2–6 times better than the DE model and 18–540 times better than the LE model. Standard deviations of the QE model were approximately 2–3 times smaller than those of the DE model. PMID:22989489
Dyson-Schwinger equations for the non-linear σ-model
International Nuclear Information System (INIS)
Drouffe, J.M.; Flyvbjerg, H.
1989-08-01
Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Using of Structural Equation Modeling Techniques in Cognitive Levels Validation
Directory of Open Access Journals (Sweden)
Natalija Curkovic
2012-10-01
Full Text Available When constructing knowledge tests, cognitive level is usually one of the dimensions comprising the test specifications with each item assigned to measure a particular level. Recently used taxonomies of the cognitive levels most often represent some modification of the original Bloom’s taxonomy. There are many concerns in current literature about existence of predefined cognitive levels. The aim of this article is to investigate can structural equation modeling techniques confirm existence of different cognitive levels. For the purpose of the research, a Croatian final high-school Mathematics exam was used (N = 9626. Confirmatory factor analysis and structural regression modeling were used to test three different models. Structural equation modeling techniques did not support existence of different cognitive levels in this case. There is more than one possible explanation for that finding. Some other techniques that take into account nonlinear behaviour of the items as well as qualitative techniques might be more useful for the purpose of the cognitive levels validation. Furthermore, it seems that cognitive levels were not efficient descriptors of the items and so improvements are needed in describing the cognitive skills measured by items.
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
Energy Technology Data Exchange (ETDEWEB)
Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
International Nuclear Information System (INIS)
Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Kim, Seohyun; Lu, Zhenqiu; Cohen, Allan S.
2018-01-01
Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…
Simplified TBA equations of the AdS5 × S5 mirror model
Arutyunov, G.E.; Frolov, S.
2009-01-01
We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS5 × S5 mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies.
Blowup with vorticity control for a 2D model of the Boussinesq equations
Hoang, V.; Orcan-Ekmekci, B.; Radosz, M.; Yang, H.
2018-06-01
We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.
Evaluating Neighborhoods Livability in Nigeria: A Structural Equation Modelling (SEM Approach
Directory of Open Access Journals (Sweden)
Sule Abass Iyanda
2018-01-01
Full Text Available There is a growing concern about city livability around the world and of particular concern is the aspects of the person-environment relationship which encompasses many characteristics suffice to make a place livable. Extant literature provides livability dimensions such as housing unit characteristics, neighborhood facilities, economic vitality and safety environment. These livability dimensions as well as their attributes found in the extant literature have been reported to have high reliability measurement level. Although, various methods have been applied to examine relationships among the variables however structural equation modeling (SEM has been found more holistic as a modeling technique to understand and explain the relationships that may exist among variable measurements. Structural equation modeling simultaneously performs multivariate analysis including multiple regression, path and factor analysis in the cause-effect relationships between latent constructs. Therefore, this study investigates the key factors of livability of planned residential neighborhoods in Minna, Nigeria with the research objectives of – (a to study the livability level of the selected residential neighborhoods, (b to determine the dimensions and indicators which most influence the level of livability in the selected residential neighborhoods, and (c to reliably test the efficacy of structural equation modeling (SEM in the assessment of livability. The methodology adopted in this study includes- Data collection with the aid of structured questionnaire survey administered to the residents of the study area based on stratified random sampling. The data collected was analyzed with the aid of the Statistical Package for Social Sciences (SPSS 22.0 and AMOS 22.0 software for structural equation modeling (a second-order factor. The study revealed that livability as a second-order factor is indicated by economic vitality, safety environment, neighborhood facilities
Modeling adsorption of cationic surfactants at air/water interface without using the Gibbs equation.
Phan, Chi M; Le, Thu N; Nguyen, Cuong V; Yusa, Shin-ichi
2013-04-16
The Gibbs adsorption equation has been indispensable in predicting the surfactant adsorption at the interfaces, with many applications in industrial and natural processes. This study uses a new theoretical framework to model surfactant adsorption at the air/water interface without the Gibbs equation. The model was applied to two surfactants, C14TAB and C16TAB, to determine the maximum surface excesses. The obtained values demonstrated a fundamental change, which was verified by simulations, in the molecular arrangement at the interface. The new insights, in combination with recent discoveries in the field, expose the limitations of applying the Gibbs adsorption equation to cationic surfactants at the air/water interface.
Introduction of the Notion of Differential Equations by Modelling Based Teaching
Budinski, Natalija; Takaci, Djurdjica
2011-01-01
This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…
Study of the Bellman equation in a production model with unstable demand
Obrosova, N. K.; Shananin, A. A.
2014-09-01
A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by the urgency of analyzing well-known problems of functioning low competitive macroeconomic structures. The original formulation of the task represents an infinite-horizon optimal control problem. As a result, the model is formalized in the form of a Bellman equation. It is proved that the corresponding Bellman operator is a contraction and has a unique fixed point in the chosen class of functions. A closed-form solution of the Bellman equation is found using the method of steps. The influence of the credit interest rate on the firm market value assessment is analyzed by applying the developed model.
Modelling of phase equilibria for associating mixtures using an equation of state
International Nuclear Information System (INIS)
Ferreira, Olga; Brignole, Esteban A.; Macedo, Eugenia A.
2004-01-01
In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures
A six-factor model of brand personality and its predictive validity
Directory of Open Access Journals (Sweden)
Živanović Marko
2017-01-01
Full Text Available The study examines applicability and usefulness of HEXACO-based model in the description of brand personality. Following contemporary theoretical developments in human personality research, Study 1 explored the latent personality structure of 120 brands using descriptors of six personality traits as defined in HEXACO model: Honesty-Humility, Emotionality, Extraversion, Agreeableness, Conscientiousness, and Openness. The results of exploratory factor analyses have supported HEXACO personality six-factor structure to a large extent. In Study 2 we addressed the question of predictive validity of HEXACO-based brand personality. Brand personality traits, but predominantly Honesty-Humility, accounted for substantial amount of variance in prediction of important aspects of consumer-brand relationship: attitude toward brand, perceived quality of a brand, and brand loyalty. The implications of applying HEXACO-based brand personality in marketing research are discussed. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 179018 and Grant no. 175012
The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation
Campbell, Joel
2007-01-01
A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
Nonlinear model of a rotating hub-beams structure: Equations of motion
Warminski, Jerzy
2018-01-01
Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.
Physiological breakdown of Jeffrey six constant nanofluid flow in an endoscope with nonuniform wall
Directory of Open Access Journals (Sweden)
S. Nadeem
2015-12-01
Full Text Available This paper analyse the endoscopic effects of peristaltic nanofluid flow of Jeffrey six-constant fluid model in the presence of magnetohydrodynamics flow. The current problem is modeled in the cylindrical coordinate system and exact solutions are managed (where possible under low Reynolds number and long wave length approximation. The influence of emerging parameters on temperature and velocity profile are discussed graphically. The velocity equation is solved analytically by utilizing the homotopy perturbation technique strongly, while the exact solutions are computed from temperature equation. The obtained expressions for velocity , concentration and temperature is sketched during graphs and the collision of assorted parameters is evaluate for transform peristaltic waves. The solution depend on thermophoresis number Nt, local nanoparticles Grashof number Gr, and Brownian motion number Nb. The obtained expressions for the velocity, temperature, and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves.
Chen, Haiwen; Holland, Paul
2010-01-01
In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…
Exact results for the Boltzmann equation and Smoluchowski's coagulation equation
International Nuclear Information System (INIS)
Hendriks, E.M.
1983-01-01
Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)
Structural Equation Modeling with Mplus Basic Concepts, Applications, and Programming
Byrne, Barbara M
2011-01-01
Modeled after Barbara Byrne's other best-selling structural equation modeling (SEM) books, this practical guide reviews the basic concepts and applications of SEM using Mplus Versions 5 & 6. The author reviews SEM applications based on actual data taken from her own research. Using non-mathematical language, it is written for the novice SEM user. With each application chapter, the author "walks" the reader through all steps involved in testing the SEM model including: an explanation of the issues addressed illustrated and annotated testing of the hypothesized and post hoc models expl
Modelling opinion formation by means of kinetic equations
Boudin , Laurent; Salvarani , Francesco
2010-01-01
In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics.
Structural Equation Modeling with Lisrel: An Initial Vision
Directory of Open Access Journals (Sweden)
Naresh K Malhotra
2014-05-01
Full Text Available LISREL is considered one of the most robust software packages for Structural Equation Modeling with covariance matrices, while it is also considered complex and difficult to use. In this special issue of the Brazilian Journal of Marketing, we aim to present the main functions of LISREL, its features and, through a didactic example, reduce the perceived difficulty of using it. We also provide helpful guidelines to properly using this technique.
Directory of Open Access Journals (Sweden)
Li-ren Yu
2012-03-01
Full Text Available This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k˜−ε˜,k˜−w˜, and k˜−ω˜ , were used to close the non-simplified quasi-three dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k˜−ω˜ model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.
Modeling for cardiac excitation propagation based on the Nernst-Planck equation and homogenization.
Okada, Jun-ichi; Sugiura, Seiryo; Hisada, Toshiaki
2013-06-01
The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.
Brane solutions of a spherical sigma model in six dimensions
International Nuclear Information System (INIS)
Lee, Hyun Min; Papazoglou, Antonios
2005-01-01
We explore solutions of six-dimensional gravity coupled to a non-linear sigma model, in the presence of codimension-two branes. We investigate the compactifications induced by a spherical scalar manifold and analyze the conditions under which they are of finite volume and singularity free. We discuss the issue of single-valuedness of the scalar fields and provide some special embedding of the scalar manifold to the internal space which solves this problem. These brane solutions furnish some self-tuning features, however they do not provide a satisfactory explanation of the vanishing of the effective four-dimensional cosmological constant. We discuss the properties of this model in relation with the self-tuning example based on a hyperbolic sigma model
Matrix Solution of Coupled Differential Equations and Looped Car Following Models
McCartney, Mark
2008-01-01
A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…
Equations of motion for a spectrum-generating algebra: Lipkin-Meshkov-Glick model
International Nuclear Information System (INIS)
Rosensteel, G; Rowe, D J; Ho, S Y
2008-01-01
For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 10 6 , computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point
A Critical Technical Review of Six Hazard Assessment Models
1975-12-01
temperature is 3000K. Vi The equation describing flame length is taken from a paper of Hawthorne, Weddell, and Hottel [3] who obtained the equation by...should be noted that the flame length given by equation (6.1) in AMSHAH is independent of the flow rate; flame length independence of flow rate does not...experiments and analyses upon which the formula for flame length is based are for jets issuing from circular orifices. Substantial departures from this
Directory of Open Access Journals (Sweden)
L. M. Kistler
Full Text Available During the main and early recovery phase of a geomagnetic storm on February 18, 1998, the Equator-S ion composition instrument (ESIC observed spectral features which typically represent the differences in loss along the drift path in the energy range (5–15 keV/e where the drift changes from being E × B dominated to being gradient and curvature drift dominated. We compare the expected energy spectra modeled using a Volland-Stern electric field and a Weimer electric field, assuming charge exchange along the drift path, with the observed energy spectra for H^{+} and O^{+}. We find that using the Weimer electric field gives much better agreement with the spectral features, and with the observed losses. Neither model, however, accurately predicts the energies of the observed minima.
Key words. Magnetospheric physics (energetic particles trapped; plasma convection; storms and substorms
Investigating market efficiency through a forecasting model based on differential equations
de Resende, Charlene C.; Pereira, Adriano C. M.; Cardoso, Rodrigo T. N.; de Magalhães, A. R. Bosco
2017-05-01
A new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market. Its predictive power showed statistically to be higher than the one of a completely random model, signaling towards the presence of arbitrage opportunities. Conditions for accuracy to be enhanced are investigated, and application of the model as part of a trading strategy is discussed.
On the specification of structural equation models for ecological systems
Grace, James B.; Anderson, T. Michael; Olff, Han; Scheiner, Samuel M.
The use of structural equation modeling (SEM) is often motivated by its utility for investigating complex networks of relationships, but also because of its promise as a means of representing theoretical Concepts using latent variables. In this paper, we discuss characteristics of ecological theory
EVALUATION OF DYNAMIC INDICATORS OF SIX-AXLE LOCOMOTIVE
Directory of Open Access Journals (Sweden)
S. V. Myamlin
2015-04-01
Full Text Available Purpose. The paper is devoted to dynamic characteristics evaluation of the locomotive with prospective design and determination the feasibility of its use on the Ukrainian railways. Methodology. The methods of mathematical and computer modeling of the dynamics of railway vehicles, as well as methods for the numerical integration of systems of ordinary nonlinear differential equations were used to solve the problem. Findings. The calculated diagram of a locomotive on three-axle bogies was built to solve the problem, and it is a system of rigid bodies connected by various elements of rheology. The mathematical model of the locomotive movement, allowing studying its spatial vibrations at driving on straight and curved sections of the track with random irregularities in plan and profile was developed with use of this calculated diagram. At compiling the mathematical model took into account both geometric (nonlinearity profile of the wheel roll surface and physical nonlinearity of the system (the work forces of dry friction, nonlinearity characteristics of interaction forces between wheels and rails. The multivariate calculations, which allowed assessing the dynamic qualities of the locomotive at its movement along straight and curved sections of the track, were realized with the use of computer modeling. The smoothness movement indicators of the locomotive in horizontal and vertical planes, frame strength, coefficients of vertical dynamics in the first and second stages of the suspension, the load factor of resistance against the derailment of the wheel from the rail were determined at the period of research. In addition, a comparison of the obtained results with similar characteristics is widely used on the Ukrainian railways in six-axle locomotive TE 116. The influence of speed and technical state of the track on the locomotive traffic safety was determined.Originality. A mathematical model of the spatial movement of a six-axle locomotive with
Hydrodynamic Equations for Flocking Models without Velocity Alignment
Peruani, Fernando
2017-10-01
The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previous reported results. In particular, we show that three distinct macroscopic collective behaviors can be observed: i) the coarsening of aggregates with no orientational order, ii) the emergence of static, elongated nematic bands, and iii) the formation of moving, locally polar structures, which we call worms. The derived hydrodynamic equations indicate that active particles interacting via position-based interactions belong to a distinct class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems.
Undergraduate Students' Mental Operations in Systems of Differential Equations
Whitehead, Karen; Rasmussen, Chris
2003-01-01
This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
six six six paradox : [luuletused] / Triin Tasuja
Tasuja, Triin
2008-01-01
Sisu: six six six paradox ; cat stevens ; "vahel tundub, et mu ümber..." ; sääse ; Salaalaealised ; kolkalapsed ; longin mööda lumiseid tänavaid ; punkrock dekadents ; "Igast kirjaneitsist..." ; "mina olengi see saikochick..."
Modelling with the master equation solution methods and applications in social and natural sciences
Haag, Günter
2017-01-01
This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience...
Nonlinear integral equations for thermodynamics of the sl(r + 1) Uimin-Sutherland model
International Nuclear Information System (INIS)
Tsuboi, Zengo
2003-01-01
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the those from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIEs). In particular, a subset of these NLIEs forms a system of NLIEs which contains only a finite number of unknown functions. For r=1, this subset of NLIEs reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIEs is clarified. Based on our new NLIEs, we also calculate the high-temperature expansion of the free energy
semPLS: Structural Equation Modeling Using Partial Least Squares
Directory of Open Access Journals (Sweden)
Armin Monecke
2012-05-01
Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.
Applying a Hybrid MCDM Model for Six Sigma Project Selection
Directory of Open Access Journals (Sweden)
Fu-Kwun Wang
2014-01-01
Full Text Available Six Sigma is a project-driven methodology; the projects that provide the maximum financial benefits and other impacts to the organization must be prioritized. Project selection (PS is a type of multiple criteria decision making (MCDM problem. In this study, we present a hybrid MCDM model combining the decision-making trial and evaluation laboratory (DEMATEL technique, analytic network process (ANP, and the VIKOR method to evaluate and improve Six Sigma projects for reducing performance gaps in each criterion and dimension. We consider the film printing industry of Taiwan as an empirical case. The results show that our study not only can use the best project selection, but can also be used to analyze the gaps between existing performance values and aspiration levels for improving the gaps in each dimension and criterion based on the influential network relation map.
Some New Integrable Equations from the Self-Dual Yang-Mills Equations
International Nuclear Information System (INIS)
Ivanova, T.A.; Popov, A.D.
1994-01-01
Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs
Analytic solution of vector model kinetic equations with constant kernel and their applications
International Nuclear Information System (INIS)
Latyshev, A.V.
1993-01-01
For the first time exact solutions the heif-space boundary value problems for model kinetic equations is obtained. Here x > 0, μ is an element of (-∞, 0) union (0, +∞), Σ = diag {σ 1 , σ 2 }, C = [c ij ] - 2 x 2-matrix, Ψ (x, μ) is vector-column with elements ψ 1 and ψ 2 . Exact solution of the diffusion slip flow of the binary gas mixture as a application for the model Boltzmann equation with collision operator in the McCormack's form is found. 18 refs
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
International Nuclear Information System (INIS)
Aktaa, J.; Weth, A. von der
2000-01-01
The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations
Acidity in DMSO from the embedded cluster integral equation quantum solvation model.
Heil, Jochen; Tomazic, Daniel; Egbers, Simon; Kast, Stefan M
2014-04-01
The embedded cluster reference interaction site model (EC-RISM) is applied to the prediction of acidity constants of organic molecules in dimethyl sulfoxide (DMSO) solution. EC-RISM is based on a self-consistent treatment of the solute's electronic structure and the solvent's structure by coupling quantum-chemical calculations with three-dimensional (3D) RISM integral equation theory. We compare available DMSO force fields with reference calculations obtained using the polarizable continuum model (PCM). The results are evaluated statistically using two different approaches to eliminating the proton contribution: a linear regression model and an analysis of pK(a) shifts for compound pairs. Suitable levels of theory for the integral equation methodology are benchmarked. The results are further analyzed and illustrated by visualizing solvent site distribution functions and comparing them with an aqueous environment.
Characteristic evolutions in numerical relativity using six angular patches
International Nuclear Information System (INIS)
Reisswig, Christian; Bishop, Nigel T; Lai, Chi Wai; Thornburg, Jonathan; Szilagyi, Bela
2007-01-01
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50
Characteristic evolutions in numerical relativity using six angular patches
Energy Technology Data Exchange (ETDEWEB)
Reisswig, Christian [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Bishop, Nigel T [Department of Mathematical Sciences, University of South Africa, PO Box 392, Unisa 0003, South Africa (South Africa); Lai, Chi Wai [Department of Mathematical Sciences, University of South Africa, PO Box 392, Unisa 0003, South Africa (South Africa); Thornburg, Jonathan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Szilagyi, Bela [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)
2007-06-21
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.
Stochastic modeling of mode interactions via linear parabolized stability equations
Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo
2017-11-01
Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.
Effective dark energy equation of state in interacting dark energy models
International Nuclear Information System (INIS)
Avelino, P.P.; Silva, H.M.R. da
2012-01-01
In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.
Effective dark energy equation of state in interacting dark energy models
Energy Technology Data Exchange (ETDEWEB)
Avelino, P.P., E-mail: ppavelin@fc.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Silva, H.M.R. da, E-mail: hilberto.silva@gmail.com [Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2012-07-24
In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.
IT vendor selection model by using structural equation model & analytical hierarchy process
Maitra, Sarit; Dominic, P. D. D.
2012-11-01
Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.
Reflected stochastic differential equation models for constrained animal movement
Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.
2017-01-01
Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.
Kinematic equations for resolved-rate control of an industrial robot arm
Barker, L. K.
1983-01-01
An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
International Nuclear Information System (INIS)
Ding Qing
2007-01-01
We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model
Barbarossa, Maria Vittoria; Kuttler, Christina; Zinsl, Jonathan
2012-04-01
In this work we present a mathematical model for tumor growth based on the biology of the cell cycle. For an appropriate description of the effects of phase-specific drugs, it is necessary to look at the cell cycle and its phases. Our model reproduces the dynamics of three different tumor cell populations: quiescent cells, cells during the interphase and mitotic cells. Starting from a partial differential equations (PDEs) setting, a delay differential equations (DDE) model is derived for an easier and more realistic approach. Our equations also include interactions of tumor cells with immune system effectors. We investigate the model both from the analytical and the numerical point of view, give conditions for positivity of solutions and focus on the stability of the cancer-free equilibrium. Different immunotherapeutic strategies and their effects on the tumor growth are considered, as well.
On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations
International Nuclear Information System (INIS)
Rozikov, Utkir A.; Eshkobilov, Yusup Kh.
2010-01-01
We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. We reduce the problem of describing the 'splitting Gibbs measures' of the model to the description of the solutions of some nonlinear integral equation. For k = 1 we show that the integral equation has a unique solution. In case k ≥ 2 some models (with the set [0, 1] of spin values) which have a unique splitting Gibbs measure are constructed. Also for the Potts model with uncountable set of spin values it is proven that there is unique splitting Gibbs measure.
Cuenca-Carlino, Yojanna; Freeman-Green, Shaqwana; Stephenson, Grant W.; Hauth, Clara
2016-01-01
Six middle school students identified as having a specific learning disability or at risk for mathematical difficulties were taught how to solve multi-step equations by using the self-regulated strategy development (SRSD) model of instruction. A multiple-probe-across-pairs design was used to evaluate instructional effects. Instruction was provided…
Sensitivity Analysis in Structural Equation Models: Cases and Their Influence
Pek, Jolynn; MacCallum, Robert C.
2011-01-01
The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model…
Anti-Transgender Prejudice: A Structural Equation Model of Associated Constructs
Tebbe, Esther N.; Moradi, Bonnie
2012-01-01
This study aimed to identify theoretically relevant key correlates of anti-transgender prejudice. Specifically, structural equation modeling was used to test the unique relations of anti-lesbian, gay, and bisexual (LGB) prejudice; traditional gender role attitudes; need for closure; and social dominance orientation with anti-transgender prejudice.…
Implementation of two-equation soot flamelet models for laminar diffusion flames
Energy Technology Data Exchange (ETDEWEB)
Carbonell, D.; Oliva, A.; Perez-Segarra, C.D. [Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), ETSEIAT, Colom 11, E-08222, Terrassa (Barcelona) (Spain)
2009-03-15
The two-equation soot model proposed by Leung et al. [K.M. Leung, R.P. Lindstedt, W.P. Jones, Combust. Flame 87 (1991) 289-305] has been derived in the mixture fraction space. The model has been implemented using both Interactive and Non-Interactive flamelet strategies. An Extended Enthalpy Defect Flamelet Model (E-EDFM) which uses a flamelet library obtained neglecting the soot formation is proposed as a Non-Interactive method. The Lagrangian Flamelet Model (LFM) is used to represent the Interactive models. This model uses direct values of soot mass fraction from flamelet calculations. An Extended version (E-LFM) of this model is also suggested in which soot mass fraction reaction rates are used from flamelet calculations. Results presented in this work show that the E-EDFM predict acceptable results. However, it overpredicts the soot volume fraction due to the inability of this model to couple the soot and gas-phase mechanisms. It has been demonstrated that the LFM is not able to predict accurately the soot volume fraction. On the other hand, the extended version proposed here has been shown to be very accurate. The different flamelet mathematical formulations have been tested and compared using well verified reference calculations obtained solving the set of the Full Transport Equations (FTE) in the physical space. (author)
Development of a Mathematical Model for Multivariate Process by Balanced Six Sigma
Directory of Open Access Journals (Sweden)
Díaz-Castellanos Elizabeth Eugenia
2015-07-01
Full Text Available The Six Sigma methodology is widely used in business to improve quality, increase productivity and lower costs, impacting on business improvement. However, today the challenge is to use those tools for improvements that will have a direct impact on the differentiation of value, which requires the alignment of Six Sigma with the competitive strategies of the organization.Hence the importance of a strategic management system to measure, analyze, improve and control corporate performance, while setting out responsibilities of leadership and commitment. The specific purpose of this research is to provide a mathematical model through the alignment of strategic objectives (Balanced Scorecard and tools for productivity improvement (Six Sigma for processes with multiple answers, which is sufficiently robust so that it can serve as basis for application in manufacturing and thus effectively link strategy performance and customer satisfaction. Specifically we worked with a case study: Córdoba, Ver. The model proposes that is the strategy, performance and customer satisfaction are aligned, the organization will benefit from the intense relationship between process performance and strategic initiatives. These changes can be measured by productivity and process metrics such as cycle time, production rates, production efficiency and percentage of reprocessing, among others.
Superstring motivated gauge models based on a rank six subgroup of E6
International Nuclear Information System (INIS)
Lazarides, G.; Panagiotakopoulos, C.; Shafi, Q.
1987-01-01
We discuss gauge models based on a superstring motivated rank six subgroup of E 6 . Lepton number is an accidental unbroken symmetry of the models which leads to an essential stable proton. One of the neutral gauge bosons couples to B-L and may have mass below a TeV. (orig.)
International Nuclear Information System (INIS)
Ng, Felix S.L.
2016-01-01
We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.
The state equation of Yang-Mills field dark energy models
International Nuclear Information System (INIS)
Zhao Wen; Zhang Yang
2006-01-01
In this paper, we study the possibility of building Yang-Mills (YM) field dark energy models with equation of state (EoS) crossing -1, and find that it cannot be realized by the single YM field models, no matter what kind of Lagrangian or initial condition. But the states of -1 -1 to <-1, and it will go to the critical state of ω = -1 with the expansion of the universe, which character is the same as the single YM field models, and the big rip is naturally avoided
Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang
2006-01-01
This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…
Parameter Estimation of Partial Differential Equation Models.
Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab
2013-01-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.
Constitutive equations for two-phase flows
International Nuclear Information System (INIS)
Boure, J.A.
1974-12-01
The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr
Modeling and Robust Trajectory Tracking Control for a Novel Six-Rotor Unmanned Aerial Vehicle
Directory of Open Access Journals (Sweden)
Chengshun Yang
2013-01-01
Full Text Available Modeling and trajectory tracking control of a novel six-rotor unmanned aerial vehicle (UAV is concerned to solve problems such as smaller payload capacity and lack of both hardware redundancy and anticrosswind capability for quad-rotor. The mathematical modeling for the six-rotor UAV is developed on the basis of the Newton-Euler formalism, and a second-order sliding-mode disturbance observer (SOSMDO is proposed to reconstruct the disturbances of the rotational dynamics. In consideration of the under-actuated and strong coupling properties of the six-rotor UAV, a nested double loops trajectory tracking control strategy is adopted. In the outer loop, a position error PID controller is designed, of which the task is to compare the desired trajectory with real position of the six-rotor UAV and export the desired attitude angles to the inner loop. In the inner loop, a rapid-convergent nonlinear differentiator (RCND is proposed to calculate the derivatives of the virtual control signal, instead of using the analytical differentiation, to avoid “differential expansion” in the procedure of the attitude controller design. Finally, the validity and effectiveness of the proposed technique are demonstrated by the simulation results.
An improved nucleate boiling design equation
International Nuclear Information System (INIS)
Basu, D.K.; Pinder, K.L.
1976-01-01
The effect of varying ΔT, the primary variable, on the value of heat transfer coefficient (h) in nucleate boiling is discussed. The three-parameter quadratic equation, h=P 1 + P 2 (ΔT) + P 3 (ΔT) 2 (where the constants, P 1 ,P 2 ,P 3 are functions of pressure, liquid properties and surface properties of the heater) is suggested. Ten sets of data at atmospheric pressure from six different workers and two more sets for pressure variation have been tested. The above quadratic equation fits the experimental data better than the existing two-parameter power relation, h=C(ΔT)sup(n) (where C is constant). The values of the three coeffcients in the quadratic equations are dependent on pressure, liquid properties and surface properties. A generalized empirical equation has been derived, which fits the selected pressure data well. (author)
Application of Peleg\\'s Equation to Model Water Absorption in ...
African Journals Online (AJOL)
Sorghum and millet water absorption characteristics at temperature range 20 to 500C were investigated using the Peleg\\'s model or equation. Two sorghum varieties and one pearl millet variety were used in this investigation. Water absorption characteristics of the grain were investigated by soaking samples of the grain in ...
Analysing outsourcing policies in an asset management context : A six-stage model
Schoenmaker, R.; Verlaan, J.G.
2013-01-01
Asset managers of civil infrastructure are increasingly outsourcing their maintenance. Whereas maintenance is a cyclic process, decisions to outsource decisions are often project-based, and confusing the discussion on the degree of outsourcing. This paper presents a six-stage model that facilitates
Gas-evolution oscillators. 10. A model based on a delay equation
Energy Technology Data Exchange (ETDEWEB)
Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)
1992-09-17
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.
Gas-evolution oscillators. 10. A model based on a delay equation
International Nuclear Information System (INIS)
Bar-Eli, K.; Noyes, R.M.
1992-01-01
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas
Petko, Dominik; Prasse, Doreen; Cantieni, Andrea
2018-01-01
Decades of research have shown that technological change in schools depends on multiple interrelated factors. Structural equation models explaining the interplay of factors often suffer from high complexity and low coherence. To reduce complexity, a more robust structural equation model was built with data from a survey of 349 Swiss primary school…
Effective methods of solving of model equations of certain class of thermal systems
International Nuclear Information System (INIS)
Lach, J.
1985-01-01
A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying
2018-04-01
Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.
Bethe ansatz and ordinary differential equation correspondence for degenerate Gaudin models
El Araby, Omar; Gritsev, Vladimir; Faribault, Alexandre
2012-03-01
In this work, we generalize the numerical approach to Gaudin models developed earlier by us [Faribault, El Araby, Sträter, and Gritsev, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.235124 83, 235124 (2011)] to degenerate systems, showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non-negligible fraction, they also allow us to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce an inversion method based on a basis of barycentric polynomials that leads to a more stable and efficient root extraction, which most importantly avoids the necessity of working with arbitrary precision. As an example, we show the results of our procedure applied to the Richardson model on a square lattice.
International Nuclear Information System (INIS)
Granita; Bahar, A.
2015-01-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
Computationally efficient statistical differential equation modeling using homogenization
Hooten, Mevin B.; Garlick, Martha J.; Powell, James A.
2013-01-01
Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.
Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations
Thieulot, C; Janssen, LPBM; Espanol, P
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Espanol and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by
Robust estimation for ordinary differential equation models.
Cao, J; Wang, L; Xu, J
2011-12-01
Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data. © 2011, The International Biometric Society.
NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models
Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.
2014-01-01
The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.
Hadronic equation of state in the statistical bootstrap model and linear graph theory
International Nuclear Information System (INIS)
Fre, P.; Page, R.
1976-01-01
Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed
On an adaptive time stepping strategy for solving nonlinear diffusion equations
International Nuclear Information System (INIS)
Chen, K.; Baines, M.J.; Sweby, P.K.
1993-01-01
A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs
Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.
2008-01-01
Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…
Directory of Open Access Journals (Sweden)
Masuda Kazuhiko
2016-01-01
Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.
Building Context with Tumor Growth Modeling Projects in Differential Equations
Beier, Julie C.; Gevertz, Jana L.; Howard, Keith E.
2015-01-01
The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss…
OpenMx: An Open Source Extended Structural Equation Modeling Framework
Boker, Steven; Neale, Michael; Maes, Hermine; Wilde, Michael; Spiegel, Michael; Brick, Timothy; Spies, Jeffrey; Estabrook, Ryne; Kenny, Sarah; Bates, Timothy; Mehta, Paras; Fox, John
2011-01-01
OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…
A Structural Equation Modelling of the Academic Self-Concept Scale
Matovu, Musa
2014-01-01
The study aimed at validating the academic self-concept scale by Liu and Wang (2005) in measuring academic self-concept among university students. Structural equation modelling was used to validate the scale which was composed of two subscales; academic confidence and academic effort. The study was conducted on university students; males and…
Energy Technology Data Exchange (ETDEWEB)
Dana, Scott [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Van Dam, Jeroen J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Damiani, Rick R [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2018-04-24
As part of an ongoing effort to improve the modeling and prediction of small wind turbine dynamics, the National Renewable Energy Laboratory (NREL) tested a small horizontal-axis wind turbine in the field at the National Wind Technology Center. The test turbine was a 2.1-kW downwind machine mounted on an 18-m multi-section fiberglass composite tower. The tower was instrumented and monitored for approximately 6 months. The collected data were analyzed to assess the turbine and tower loads and further validate the simplified loads equations from the International Electrotechnical Commission (IEC) 61400-2 design standards. Field-measured loads were also compared to the output of an aeroelastic model of the turbine. In particular, we compared fatigue loads as measured in the field, predicted by the aeroelastic model, and calculated using the simplified design equations. Ultimate loads at the tower base were assessed using both the simplified design equations and the aeroelastic model output. The simplified design equations in IEC 61400-2 do not accurately model fatigue loads and a discussion about the simplified design equations is discussed.
Supersymmetric two-particle equations
International Nuclear Information System (INIS)
Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.
1986-01-01
In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found
Structural equation modelling based data fusion for technology forecasting: A generic framework
CSIR Research Space (South Africa)
Staphorst, L
2013-07-01
Full Text Available to explain the variations in independent variables as functions (commonly referred to regression functions) of variations in dependent variables [13]. With this knowledge it is then possible to perform prediction and forecasting of the values that dependent....G.; “A General Method for Estimating a Linear Structural Equation System,” in Structural Equation Models in the Social Sciences, eds.: A.S. Goldberger and O. D. Duncan, New York: Seminar, 1973. [15] Steinberg, A.N. and Rogova, G.; "Situation...
International Nuclear Information System (INIS)
Parisot, M.
2011-01-01
This work is dedicated study of a problem resulting from plasma physics: the thermal transfer of electrons in a plasma close to equilibrium Maxwellian. Firstly, a dimensional study of the Vlasov-Fokker-Planck-Maxwell system is performed, allowing one hand to identify a physically relevant parameter of scale and also to define mathematically the contours of validity domain. The asymptotic regime called Spitzer-Harm is studied for a relatively general class of collision operator. The following part of this work is devoted to the derivation and study of the hydrodynamic limit of the system of Vlasov-Maxwell-Landau outside the strictly asymptotic. A model proposed by Schurtz and Nicolais located in this context and analyzed. The particularity of this model lies in the application of a delocalization operation in the heat flux. The link with non-local models of Luciani and Mora is established as well as mathematics properties as the principle of maximum and entropy dissipation. Then a formal derivation from the Vlasov equations with a simplified collision operator, is proposed. The derivation, inspired by the recent work of D. Levermore, involves decomposition methods according to the spherical harmonics and methods of closing called diffusion methods. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular a new hydrodynamic system integro-differential by nature, is proposed. The Schurtz and Nicolai model appears as a simplification of the system resulting from the derivation, assuming a steady flow of heat. The above results are then generalized to account for the internal energy dependence which appears naturally in the equation establishment. The existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted was the implementation of a specific numerical scheme to solve these models. We propose a finite volume approach can be
A generalized master equation approach to modelling anomalous transport in animal movement
International Nuclear Information System (INIS)
Giuggioli, Luca; Sevilla, Francisco J; Kenkre, V M
2009-01-01
We present some models of random walks with internal degrees of freedom that have the potential to find application in the context of animal movement and stochastic search. The formalism we use is based on the generalized master equation which is particularly convenient here because of its inherent coarse-graining procedure whereby a random walker position is averaged over the internal degrees of freedom. We show some instances in which non-local jump probabilities emerge from the coupling of the motion to the internal degrees of freedom, and how the tuning of one parameter can give rise to sub-, super- and normal diffusion at long times. Remarks on the relation between the generalized master equation, continuous time random walks and fractional diffusion equations are also presented.
Prescriptive Statements and Educational Practice: What Can Structural Equation Modeling (SEM) Offer?
Martin, Andrew J.
2011-01-01
Longitudinal structural equation modeling (SEM) can be a basis for making prescriptive statements on educational practice and offers yields over "traditional" statistical techniques under the general linear model. The extent to which prescriptive statements can be made will rely on the appropriate accommodation of key elements of research design,…
MODELING SUSTAINABLE DEVELOPMENT OF THE ARCTIC REGION OF RUSSIA
Directory of Open Access Journals (Sweden)
K. N. Kikkas
2015-01-01
Full Text Available The article describes a model of six econometric equations, designed for the analysis of the sustainability of development in the Arctic region of the Russian Federation - Chukotka Autonomous Okrug. The article analyzes the spheres of human activity in the Chukchi Autonomous District: social, industrial, natural resources. Each sphere is estimated indicators. The theoretical views of various researchers on sustainable development and defi nes the concept of sustainable development of the spheres of human activity in the Arctic region. Under the sustainable development of the Arctic region of space refers to such changes in the indices of spheres of human activity in the region, which increase the potential for human development. The numerical value of the potential of human development is estimated Human Development Index. The article describes the methodological principles of constructing a model of six equations econometric analysis of the sustainable development of the Arctic region. Each of the six equations presented in the form of ADL-model, because it allows us to estimate the dependence of ADL values of the spheres of human activity in the region from the current and past values of the series of other indicators. Selected endogenous and exogenous variables for the model. We discuss the algorithm for fi nding the model parameters. On the basis of the Chukotka Autonomous Okrug are six coeffi cients of econometric equations. The analysis of the results of the decision model. Methodological principles and results of the decision model can be used to develop strategies for sustainable development of the municipality, a separate Arctic, or a combination of all the Arctic regions of Russia.
Putting hydrological modelling practice to the test
Melsen, Lieke Anna
2017-01-01
Six steps can be distinguished in the process of hydrological modelling: the perceptual model (deciding on the processes), the conceptual model (deciding on the equations), the procedural model (get the code to run on a computer), calibration (identify the parameters), evaluation (confronting
Briggs, Andrew H; Baker, Timothy; Risebrough, Nancy A; Chambers, Mike; Gonzalez-McQuire, Sebastian; Ismaila, Afisi S; Exuzides, Alex; Colby, Chris; Tabberer, Maggie; Muellerova, Hana; Locantore, Nicholas; Rutten van Mölken, Maureen P M H; Lomas, David A
2017-05-01
The recent joint International Society for Pharmacoeconomics and Outcomes Research / Society for Medical Decision Making Modeling Good Research Practices Task Force emphasized the importance of conceptualizing and validating models. We report a new model of chronic obstructive pulmonary disease (COPD) (part of the Galaxy project) founded on a conceptual model, implemented using a novel linked-equation approach, and internally validated. An expert panel developed a conceptual model including causal relationships between disease attributes, progression, and final outcomes. Risk equations describing these relationships were estimated using data from the Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints (ECLIPSE) study, with costs estimated from the TOwards a Revolution in COPD Health (TORCH) study. Implementation as a linked-equation model enabled direct estimation of health service costs and quality-adjusted life years (QALYs) for COPD patients over their lifetimes. Internal validation compared 3 years of predicted cohort experience with ECLIPSE results. At 3 years, the Galaxy COPD model predictions of annual exacerbation rate and annual decline in forced expiratory volume in 1 second fell within the ECLIPSE data confidence limits, although 3-year overall survival was outside the observed confidence limits. Projections of the risk equations over time permitted extrapolation to patient lifetimes. Averaging the predicted cost/QALY outcomes for the different patients within the ECLIPSE cohort gives an estimated lifetime cost of £25,214 (undiscounted)/£20,318 (discounted) and lifetime QALYs of 6.45 (undiscounted/5.24 [discounted]) per ECLIPSE patient. A new form of model for COPD was conceptualized, implemented, and internally validated, based on a series of linked equations using epidemiological data (ECLIPSE) and cost data (TORCH). This Galaxy model predicts COPD outcomes from treatment effects on disease attributes such as lung function
Modeling the Informal Economy in Mexico. A Structural Equation Approach
Brambila Macias, Jose
2008-01-01
This paper uses annual data for the period 1970-2006 in order to estimate and investigate the evolution of the Mexican informal economy. In order to do so, we model the informal economy as a latent variable and try to explain it through relationships between possible cause and indicator variables using structural equation modeling (SEM). Our results indicate that the Mexican informal sector at the beginning of the 1970’s initially accounted for 40 percent of GDP while slightly decreasing to s...
The Analysis of Organizational Diagnosis on Based Six Box Model in Universities
Hamid, Rahimi; Siadat, Sayyed Ali; Reza, Hoveida; Arash, Shahin; Ali, Nasrabadi Hasan; Azizollah, Arbabisarjou
2011-01-01
Purpose: The analysis of organizational diagnosis on based six box model at universities. Research method: Research method was descriptive-survey. Statistical population consisted of 1544 faculty members of universities which through random strafed sampling method 218 persons were chosen as the sample. Research Instrument were organizational…
Fast integration-based prediction bands for ordinary differential equation models.
Hass, Helge; Kreutz, Clemens; Timmer, Jens; Kaschek, Daniel
2016-04-15
To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models. In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points. The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org helge.hass@fdm.uni-freiburg.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e
Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation
Vitanov, Nikolay K.; Dimitrova, Zlatinka I.
2018-03-01
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.
Neutron star evolutions using tabulated equations of state with a new execution model
Anderson, Matthew; Kaiser, Hartmut; Neilsen, David; Sterling, Thomas
2012-03-01
The addition of nuclear and neutrino physics to general relativistic fluid codes allows for a more realistic description of hot nuclear matter in neutron star and black hole systems. This additional microphysics requires that each processor have access to large tables of data, such as equations of state, and in large simulations the memory required to store these tables locally can become excessive unless an alternative execution model is used. In this talk we present neutron star evolution results obtained using a message driven multi-threaded execution model known as ParalleX as an alternative to using a hybrid MPI-OpenMP approach. ParalleX provides the user a new way of computation based on message-driven flow control coordinated by lightweight synchronization elements which improves scalability and simplifies code development. We present the spectrum of radial pulsation frequencies for a neutron star with the Shen equation of state using the ParalleX execution model. We present performance results for an open source, distributed, nonblocking ParalleX-based tabulated equation of state component capable of handling tables that may even be too large to read into the memory of a single node.
Structural Equation Models in a Redundancy Analysis Framework With Covariates.
Lovaglio, Pietro Giorgio; Vittadini, Giorgio
2014-01-01
A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects. To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.
Acoustic 3D modeling by the method of integral equations
Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.
2018-02-01
This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.
Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model
Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix
2012-01-01
We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.
Neutron stars with equation of state given by nuclear Thomas-Fermi model
International Nuclear Information System (INIS)
Chung, K.C.; Kodama, T.
1978-01-01
A equation of state for neutron gas, based on Thomas-Fermi model, is used to recalculate the maximum mass of neutron stars. The complete equation of state is found to present a first order phase transition between the subnuclear regime without free neutron and the nuclear regime. This suggests that the sudden disintegration of the neutron-rich-nuclei may be very competitive with relation to the continuous neutron drip process. The mass limit for neutron stars was found to be 3.26 M 0 [pt
Fast Estimation of Strains for Cross-Beams Six-Axis Force/Torque Sensors by Mechanical Modeling
Directory of Open Access Journals (Sweden)
Junqing Ma
2013-05-01
Full Text Available Strain distributions are crucial criteria of cross-beams six-axis force/torque sensors. The conventional method for calculating the criteria is to utilize Finite Element Analysis (FEA to get numerical solutions. This paper aims to obtain analytical solutions of strains under the effect of external force/torque in each dimension. Genetic mechanical models for cross-beams six-axis force/torque sensors are proposed, in which deformable cross elastic beams and compliant beams are modeled as quasi-static Timoshenko beam. A detailed description of model assumptions, model idealizations, application scope and model establishment is presented. The results are validated by both numerical FEA simulations and calibration experiments, and test results are found to be compatible with each other for a wide range of geometric properties. The proposed analytical solutions are demonstrated to be an accurate estimation algorithm with higher efficiency.
Directory of Open Access Journals (Sweden)
Linares OA
2015-07-01
Full Text Available Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic Medicine Lab, Plymouth Pharmacokinetic Modeling Study Group, Plymouth, MI, 2Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA, 3University of Connecticut School of Pharmacy, Storrs, CT, 4Western New England College of Pharmacy, Springfield, MA, 5Albany College of Pharmacy and Health Sciences, Albany, NY, 6Stratton VA Medical Center, Albany, NY, 7Grace Hospice of Ann Arbor, Ann Arbor, MI, USA Background: There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim: To build a one-dimensional (1-D, hollow-fiber geometry, ordinary differential equation (ODE and partial differential equation (PDE countercurrent hemodialyzer model (ODE/PDE model. Methodology: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results: The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δ km=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11. This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11. The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value
Six Sigma software development
Tayntor, Christine B
2002-01-01
Since Six Sigma has had marked success in improving quality in other settings, and since the quality of software remains poor, it seems a natural evolution to apply the concepts and tools of Six Sigma to system development and the IT department. Until now however, there were no books available that applied these concepts to the system development process. Six Sigma Software Development fills this void and illustrates how Six Sigma concepts can be applied to all aspects of the evolving system development process. It includes the traditional waterfall model and in the support of legacy systems,
Equilibrium models of trade equations : a critical review
Portugal, Marcelo Savino
1993-01-01
Neste artigo, revisa-se a literatura teórica sobre equações de comércio exterior, inclusive o modelo de comércio baseado na teoria da produção. Discute-se vários problemas comumente encontrados em trabalhos empíricos e também a literatura existente sobre equações relativas ao comércio exterior brasileiro. In this paper we review the theoretical literature on trade equation models, including the production theory approach. We discuss several empirical problems commonly found in the applied ...
New equation of state model for hydrodynamic applications
Energy Technology Data Exchange (ETDEWEB)
Young, D.A.; Barbee, T.W. III; Rogers, F.J.
1997-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed.The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
New equation of state models for hydrodynamic applications
Young, David A.; Barbee, Troy W.; Rogers, Forrest J.
1998-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
Development of a polynomial nodal model to the multigroup transport equation in one dimension
International Nuclear Information System (INIS)
Feiz, M.
1986-01-01
A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model
International Nuclear Information System (INIS)
Portugal, R.; Soares, I.D.
1985-01-01
Two new classes of spatially homogeneous cosmological solutions of Einstein-Maxwell equations are obtained by considering a class of exact perturbations of the static Bertotti-Robinson (BR) model. The BR solution is shown to be unstable under these perturbations, being perturbed into exact cosmological solutions with perfect fluid (equations of state p = lambda rho, O [pt
From Ordinary Differential Equations to Structural Causal Models: the deterministic case
Mooij, J.M.; Janzing, D.; Schölkopf, B.; Nicholson, A.; Smyth, P.
2013-01-01
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of
Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Vitanov Nikolay K.
2018-03-01
Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.
Cosmological model with viscosity media (dark fluid) described by an effective equation of state
International Nuclear Information System (INIS)
Ren Jie; Meng Xinhe
2006-01-01
A generally parameterized equation of state (EOS) is investigated in the cosmological evolution with bulk viscosity media modelled as dark fluid, which can be regarded as a unification of dark energy and dark matter. Compared with the case of the perfect fluid, this EOS has possessed four additional parameters, which can be interpreted as the case of the non-perfect fluid with time-dependent viscosity or the model with variable cosmological constant. From this general EOS, a completely integrable dynamical equation to the scale factor is obtained with its solution explicitly given out. (i) In this parameterized model of cosmology, for a special choice of the parameters we can explain the late-time accelerating expansion universe in a new view. The early inflation, the median (relatively late time) deceleration, and the recently cosmic acceleration may be unified in a single equation. (ii) A generalized relation of the Hubble parameter scaling with the redshift is obtained for some cosmology interests. (iii) By using the SNe Ia data to fit the effective viscosity model we show that the case of matter described by p=0 plus with effective viscosity contributions can fit the observational gold data in an acceptable level
[A Structural Equation Model on Family Strength of Married Working Women].
Hong, Yeong Seon; Han, Kuem Sun
2015-12-01
The purpose of this study was to identify the effect of predictive factors related to family strength and develop a structural equation model that explains family strength among married working women. A hypothesized model was developed based on literature reviews and predictors of family strength by Yoo. This constructed model was built of an eight pathway form. Two exogenous variables included in this model were ego-resilience and family support. Three endogenous variables included in this model were functional couple communication, family stress and family strength. Data were collected using a self-report questionnaire from 319 married working women who were 30~40 of age and lived in cities of Chungnam province in Korea. Data were analyzed with PASW/WIN 18.0 and AMOS 18.0 programs. Family support had a positive direct, indirect and total effect on family strength. Family stress had a negative direct, indirect and total effect on family strength. Functional couple communication had a positive direct and total effect on family strength. These predictive variables of family strength explained 61.8% of model. The results of the study show a structural equation model for family strength of married working women and that predicting factors for family strength are family support, family stress, and functional couple communication. To improve family strength of married working women, the results of this study suggest nursing access and mediative programs to improve family support and functional couple communication, and reduce family stress.
Spurious solutions in few-body equations
International Nuclear Information System (INIS)
Adhikari, S.K.; Gloeckle, W.
1979-01-01
After Faddeev and Yakubovskii showed how to write connected few-body equations which are free from discrete spurious solutions various authors have proposed different connected few-body scattering equations. Federbush first pointed out that Weinberg's formulation admits the existence of discrete spurious solutions. In this paper we investigate the possibility and consequence of the existence of spurious solutions in some of the few-body formulations. Contrary to a proof by Hahn, Kouri, and Levin and by Bencze and Tandy the channel coupling array scheme of Kouri, Levin, and Tobocman which is also the starting point of a formulation by Hahn is shown to admit spurious solutions. We can show that the set of six coupled four-body equations proposed independently by Mitra, Gillespie, Sugar, and Panchapakesan, by Rosenberg, by Alessandrini, and by Takahashi and Mishima and the seven coupled four-body equations proposed by Sloan and related by matrix multipliers to basic sets which correspond uniquely to the Schroedinger equation. These multipliers are likely to give spurious solutions to these equations. In all these cases spuriosities are shown to have no hazardous consequence if one is interested in studying the scattering problem
DEFF Research Database (Denmark)
Maia, Filipa Meireles; Tsivintzelis, Ioannis; Rodriguez, Oscar
2012-01-01
For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour and their ......For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour...... and their interactions with other components is still needed. In this work, we made a review of literature studies on modelling systems with ionic liquids using equation of state models. Furthermore, we applied the Cubic Plus Association (CPA) equation of state to describe the phase behaviour of two ionic liquids, 1...... is in progress for improving the modelling of LLE with the CPA equation of state....
Cause and cure of sloppiness in ordinary differential equation models.
Tönsing, Christian; Timmer, Jens; Kreutz, Clemens
2014-08-01
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.
Cause and cure of sloppiness in ordinary differential equation models
Tönsing, Christian; Timmer, Jens; Kreutz, Clemens
2014-08-01
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.
The Landau-Lifshitz equation describes the Ising spin correlation function in the free-fermion model
Rutkevich, S B
1998-01-01
We consider time and space dependence of the Ising spin correlation function in a continuous one-dimensional free-fermion model. By the Ising spin we imply the 'sign' variable, which takes alternating +-1 values in adjacent domains bounded by domain walls (fermionic world paths). The two-point correlation function is expressed in terms of the solution of the Cauchy problem for a nonlinear partial differential equation, which is proved to be equivalent to the exactly solvable Landau-Lifshitz equation. A new zero-curvature representation for this equation is presented. In turn, the initial condition for the Cauchy problem is given by the solution of a nonlinear ordinary differential equation, which has also been derived. In the Ising limit the above-mentioned partial and ordinary differential equations reduce to the sine-Gordon and Painleve III equations, respectively. (author)
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
Przedborski, Michelle; Anco, Stephen C.
2017-09-01
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.
A Methodological Review of Structural Equation Modelling in Higher Education Research
Green, Teegan
2016-01-01
Despite increases in the number of articles published in higher education journals using structural equation modelling (SEM), research addressing their statistical sufficiency, methodological appropriateness and quantitative rigour is sparse. In response, this article provides a census of all covariance-based SEM articles published up until 2013…
A Structural Equation Modelling Approach for Massive Blended Synchronous Teacher Training
Kannan, Kalpana; Narayanan, Krishnan
2015-01-01
This paper presents a structural equation modelling (SEM) approach for blended synchronous teacher training workshop. It examines the relationship among various factors that influence the Satisfaction (SAT) of participating teachers. Data were collected with the help of a questionnaire from about 500 engineering college teachers. These teachers…
Climate models with delay differential equations.
Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire M
2017-11-01
A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.
Climate models with delay differential equations
Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire M.
2017-11-01
A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.
Parameter Estimation of Partial Differential Equation Models
Xun, Xiaolei
2013-09-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.
International Nuclear Information System (INIS)
Kraloua, B.; Hennad, A.
2008-01-01
The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.
International Nuclear Information System (INIS)
Rupšys, P.
2015-01-01
A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE
Energy Technology Data Exchange (ETDEWEB)
Rupšys, P. [Aleksandras Stulginskis University, Studenų g. 11, Akademija, Kaunas district, LT – 53361 Lithuania (Lithuania)
2015-10-28
A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.
Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.
Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes
2014-08-01
In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
Directory of Open Access Journals (Sweden)
Nikola V. Georgiev
2003-01-01
Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.
Xie, Qin; Andrews, Stephen
2013-01-01
This study introduces Expectancy-value motivation theory to explain the paths of influences from perceptions of test design and uses to test preparation as a special case of washback on learning. Based on this theory, two conceptual models were proposed and tested via Structural Equation Modeling. Data collection involved over 870 test takers of…
Yan, David
This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
International Nuclear Information System (INIS)
Gurau, Razvan
2012-01-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
Lai, Changliang; Wang, Junbiao; Liu, Chuang
2014-10-01
Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.
Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux
International Nuclear Information System (INIS)
Kawamura, Hiroshi
1978-01-01
Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)
Correlation functions and Schwinger-Dyson equations for Penner's model
International Nuclear Information System (INIS)
Chair, N.; Panda, S.
1991-05-01
The free energy of Penner's model exhibits logarithmic singularity in the continuum limit. We show, however, that the one and two point correlators of the usual loop-operators do not exhibit logarithmic singularity. The continuum Schwinger-Dyson equations involving these correlation functions are derived and it is found that within the space of the corresponding couplings, the resulting constraints obey a Virasoro algebra. The puncture operator having the correct (logarithmic) scaling behaviour is identified. (author). 13 refs
A Robust Bayesian Approach for Structural Equation Models with Missing Data
Lee, Sik-Yum; Xia, Ye-Mao
2008-01-01
In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…
Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.
Hwang, Chi-en; Cleary, T. Anne
The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…
International Nuclear Information System (INIS)
Kataoka, Isao; Tomiyama, Akio
2004-01-01
The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill
Structural Equation Modeling: Theory and Applications in Forest Management
Directory of Open Access Journals (Sweden)
Tzeng Yih Lam
2012-01-01
Full Text Available Forest ecosystem dynamics are driven by a complex array of simultaneous cause-and-effect relationships. Understanding this complex web requires specialized analytical techniques such as Structural Equation Modeling (SEM. The SEM framework and implementation steps are outlined in this study, and we then demonstrate the technique by application to overstory-understory relationships in mature Douglas-fir forests in the northwestern USA. A SEM model was formulated with (1 a path model representing the effects of successively higher layers of vegetation on late-seral herbs through processes such as light attenuation and (2 a measurement model accounting for measurement errors. The fitted SEM model suggested a direct negative effect of light attenuation on late-seral herbs cover but a direct positive effect of northern aspect. Moreover, many processes have indirect effects mediated through midstory vegetation. SEM is recommended as a forest management tool for designing silvicultural treatments and systems for attaining complex arrays of management objectives.
Latest improvements on TRACPWR six-equations thermohydraulic code
International Nuclear Information System (INIS)
Rivero, N.; Batuecas, T.; Martinez, R.; Munoz, J.; Lenhardt, G.; Serrano, P.
1999-01-01
The paper presents the latest improvements on TRACPWR aimed at adapting the code to present trends on computer platforms, architectures and training requirements as well as extending the scope of the code itself and its applicability to other technologies different from Westinghouse PWR one. Firstly major features of TRACPWR as best estimate and real time simulation code are summed, then the areas where TRACPWR is being improved are presented. These areas comprising: (1) Architecture: integrating TRACPWR and RELAP5 codes, (2) Code scope enhancement: modelling the Mid-Loop operation, (3) Code speed-up: applying parallelization techniques, (4) Code platform downswing: porting to Windows N1 platform, (5) On-line performance: allowing simulation initialisation from a Plant Process Computer, and (6) Code scope extension: using the code for modelling VVER and PHWR technology. (author)
Ganzert, Steven; Guttmann, Josef; Steinmann, Daniel; Kramer, Stefan
Lung protective ventilation strategies reduce the risk of ventilator associated lung injury. To develop such strategies, knowledge about mechanical properties of the mechanically ventilated human lung is essential. This study was designed to develop an equation discovery system to identify mathematical models of the respiratory system in time-series data obtained from mechanically ventilated patients. Two techniques were combined: (i) the usage of declarative bias to reduce search space complexity and inherently providing the processing of background knowledge. (ii) A newly developed heuristic for traversing the hypothesis space with a greedy, randomized strategy analogical to the GSAT algorithm. In 96.8% of all runs the applied equation discovery system was capable to detect the well-established equation of motion model of the respiratory system in the provided data. We see the potential of this semi-automatic approach to detect more complex mathematical descriptions of the respiratory system from respiratory data.