Computational studies on 1,2,4-Triazolium-based salts as energetic materials
Indian Academy of Sciences (India)
Rakhi Singh; Hari Ji Singh; S K Sengupta
2015-06-01
The results of the computational studies performed on 1,2,4-triazolium cation-based salts designed by pairing it with energetic nitro-substituted 5- membered N-heterocyclic anions such as 5-nitrotetrazolate, 3,5-dinitrotriazolate, and 2,4,5 trinitroimidazolate are reported. Condensed phase heats of formation of the designed ionic salts and their thermodynamic and energetic properties have also been calculated. The results show that these salts are potential energetic materials and possess high positive heats of formation. The detonation velocity, D, and detonation pressure, P, have been calculated using the Kamlet-Jacobs equation and found to be 7–8 km/s and 25–29 GPa, respectively. These values fall in the range of the criteria to designate them as high-energy-density materials. Nucleus independent chemical shift (NICS) studies performed on the designed molecules show that these salts are stable in nature.
Solving Operator Equation Based on Expansion Approach
Directory of Open Access Journals (Sweden)
A. Aminataei
2014-01-01
Full Text Available To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form Lu+Nu=g(x,x∈Γ, with respect to boundary condition Bu=λ, where L, N and B are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, Γ is the domain of approximation, λ is an arbitrary constant, and g(x∈L2(Γ is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in L2(Γ norm.
Adaptive Rendering Based on Visual Acuity Equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new method of adaptable rendering for interaction in Virtual Environment(VE) through different visual acuity equations is proposed. An acuity factor equation of luminance vision is first given. Secondly, five equations which calculate the visual acuity through visual acuity factors are presented, and adaptive rendering strategy based on different visual acuity equations is given. The VE system may select one of them on the basis of the host's load, hereby select LOD for each model which would be rendered. A coarser LOD is selected where the visual acuity is lower, and a better LOD is used where it is higher. This method is tested through experiments and the experimental results show that it is effective.
Institute of Scientific and Technical Information of China (English)
Xiao-hong Li; Geng-xin Yin; Xian-zhou Zhang
2012-01-01
Based on the full optimized molecular geometrical structures at the DFT-B3LYP/6-311+G** level,there exists intramolecular hydrogen bond interaction for cyclic 2-diazo-4,6-dinitrophenol.The assigned infrared spectrum is obtained and used to compute the thermodynamic properties.The results show that there are four main characteristic regions in the calculated IR spectra of the title compound.The detonation velocities and pressures are also evaluated by using Kamlet-Jacobs equations based on the calculated density and condensed phase heat of formation.Thermal stability and the pyrolysis mechanism of 2-diazo-4,6-dinitrophenol are investigated by calculating the bond dissociation energies at the B3LYP/6-311+G** level.
Xiao-Hong, Li; Rui-Zhou, Zhang; Xian-Zhou, Zhang
2012-07-01
The thermal stability and pyrolysis mechanism of 1,2-bis(2,4,6-trinitrophenyl) hydrazine were investigated based on fully optimized molecular geometric structures. The results demonstrate the existence of intramolecular hydrogen bond interactions 1,2-bis(2,4,6-trinitrophenyl) hydrazine. The assigned infrared spectrum was also obtained; the results reveal four main characteristic regions in the calculated IR spectra of the title compound. Detonation velocities (D) and pressures (P) were also evaluated by using Kamlet-Jacobs equations based on the calculated density and heat of formation. Thermal stability and the pyrolysis mechanism of 1,2-bis(2,4,6-trinitrophenyl) hydrazine were investigated by calculating the bond dissociation energies at the B3LYP/6-31 G* level.
Indian Academy of Sciences (India)
Li Xiao-Hong; Cui Hong-Ling; Li Li-Ben; Zhang Xian-Zhou
2013-07-01
Density functional theory calculations were performed to study the new polynitro cage compound with the similar framework of HNIW. IR spectrum, heat of formation and thermodynamic properties were predicted. The bond dissociation energies and bond orders for the weakest bonds were analysed to investigate the thermal stability of the title compound. The detonation and pressure were evaluated by using the Kamlet-Jacobs equations based on the theoretical density and condensed HOFs. In addition, the results show that there exists an essentially linear relationship between the WBIs of N-NO2 bonds and the charges -QNO2 on the nitro groups. The crystal structure obtained by molecular mechanics belongs to P21/C space group, with lattice parameters Z = 4, a = 12.3421 Å, b = 24.6849 Å, c = 20.4912 Å, = 1.896 g cm-3. The designed compound has high thermal stability and good detonation properties and is a promising high energy density compound.
Acoustic wave-equation-based earthquake location
Tong, Ping; Yang, Dinghui; Liu, Qinya; Yang, Xu; Harris, Jerry
2016-04-01
We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt0, δxs) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t0, xs) with respect to the earthquake location (t0, xs), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t0, xs) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.
Novel SVPWM based on first order equation
Directory of Open Access Journals (Sweden)
Ahmed A. Mansour
2015-09-01
Full Text Available PWM plays an important role in generating sinusoidal waveform for variable voltage variable frequency drives (VVVFD's with a minimum harmonic level. PWM techniques have many methods in implementation ranging from a relatively simple method such as modulating sine wave to the advanced Space Vector PWM technique SVPWM. The SVPWM has a dense calculation that requires considerable processor time for execution. The proposed technique requires simple calculations and can be implemented using simple microcontrollers. The calculations of the proposed SVPWM are based on first order equations rather than trigonometric functions requiring either huge lookup tables for fetching or too many instruction cycles for calculation on a digital controller.
Symbolic derivation of potential based constitutive equations
Arnold, S. M.; Tan, H. Q.
1990-05-01
Structural alloys used in high temperature applications exhibit complex thermomechanical behavior that is inherently time dependent and hereditary, as the current behavior depends not only on current conditions but on the thermomechanical history. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved, and error-prone, thus intelligent application of symbolic systems to facilitate this tedious processes can be of significant benefit. Here a computerized package, running under MACSYMA, capable of efficiently deriving potential based constitutive models, in analytical form (involving tensors, partial differentiation, invariants, and the like) is presented. Special purpose utility algorithms are designed and implemented to perform partial differentiation (chain rule), tensor manipulation, case distinction and simplification. Four constitutive theories reported in the literature are utilized to verify implementation accuracy. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.
The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation
Frank, Martin; Larsen, Edward W; Vasques, Richard
2014-01-01
We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo, with only statistical errors - no truncation errors.
Wave-equation Based Earthquake Location
Tong, P.; Yang, D.; Yang, X.; Chen, J.; Harris, J.
2014-12-01
Precisely locating earthquakes is fundamentally important for studying earthquake physics, fault orientations and Earth's deformation. In industry, accurately determining hypocenters of microseismic events triggered in the course of a hydraulic fracturing treatment can help improve the production of oil and gas from unconventional reservoirs. We develop a novel earthquake location method based on solving full wave equations to accurately locate earthquakes (including microseismic earthquakes) in complex and heterogeneous structures. Traveltime residuals or differential traveltime measurements with the waveform cross-correlation technique are iteratively inverted to obtain the locations of earthquakes. The inversion process involves the computation of the Fréchet derivative with respect to the source (earthquake) location via the interaction between a forward wavefield emitting from the source to the receiver and an adjoint wavefield reversely propagating from the receiver to the source. When there is a source perturbation, the Fréchet derivative not only measures the influence of source location but also the effects of heterogeneity, anisotropy and attenuation of the subsurface structure on the arrival of seismic wave at the receiver. This is essential for the accuracy of earthquake location in complex media. In addition, to reduce the computational cost, we can first assume that seismic wave only propagates in a vertical plane passing through the source and the receiver. The forward wavefield, adjoint wavefield and Fréchet derivative with respect to the source location are all computed in a 2D vertical plane. By transferring the Fréchet derivative along the horizontal direction of the 2D plane into the ones along Latitude and Longitude coordinates or local 3D Cartesian coordinates, the source location can be updated in a 3D geometry. The earthquake location obtained with this combined 2D-3D approach can then be used as the initial location for a true 3D wave-equation
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Riccati equation-based generalization of Dawson's integral function
Messina, R; Messina, A; Napoli, A
2007-01-01
A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for a generic cofactor of a triangular matrix is deduced.
The inverse problem based on a full dispersive wave equation
Institute of Scientific and Technical Information of China (English)
Gegentana Bao; Naranmandula Bao
2012-01-01
The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation. First, a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory, and the dispersion characteristics are discussed. Second, based on the full dispersive wave equation, an inverse problem for determining the four unknown coefficients of wave equa- tion is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves, and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequen- cies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Stabilisation of difference equations with noisy prediction-based control
Braverman, E.; Kelly, C.; Rodkina, A.
2016-07-01
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative We begin by relaxing the control parameter in the deterministic equation, and deriving a range of values for the parameter over which all solutions eventually enter an invariant interval. Then, by allowing the variation to be stochastic, we derive sufficient conditions (less restrictive than known ones for the unperturbed equation) under which the positive equilibrium will be globally a.s. asymptotically stable: i.e. the presence of noise improves the known effectiveness of prediction-based control. Finally, we show that systemic noise has a "blurring" effect on the positive equilibrium, which can be made arbitrarily small by controlling the noise intensity. Numerical examples illustrate our results.
New Density-based Thermal Conductivity Equation for Snow
Directory of Open Access Journals (Sweden)
R.K. Aggarwal
2009-03-01
Full Text Available More than two hundred thermal conductivity measurements for different snow densities and snow types were carried out in-situ at a field research station located in greater Himalayan range of India. These measurements were carried out using a commercially available portable thermal conductivity meter. Thermal conductivity measurements were carried out on the fresh snow, equi-temperature snow, and surface hoar and temperaturegradient snow. Average thermal conductivity of snow varied from 0.08 W/mK (Fresh snow of 120 kg/m3 density to 0.32 W/m K (Equi-temperature snow of 420 kg/m3 density. Based on these measurements, a new density-based thermal conductivity equation is proposed. Using this proposed equation, modeled snowpack temperatures showed closer agreement with the observed data as compared to the predictions based on other well-known empirical and theoretical thermal conductivity equations for snow. This study highlights the advantages and limitations of empirical based thermal conductivity equations over the complex models based on snow microstructure.Defence Science Journal, 2009, 59(2, pp.126-130, DOI:http://dx.doi.org/10.14429/dsj.59.1499
A modified soil water based Richards equation for layered soils
Kalinka, F.; Ahrens, B.
2010-09-01
Most Soil-Vegetation-Atmosphere-Transfer (SVAT) models like TERRA-ML (implemented e.g. in the CCLM model (www.clm-community.eu)) use the soil moisture based Richards equation to simulate vertical water fluxes in soils, assuming a homogeneous soil type. Recently, high-resolution soil type datasets (e.g. BüK 1000, only for Germany (Federal Institute for Geosciences and Natural Resources, BGR, www.bgr.bund.de) or Harmonized World Soil Database (HWSD, version 1.1, FAO/IIASA/ISRIC/ISSCAS/JRC, March 2009)) have been developed. Deficiencies in the numerical solution of the soil moisture based Richards equation may occur if inhomogeneous soil type data is implemented, because there are possibly discontinuities in soil moisture due to various soil type characteristics. One way to fix this problem is to use the potential based Richards equation, but this may lead to problems in conservation of mass. This presentation will suggest a possible numerical solution of the soil moisture based Richards equation for inhomogeneous soils. The basic idea is to subtract the equilibrium state of it from soil moisture fluxes. This should reduce discontinuities because each soil layer aspires the equilibrium state and therefore differences might be of the same order. First sensitivity studies have been done for the Main river basin, Germany.
Homotopy-based methods for fractional differential equations
Ateş, Inan
2017-01-01
The intention of this thesis is two-fold. The first aim is to describe and apply, series-based, numerical methods to fractional differential equation models. For this, it is needed to distinguish between space-fractional and time-fractional derivatives. The second goal of this thesis is to give a
Control theory based airfoil design using the Euler equations
Jameson, Antony; Reuther, James
1994-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.
Study on visualization simulation soybean leaf based on growth equation
Institute of Scientific and Technical Information of China (English)
ZHANG Jicheng; SU Zhongbin; XING Lichao
2007-01-01
According to the virtual crops model research's need, the paper emphasized on the modeling theory and dynamic modeling methods, and took the soybean leaf as the example, introduced the establishment of leaf growth model based on growth equation, finally realized the visualization result based on OpenGL in VC++ platform. The paper has great significance on establishing the whole growth model and researching the crops growth principles.
From equation to inequality using a function-based approach
Verikios, Petros; Farmaki, Vassiliki
2010-06-01
This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to investigate if and how our approach could facilitate students to comprehend inequality and to solve problems related to this concept. Data analysis showed that, in order to comprehend the new concept, the students should make a transition from equation to inequality. The role of the situation context proved decisive in this transition and in making sense of involved symbols. Also, students used function representations as problem-solving strategies in problems that included inequalities. However, the extension of the function-based approach in solving an abstract equation or inequality proved problematic for the students.
Seismic traveltime inversion based on tomographic equation without integral terms
Huang, Guangnan; Zhou, Bing; Li, Hongxing; Nobes, David C.
2017-07-01
The Jacobian matrix in the seismic traveltime tomographic equations usually contains several integral terms. These integral expressions not only greatly increase the computational complexity of seismic traveltime tomography, but also increase difficulty for programming these expressions. Therefore, if these integral expressions of the Jacobian matrix can be eliminated, the program of seismic traveltime tomography can be greatly simplified. In order to solve the computational complexity of the traditional seismic traveltime tomography, we found an anisotropic seismic traveltime tomographic equation which does not contain integral expressions. Then, it is degenerated into an isotropic seismic traveltime tomographic equation. In order to verify the effectiveness of this seismic traveltime tomographic equation based on the node network, a program has been coded to execute seismic traveltime inversion. For a crosswell checkerboard velocity model, the same results are obtained by this proposed tomographic method and the traditional method (with integral terms). Besides, two undulating topography velocity models are used as testing models. Numerical simulation results show that this proposed tomographic method can achieve good tomograms. Finally, this proposed tomographic method is used to investigate near surface velocity distribution near a power plant. Tomogram indicates that contaminated liquid diffuses and aggregates along strata at a certain depth. And velocity is lower near pollutant source than that away from it.
Structural Identification and Validation in Stochastic Differential Equation based Models
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
2011-01-01
Stochastic differential equations (SDEs) for ecosystem modelling have attracted increasing attention during recent years. The modelling has mostly been through simulation based experiments. Estimation of parameters in SDEs is, however, possible by combining Kalman filter and likelihood techniques...... as a function of the state variables and global radiation. Further improvements of both the drift and the diffusion term are achieved by comparing simulated densities and data....
BUNDLE ADJUSTMENTS CCD CAMERA CALIBRATION BASED ON COLLINEARITY EQUATION
Institute of Scientific and Technical Information of China (English)
Liu Changying; Yu Zhijing; Che Rensheng; Ye Dong; Huang Qingcheng; Yang Dingning
2004-01-01
The solid template CCD camera calibration method of bundle adjustments based on collinearity equation is presented considering the characteristics of space large-dimension on-line measurement. In the method, a more comprehensive camera model is adopted which is based on the pinhole model extended with distortions corrections. In the process of calibration, calibration precision is improved by imaging at different locations in the whole measurement space, multi-imaging at the same location and bundle adjustments optimization. The calibration experiment proves that the calibration method is able to fulfill calibration requirement of CCD camera applied to vision measurement.
Optimum Transonic Airfoils Based on the Euler Equations
Iollo, Angelo; Salas, Manuel, D.
1996-01-01
We solve the problem of determining airfoils that approximate, in a least square sense, given surface pressure distributions in transonic flight regimes. The flow is modeled by means of the Euler equations and the solution procedure is an adjoint- based minimization algorithm that makes use of the inverse Theodorsen transform in order to parameterize the airfoil. Fast convergence to the optimal solution is obtained by means of the pseudo-time method. Results are obtained using three different pressure distributions for several free stream conditions. The airfoils obtained have given a trailing edge angle.
A Sumudu based algorithm for solving differential equations
Directory of Open Access Journals (Sweden)
Jun Zhang
2007-11-01
Full Text Available An algorithm based on Sumudu transform is developed. The algorithm can be implemented in computer algebra systems like Maple. It can be used to solve differential equations of the following form automatically without human interaction \\begin{displaymath} \\sum_{i=0}^{m} p_i(xy^{(i}(x = \\sum_{j=0}^{k}q_j(xh_j(x \\end{displaymath} where pi(x(i=0, 1, 2, ..., m and qj(x(j=0, 1, 2, ..., k are polynomials. hj(x are non-rational functions, but their Sumudu transforms are rational. m, k are nonnegative integers.
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.
A spectral-based numerical method for Kolmogorov equations in Hilbert spaces
Delgado-Vences, Francisco; Flandoli, Franco
2016-08-01
We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.
Elliptic grid generation based on Laplace equations and algebraic transformations
Energy Technology Data Exchange (ETDEWEB)
Spekreuse, S.P. [National Aerospace Lab., Amsterdam (Netherlands)
1995-04-01
An elliptic grid generation method is presented to generate boundary conforming grids in domains in 2D and 3D physical space and on minimal surfaces and parametrized surfaces in 3D physical space. The elliptic grid generation method is based on the use of a composite mapping. This composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation. The elliptic transformation is based on the Laplace equations for domains, or on the Laplace-Beltrami equations for surfaces. The algebraic transformation maps the computational space one to-one onto a parameter space. The elliptic transformation maps the parameter space one-to-one onto the domains or surfaces. The composition of these two mapping is a differentiable one-to-one mapping from computational space onto the domains or surfaces and has a nonvanishing Jacobian. This composite mapping defines the grid point distribution in the interior of the domains or surfaces. For domains and minimal surfaces, the composite mapping obeys a nonlinear elliptic Poisson system with control functions completely defined by the algebraic transformation. The solution of the Poisson systems is obtained by Picard iteration and black-box multigrid solvers. For parametrized curved surfaces, it is not necessary to define and solve a nonlinear elliptic Poisson system. Instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface.
Wave equation based microseismic source location and velocity inversion
Zheng, Yikang; Wang, Yibo; Chang, Xu
2016-12-01
The microseismic event locations and velocity information can be used to infer the stress field and guide hydraulic fracturing process, as well as to image the subsurface structures. How to get accurate microseismic event locations and velocity model is the principal problem in reservoir monitoring. For most location methods, the velocity model has significant relation with the accuracy of the location results. The velocity obtained from log data is usually too rough to be used for location directly. It is necessary to discuss how to combine the location and velocity inversion. Among the main techniques for locating microseismic events, time reversal imaging (TRI) based on wave equation avoids traveltime picking and offers high-resolution locations. Frequency dependent wave equation traveltime inversion (FWT) is an inversion method that can invert velocity model with source uncertainty at certain frequency band. Thus we combine TRI with FWT to produce improved event locations and velocity model. In the proposed approach, the location and model information are interactively used and updated. Through the proposed workflow, the inverted model is better resolved and the event locations are more accurate. We test this method on synthetic borehole data and filed data of a hydraulic fracturing experiment. The results verify the effectiveness of the method and prove it has potential for real-time microseismic monitoring.
Cluster-Based Distributed Algorithms for Very Large Linear Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In many applications such as computational fluid dynamics and weather prediction, as well as image processing and state of Markov chain etc., the grade of matrix n is often very large, and any serial algorithm cannot solve the problems. A distributed cluster-based solution for very large linear equations is discussed, it includes the definitions of notations, partition of matrix, communication mechanism, and a master-slaver algorithm etc., the computing cost is O(n3/N), the memory cost is O(n2/N), the I/O cost is O(n2/N), and the communication cost is O(Nn), here, N is the number of computing nodes or processes. Some tests show that the solution could solve the double type of matrix under 106×106 effectively.
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
Similarity-Based Solution of the Generalized Boussinesq Equation
Olsen, J. S.; Mortensen, J.; Telyakovskiy, A. S.; Wheatcraft, S. W.
2013-12-01
The generalized Boussinesq equation is a nonlinear diffusion equation where hydraulic conductivity is a power-law function of hydraulic head. In the traditional Boussinesq equation it is a linear function of hydraulic head. The generalized Boussinesq equation models flows of gases through porous media and flows of water in forest soils and concretes. Also, when the hydraulic conductivity is a power-law function of elevation we obtain this equation. We model a one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in rectangular coordinates. We introduce similarity variables to reduce the initial-boundary value problem to a boundary value problem for a nonlinear ordinary differential equation. We construct an approximate solution that preserves certain properties of the true solution and replicated known exact solutions.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Ghule, Vikas D
2012-09-20
Heats of formation (HOFs) for 24 designed compounds were obtained by using the density functional theory (DFT). Molecular structures were investigated at the B3PW91/6-31G(d,p) level, and isodesmic reactions were designed for calculating the gas phase heats of formation. The solid state heats of formation for designed compounds were calculated by the Politzer approach using heats of sublimation. All the designed compounds possess solid state heats of formation above 140 kJ/mol. The distance between nitro groups influences the steric and repulsive interactions. Detonation performances were evaluated by the Kamlet-Jacobs equations based on the predicted densities and solid state heats of formation, and susceptibility of decomposition was studied by the computations of bond dissociation energy (BDE). Further, the present study might provide useful information for the structure-property relationship, the laboratory synthesis of imidazole-triazole and pyrazole-triazole based nitro derivatives and the development of novel high energy materials (HEMs).
Theoretical studies on nitrogen rich energetic azoles.
Ghule, Vikas Dasharath; Sarangapani, Radhakrishnan; Jadhav, Pandurang M; Tewari, Surya P
2011-06-01
Different nitro azole isomers based on five membered heterocyclics were designed and investigated using computational techniques in order to find out the comprehensive relationships between structure and performances of these high nitrogen compounds. Electronic structure of the molecules have been calculated using density functional theory (DFT) and the heat of formation has been calculated using the isodesmic reaction approach at B3LYP/6-31G* level. All designed compounds show high positive heat of formation due to the high nitrogen content and energetic nitro groups. The crystal densities of these energetic azoles have been predicted with different force fields. All the energetic azoles show densities higher than 1.87 g/cm(3). Detonation properties of energetic azoles are evaluated by using Kamlet-Jacobs equation based on the calculated densities and heat of formations. It is found that energetic azoles show detonation velocity about 9.0 km/s, and detonation pressure of 40GPa. Stability of the designed compounds has been predicted by evaluating the bond dissociation energy of the weakest C-NO(2) bond. The aromaticity using nucleus independent chemical shift (NICS) is also explored to predict the stability via delocalization of the π-electrons. Charge on the nitro group is used to assess the impact sensitivity in the present study. Overall, the study implies that all energetic azoles are found to be stable and expected to be the novel candidates of high energy density materials (HEDMs).
Partial differential equations-based segmentation for radiotherapy treatment planning.
Gibou, Frederic; Levy, Doron; Cardenas, Carlos; Liu, Pingyu; Boyer, Arthur
2005-04-01
The purpose of this study is to develop automatic algorithms for the segmentation phase of radiotherapy treatment planning. We develop new image processing techniques that are based on solving a partial diferential equation for the evolution of the curve that identifies the segmented organ. The velocity function is based on the piecewise Mumford-Shah functional. Our method incorporates information about the target organ into classical segmentation algorithms. This information, which is given in terms of a three- dimensional wireframe representation of the organ, serves as an initial guess for the segmentation algorithm. We check the performance of the new algorithm on eight data sets of three diferent organs: rectum, bladder, and kidney. The results of the automatic segmentation were compared with a manual seg- mentation of each data set by radiation oncology faculty and residents. The quality of the automatic segmentation was measured with the k-statistics", and with a count of over- and undersegmented frames, and was shown in most cases to be very close to the manual segmentation of the same data. A typical segmentation of an organ with sixty slices takes less than ten seconds on a Pentium IV laptop.
Doubly robust and multiple-imputation-based generalized estimating equations.
Birhanu, Teshome; Molenberghs, Geert; Sotto, Cristina; Kenward, Michael G
2011-03-01
Generalized estimating equations (GEE), proposed by Liang and Zeger (1986), provide a popular method to analyze correlated non-Gaussian data. When data are incomplete, the GEE method suffers from its frequentist nature and inferences under this method are valid only under the strong assumption that the missing data are missing completely at random. When response data are missing at random, two modifications of GEE can be considered, based on inverse-probability weighting or on multiple imputation. The weighted GEE (WGEE) method involves weighting observations by the inverse of their probability of being observed. Imputation methods involve filling in missing observations with values predicted by an assumed imputation model, multiple times. The so-called doubly robust (DR) methods involve both a model for the weights and a predictive model for the missing observations given the observed ones. To yield consistent estimates, WGEE needs correct specification of the dropout model while imputation-based methodology needs a correctly specified imputation model. DR methods need correct specification of either the weight or the predictive model, but not necessarily both. Focusing on incomplete binary repeated measures, we study the relative performance of the singly robust and doubly robust versions of GEE in a variety of correctly and incorrectly specified models using simulation studies. Data from a clinical trial in onychomycosis further illustrate the method.
Wang, Tianyi; Zheng, Chunmei; Yang, Junqing; Zhang, Xueli; Gong, Xuedong; Xia, Mingzhu
2014-06-01
The derivatives of 1,2,3,4-tetrazine may be promising candidates for high-energy density compounds and are receiving more and more attentions. In this study, a new derivative 6-amino-7-nitropyrazino[2,3-e][1,2,3,4]tetrazine 1,3,5-trioxide (ANPTTO) has been designed. The geometrical structure and IR spectrum in the gas phase were studied at the B3LYP/6-31G* level of density functional theory (DFT). The crystal structure was predicted by molecular mechanics method and refined by the GGA/BOP function of periodic DFT with the basis set of TNP. The gas phase enthalpy of formation was calculated by the homodesmotic reaction method. The enthalpy of sublimation and solid phase enthalpy of formation were also predicted. The detonation properties were estimated with the Kamlet-Jacobs equations based on the predicted density and enthalpy of formation in solid state. The available free space in the lattice and resonance energy were calculated to evaluate its stability. ANPTTO has a high stability and is a promising high energetic component with the density >2 g · cm(-3), detonation velocity >9000 m · s(-1), and detonation pressure >40 GPa. A synthetic route was proposed to provide a consideration for further study.
A DFT study of tautomers of 3-amino-1-nitroso-4-nitrotriazol-5-one-2-oxide.
Ravi, Pasupala; Tewari, Surya P
2013-06-01
We report herein the structure and explosive properties of the possible isomers of 3-amino-1-nitroso-4-nitrotriazol-5-one-2-oxide computed from the B3LYP/aug-cc-pVDZ level. The optimized structures, vibrational frequencies and thermodynamic values for triazol-5-one-N-oxides were obtained in the ground state. Several designed compounds have densities varying from 2.103 to 2.177 g/cm(3). The detonation properties were evaluated by the Kamlet-Jacob equations based on the predicted density and the calculated heat of explosion. The detonation properties of triazol-5-one-N-oxides (D 9.87 to 10.11 km s(-1) and P 48.95 to 50.61 GPa) appear to be promising compared with those of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (D 9.20 km s(-1), P 42.0 Gpa) and octanitrocubane (D 9.90 km s(-1), P 48.45 GPa). The substitution of secondary amino hydrogen of the triazole ring by amino group shows better impact sensitivity/or stability however the model compounds seem to be highly sensitive.
Wang, Gui-Xiang; Gong, Xue-Dong; Liu, Yan; Du, Hong-Chen; Xu, Xiao-Juan; Xiao, He-Ming
2011-04-15
The derivatives of DPO (2,5-dipicryl-1,3,4-oxadiazole) are optimized to obtain their molecular geometries and electronic structures at the DFT-B3LYP/6-31G* level. The bond length is focused to primarily predict thermal stability and the pyrolysis mechanism of the title compounds. Detonation properties are evaluated using the modified Kamlet-Jacobs equations based on the calculated densities and heats of formation. It is found that there are good linear relationships between density, detonation velocity, detonation pressure, and the number of azido, nitrate, and nitramine groups. According to the largest exothermic principle, the relative specific impulse is investigated by calculating the enthalpy of combustion (ΔH(comb)) and the total heat capacity (C(p,gases)). It is found that the introduction of -N(3), -ONO(2), and -NNO(2) groups could increase the specific impulses and II-4, II-5, and III-5 are potential candidates for High Energy Density Materials (HEDMs). The effect of the azido, nitrate, and nitramine groups on the structure and the properties is discussed.
Density functional calculations for a high energy density compound of formula C6H 6-n (NO 2) n.
Chi, Wei-Jie; Li, Lu-Lin; Li, Bu-Tong; Wu, Hai-Shun
2012-08-01
A series of polynitroprismanes, C(6)H(6-n )(NO(2))(n) (n = 1-6) intended for use as high energy density compounds (HEDCs) were designed computationally. Their electronic structures, heats of formation, interactions between nitro groups, specific enthalpies of combustion, bond dissociation energies, and explosive performances (detonation velocities and detonation pressures) were calculated using density functional theory (DFT) with the 6-311 G** basis set. The results showed that all of the polynitroprismanes had high positive heats of formation that increased with the number of substitutions for the prismane derivatives, while the specific enthalpy of combustion decreased as the number of nitro groups increased. In addition, the range of enthalpy of combustion reducing is getting smaller. Interactions between ortho (vicinal) groups deviate from the group additivity rule and decrease as the number of nitro groups increases. In terms of thermodynamic stability, all of the polynitroprismanes had higher bond dissociation energies (BDEs) than RDX and HMX. Detonation velocities and detonation pressures were estimated using modified Kamlet-Jacobs equations based on the heat of detonation (Q) and the theoretical density of the molecule (ρ). It was found that ρ, D, and P are strongly linearly related to the number of nitro groups. Taking both their energetic properties and thermal stabilities into account, pentanitroprismane and hexanitroprismane are potential candidate HEDCs.
Zhang, Jian-ying; Du, Hong-chen; Wang, Fang; Gong, Xue-dong; Huang, Yin-sheng
2012-01-01
A new polynitro cage compound with the framework of HNIW and a tetrazole unit, i.e., 10-(1-nitro-1, 2, 3, 4-tetraazol-5-yl)) methyl-2, 4, 6, 8, 12-hexanitrohexaazaisowurtzitane (NTz-HNIW) has been proposed and studied by density functional theory (DFT) and molecular mechanics methods. Properties such as IR spectrum, heat of formation, thermodynamic properties, and crystal structure were predicted. The compound belongs to the Pbca space group, with the lattice parameters a = 15.07 Å, b = 12.56 Å, c = 18.34 Å, Z = 8, and ρ = 1.990 g·cm(-3). The stability of the compound was evaluated by the bond dissociation energies and results showed that the first step of pyrolysis is the rupture of the N-NO(2) bond in the side chain. The detonation properties were estimated by the Kamlet-Jacobs equations based on the calculated crystal density and heat of formation, and the results were 9.240 km·s(-1) for detonation velocity and 40.136 GPa for detonation pressure. The designed compound has high thermal stability and good detonation properties and is probably a promising high energy density compound (HEDC).
Wang, Fang; Wang, Guixiang; Du, Hongchen; Zhang, Jianying; Gong, Xuedong
2011-12-01
Density functional theory calculations were performed to find comprehensive relationships between the structures and performance of a series of highly energetic cyclic nitramines. The isodesmic reaction method was employed to estimate the heat of formation. The detonation properties were evaluated by using the Kamlet-Jacobs equations based on the theoretical densities and HOFs. Results indicate the N-NO(2) group and aza N atom are effective substituents for enhancing the detonation performance. All cyclic nitramines except C11 and C21 exhibit better detonation performance than HMX. The decomposition mechanism and thermal stability of these cyclic nitramines were analyzed via the bond dissociation energies. For most of these nitramines, the homolysis of N-NO(2) is the initial step in the thermolysis, and the species with the bridged N-N bond are more sensitive than others. Considering the detonation performance and thermal stability, twelve derivatives may be the promising candidates of high energy density materials (HEDMs). The results of this study may provide basic information for the further study of this kind of compounds and molecular design of novel HEDMs.
Ravi, P; Venkatesan, V; Tewari, Surya P
2013-11-01
DFT calculations at the B3LYP/aug-cc-pVDZ level have been carried out to explore the structure, stability, electron density, heat of formation, detonation velocity and detonation pressure of substituted amino- and nitroso-1,2,4-triazol-5-one-N-oxides. Heats of formation of substituted triazol-5-one-N-oxides have been computed at the B3LYP/aug-cc-pVDZ level via isodesmic reaction procedure. Materials Studio 4.1 package was used to predict the crystal density of model compounds. Kamlet-Jacob equations were used to calculate detonation properties based on the calculated heat of explosion and crystal density. The designed compounds 4, 6, 7 and 8 have shown higher performance compared with those of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane and octanitrocubane. Atoms-in-molecule (AIM) analyses have also been carried out to understand the nature of intramolecular interactions in the designed molecules.
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Institute of Scientific and Technical Information of China (English)
Jian-Wan Ding; Li-Ping Chen; Fan-Li Zhou
2006-01-01
Object-oriented modeling with declarative equation based languages often unconsciously leads to structural inconsistencies. Component-based debugging is a new structural analysis approach that addresses this problem by analyzing the structure of each component in a model to separately locate faulty components. The analysis procedure is performed recursively based on the depth-first rule. It first generates fictitious equations for a component to establish a debugging environment, and then detects structural defects by using graph theoretical approaches to analyzing the structure of the system of equations resulting from the component. The proposed method can automatically locate components that cause the structural inconsistencies, and show the user detailed error messages. This information can be a great help in finding and localizing structural inconsistencies, and in some cases pinpoints them immediately.
Solution of wave-like equation based on Haar wavelet
Directory of Open Access Journals (Sweden)
Naresh Berwal
2012-11-01
Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.
A Method for Image Decontamination Based on Partial Differential Equation
Directory of Open Access Journals (Sweden)
Hou Junping
2015-01-01
Full Text Available This paper will introduce the method to apply partial differential equations for the decontamination processing of images. It will establish continuous partial differential mathematical models for image information and use specific solving methods to conduct decontamination processing to images during the process of solving partial differential equations, such as image noise reduction, image denoising and image segmentation. This paper will study the uniqueness of solution for the partial differential equations and the monotonicity that functional constrain has on multipliers by making analysis of the ROF model in the partial differential mathematical model.
DEFF Research Database (Denmark)
Marcussen, Lis; Aasberg-Petersen, K.; Krøll, Annette Elisabeth
2000-01-01
An adsorption isotherm equation for nonideal pure component adsorption based on vacancy solution theory and the Non-Random-Two-Liquid (NRTL) equation is found to be useful for predicting pure component adsorption equilibria at a variety of conditions. The isotherm equation is evaluated successfully...... adsorption systems, spreading pressure and isosteric heat of adsorption are also calculated....
Sandia equation of state data base: seslan File
Energy Technology Data Exchange (ETDEWEB)
Kerley, G.I. [Sandia National Labs., Albuquerque, NM (US); Christian-Frear, T.L. [RE/SPEC Inc., Albuquerque, NM (US)
1993-06-24
Sandia National Laboratories maintains several libraries of equation of state tables, in a modified Sesame format, for use in hydrocode calculations and other applications. This report discusses one of those libraries, the seslan file, which contains 78 tables from the Los Alamos equation of state library. Minor changes have been made to these tables, making them more convenient for code users and reducing numerical difficulties that occasionally arise in hydrocode calculations.
Hamiltonians with Riesz Bases of Generalised Eigenvectors and Riccati Equations
Wyss, Christian
2010-01-01
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant graph subspaces of the associated Hamiltonian operator matrix are constructed by means of a Riesz basis with parentheses of generalised eigenvectors and two indefinite inner products. Under additional assumptions, the existence and a representation of all bounded solutions is obtained. The theory is applied to Riccati equations of differential operators.
Cauchy problem for Laplace equation: An observer based approach
Majeed, Muhammad Usman
2013-10-01
A method to solve Cauchy Problem for Laplace equation using state observers is proposed. It is known that this problem is ill-posed. The domain under consideration is simple lipschitz in 2 with a hole. The idea is to recover the solution over whole domain from the observations on outer boundary. Proposed approach adapts one of the space variables as a time variable. The observer developed to solve Cauchy problem for the Laplace\\'s equation is compuationally robust and accurate. © 2013 IEEE.
Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study
Energy Technology Data Exchange (ETDEWEB)
Sukumar, Sreenivas R [ORNL; Nutaro, James J [ORNL
2012-01-01
This paper is motivated by the need to design model validation strategies for epidemiological disease-spread models. We consider both agent-based and equation-based models of pandemic disease spread and study the nuances and complexities one has to consider from the perspective of model validation. For this purpose, we instantiate an equation based model and an agent based model of the 1918 Spanish flu and we leverage data published in the literature for our case- study. We present our observations from the perspective of each implementation and discuss the application of model-selection criteria to compare the risk in choosing one modeling paradigm to another. We conclude with a discussion of our experience and document future ideas for a model validation framework.
A Riccati equation based approach to isotropic scalar field cosmologies
Harko, Tiberiu; Lobo, Francisco S. N.; Mak, M. K.
2014-05-01
Gravitationally coupled scalar fields ϕ, distinguished by the choice of an effective self-interaction potential V(ϕ), simulating a temporarily nonvanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work, we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the universe.
Image Segmentation and Denoising Based on Shrira-Pesenson Equation
Pesenson, M.; Moshir, M.; Makovoz, D.; Frayer, D.; Henderson, D.
2005-12-01
We propose a nonlinear partial differential equation to control the trade-off between smoothing and segmentation of images. Its solutions approximate discontinuities, thus leading to detection of sharp boundaries in images. The performance of the approach is evaluated by applying it to images obtained by the Multiband Imaging Photometer for Spitzer (MIPS), 70 micron imaging band.
Directory of Open Access Journals (Sweden)
Yuji Liu
2014-01-01
Full Text Available We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.
Korteweg–de Vries hierarchy using the method of base equations
Indian Academy of Sciences (India)
Subhendu Chakrabarti; J Pal; B Talukdar
2002-03-01
A base-equation method is implemented to realize the hereditary algebra of the Korteweg–de Vries (KdV) hierarchy and the -soliton manifold is reconstructed. The novelty of our approach is that, it can in a rather natural way, predict other nonlinear evolution equations which admit local conservation laws. Signiﬁcantly enough, base functions themselves are found to provide a basis to regard the KdV-like equations as higher order degenerate bi-Lagrangian systems.
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati...
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulation...
Structure analysis of growing network based on partial differential equations
Directory of Open Access Journals (Sweden)
Junbo JIA
2016-04-01
Full Text Available The topological structure is one of the most important contents in the complex network research. Therein the node degree and the degree distribution are the most basic characteristic quantities to describe topological structure. In order to calculate the degree distribution, first of all, the node degree is considered as a continuous variable. Then, according to the Markov Property of growing network, the cumulative distribution function's evolution equation with time can be obtained. Finally, the partial differential equation (PDE model can be established through distortion processing. Taking the growing network with preferential and random attachment mechanism as an example, the PDE model is obtained. The analytic expression of degree distribution is obtained when this model is solved. Besides, the degree function over time is the same as the characteristic line of PDE. At last, the model is simulated. This PDE method of changing the degree distribution calculation into problem of solving PDE makes the structure analysis more accurate.
Structure analysis of growing network based on partial differential equations
Junbo JIA; Jin, Zhen
2016-01-01
The topological structure is one of the most important contents in the complex network research. Therein the node degree and the degree distribution are the most basic characteristic quantities to describe topological structure. In order to calculate the degree distribution, first of all, the node degree is considered as a continuous variable. Then, according to the Markov Property of growing network, the cumulative distribution function's evolution equation with time can be obtained. Finally...
An Interpolation Procedure for List Decoding Reed--Solomon codes Based on Generalized Key Equations
Zeh, Alexander; Augot, Daniel
2011-01-01
The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches based on Key Equations and the interpolation-based list decoding algorithms of Guruswami and Sudan for Reed-Solomon codes. The original interpolation conditions of Guruswami and Sudan for Reed-Solomon codes are reformulated in terms of a set of Key Equations. These equations provide a structured homogeneous linear system of equations of Block-Hankel form, that can be solved by an adaption of the Fundamental Iterative Algorithm. For an $(n,k)$ Reed-Solomon code, a multiplicity $s$ and a list size $\\listl$, our algorithm has time complexity \\ON{\\listl s^4n^2}.
A new pseudorandom number generator based on a complex number chaotic equation
Institute of Scientific and Technical Information of China (English)
Liu Yang; Tong Xiao-Jun
2012-01-01
In recent years,various chaotic equation based pseudorandom number generators have been proposed.However,the chaotic equations are all defined in the real number field.In this paper,an equation is proposed and proved to be chaotic in the imaginary axis.And a pseudorandom number generator is constructed based on the chaotic equation.The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations,and a new method to generate pseudorandom number sequences accordingly.Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.
Novel concepts for differential-equation-based electromagnetic field simulations
Teixeira, Fernando Lisboa
This thesis presents novel concepts for electromagetic field simulations via partial differential equation (PDE) solvers. A vital aspect for any successful general implementation of a PDE solver is the use of an efficient absorbing boundary condition (ABC). The perfectly matched layer (PML) is a recently introduced ABC in Cartesian coordinates which provides reflection errors orders of magnitude smaller than previously employed ABCs. In this work, a new interpretation of the PML as an analytic continuation of the coordinate space is used to extend the PML to other coordinate systems. Modified equations replace the original Maxwell's equations, mapping propagating solutions into exponentially decaying solutions. Alternative (Maxwellian) formulations are also put forth, where the PML is represented as an artificial media with complex constitutive tensors, and the form of Maxwell's equations is retained. The causality and dynamic stability of the PML is characterized through a spectral analysis. In addition, a rationale is presented to extend the PML to complex media, e.g., dispersive and/or (bi-)anisotropic. For the Maxwellian formulation, the general expressions for the PML tensors matched to any interior dispersive and/or (bi-)anisotropic linear media are obtained. A finite-difference time-domain (FDTD) algorithm in Cartesian coordinates which combines the PML ABC with piecewise-linear recursive convolution (PLRC) is proposed and implemented, allowing the simulation of electromagnetic fields in inhomogeneous and dispersive media with conductive loss. Two PML-PLRC-FDTD algorithms in cylindrical coordinates are also proposed and implemented. The first is developed through a split-field PML formulation, and the second through a Maxwellian (unsplit) PML formulation. A comparison is made between numerical properties of these two algorithms. The PML concept is then studied within the language of differential forms to unify the various PML formulations. Finally, the
Solving Electromagnetism Differential Equations Based on Random Walk
Institute of Scientific and Technical Information of China (English)
邱尧峰; 曹毅; 李征帆
2004-01-01
An approach of solving the finite difference equations with Monte Carlo method was presented. The accuracy of algorithm is guaranteed by the Central Limit Theorem. The computation of the value on each single node is independent of each other, which makes it easy to realize the algorithm in parallel processing and greatly improves the efficiency while dealing with local area computation. As long as different kinds of boundary conditions are statistics modeled ,wide applications can the be made where the finite difference method is of competence.
Indirect Inference for Stochastic Differential Equations Based on Moment Expansions
Ballesio, Marco
2016-01-06
We provide an indirect inference method to estimate the parameters of timehomogeneous scalar diffusion and jump diffusion processes. We obtain a system of ODEs that approximate the time evolution of the first two moments of the process by the approximation of the stochastic model applying a second order Taylor expansion of the SDE s infinitesimal generator in the Dynkin s formula. This method allows a simple and efficient procedure to infer the parameters of such stochastic processes given the data by the maximization of the likelihood of an approximating Gaussian process described by the two moments equations. Finally, we perform numerical experiments for two datasets arising from organic and inorganic fouling deposition phenomena.
A comparison of X-ray stress measurement methods \\\\based on the fundamental equation
Miyazaki, Toshiyuki; Sasaki, Toshihiko
2015-01-01
Stress measurement methods using X-ray diffraction (XRD methods) are based on so-called fundamental equations. The fundamental equation is described in the coordinate system that best suites the measurement situation, and, thus, making a comparison between different XRD methods is not straightforward. However, by using the diffraction vector representation, the fundamental equations of different methods become identical. Furthermore, the differences between the various XRD methods are in the ...
Implicit numerical scheme based on SMAC method for unsteady incompressible Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
Li Zhenlin; Zhang Yongxue
2008-01-01
An implicit numerical scheme is developed based on the simplified marker and cell (SMAC)method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional (3-D) unsteady incompressible turbulent flow.The governing equations include the Reynolds-averaged momentum equations,in which contravariant velocities are unknown variables,pressure-correction Poisson equation and k- ε turbulent equations.The governing equations are discretized in a 3-D MAC staggered grid system.To improve the numerical stability of the implicit SMAC scheme,the higherorder high-resolution Chakravarthy-Osher total variation diminishing (TVD) scheme is used to discretize the convective terms in momentum equations and k-ε equations.The discretized algebraic momentum equations and k-εequations are solved by the time-diversion multiple access (CTDMA) method.The algebraic Poisson equations are solved by the Tschebyscheff SLOR (successive linear over relaxation)method with alternating computational directions.At the end of the paper,the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme.The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data.The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.
Directory of Open Access Journals (Sweden)
F. Z. Geng
2012-01-01
Full Text Available We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.
Spherical harmonics method for neutron transport equation based on unstructured-meshes
Institute of Scientific and Technical Information of China (English)
CAO Liang-Zhi; WU Hong-Chun
2004-01-01
Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.
The Qualitative Research Method of Dynamics Vibration of a Washing Machine Based on Riccati Equation
Directory of Open Access Journals (Sweden)
Sergey P. Petrosov
2012-09-01
Full Text Available The accurate method for finding the common solutions of weakly interconnected system of nonhomogeneous differential equations with variable coefficients based on Riccati Equation was developed. This method describes the dynamics of vibration of the suspension drum type of a washing machine in spin mode.
Meshless RBF based pseudospectral solution of acoustic wave equation
Mishra, Pankaj K
2015-01-01
Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor product grids for multi-dimensions. Recent studies have shown that replacing the polynomial by radial basis functions in pseudospectral method (RBF-PS) has the advantage of using irregular grids for multivariate systems. A RBF-PS algorithm has been presented here for the numerical solution of inhomogeneous Helmholtz's equation using Gaussian RBF for derivative approximation. Efficacy of RBF approximated derivatives has been checked through error analysis comparison with PS method. Comparative study of PS, RBF-PS and finite difference approach for the solution of a linear boundary value problem has been performed. Finally, a typical frequency domain acoustic wave propagation problem has been solved using Dirichlet boundary condition and a point source. The algorithm present...
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.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
Institute of Scientific and Technical Information of China (English)
Fan Shang-Chun; Li Yan; Guo Zhan-She; Li Jing; Zhuang Hai-Han
2012-01-01
Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
Kunze, Herb E.; Davide La Torre; Franklin Mendivil; Manuel Ruiz Galán; Rachad Zaki
2014-01-01
We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on ...
Lombard, Pamela J.; Hodgkins, Glenn A.
2015-01-01
Regression equations to estimate peak streamflows with 1- to 500-year recurrence intervals (annual exceedance probabilities from 99 to 0.2 percent, respectively) were developed for small, ungaged streams in Maine. Equations presented here are the best available equations for estimating peak flows at ungaged basins in Maine with drainage areas from 0.3 to 12 square miles (mi2). Previously developed equations continue to be the best available equations for estimating peak flows for basin areas greater than 12 mi2. New equations presented here are based on streamflow records at 40 U.S. Geological Survey streamgages with a minimum of 10 years of recorded peak flows between 1963 and 2012. Ordinary least-squares regression techniques were used to determine the best explanatory variables for the regression equations. Traditional map-based explanatory variables were compared to variables requiring field measurements. Two field-based variables—culvert rust lines and bankfull channel widths—either were not commonly found or did not explain enough of the variability in the peak flows to warrant inclusion in the equations. The best explanatory variables were drainage area and percent basin wetlands; values for these variables were determined with a geographic information system. Generalized least-squares regression was used with these two variables to determine the equation coefficients and estimates of accuracy for the final equations.
Institute of Scientific and Technical Information of China (English)
GE Jian-Ya; WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schr(o)dinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
A Distributed Problem Solving Environment (PSE) for Partial Differential Equation Based Problems
National Research Council Canada - National Science Library
TERAMOTO, Takayuki; NAKAMURA, Takashi; KAWATA, Shigeo; MATIDE, Syunsuke; HAYASAKA, Koji; NONAKA, Hidetaka; SASAKI, Eiji; SANADA, Yasuhiro
2001-01-01
...) for partial differential equation (PDE) based problems. The system inputs a problem information including a discretization and computation scheme, and outputs a program flow and also a C-language source code for the problem...
Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials
Faustino, Nelson
2016-01-01
The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of solutions. The development of a well-adapted discrete Clifford calculus framework based on spinor fields allows us to represent, using solely projection based arguments, the solutions for the discretized Dirac equations from the knowledge of the solutions of the discretized Klein-Gordon equation. Implications of those findings on the interpretation of the lattice fermion doubling problem is briefly discussed.
Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations
Directory of Open Access Journals (Sweden)
Hongcai Yin
2014-01-01
Full Text Available By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations AX+YB=C and DX+YE=F in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation AXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.
A Surface Tension Model for Liquid Mixtures Based on NRTL Equation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.
Energy Technology Data Exchange (ETDEWEB)
Li, Xiao, E-mail: lixiao1228@163.com; Ji, Guanghua, E-mail: ghji@bnu.edu.cn; Zhang, Hui, E-mail: hzhang@bnu.edu.cn
2015-02-15
We use the stochastic Cahn–Hilliard equation to simulate the phase transitions of the macromolecular microsphere composite (MMC) hydrogels under a random disturbance. Based on the Flory–Huggins lattice model and the Boltzmann entropy theorem, we develop a reticular free energy suit for the network structure of MMC hydrogels. Taking the random factor into account, with the time-dependent Ginzburg-Landau (TDGL) mesoscopic simulation method, we set up a stochastic Cahn–Hilliard equation, designated herein as the MMC-TDGL equation. The stochastic term in the equation is constructed appropriately to satisfy the fluctuation-dissipation theorem and is discretized on a spatial grid for the simulation. A semi-implicit difference scheme is adopted to numerically solve the MMC-TDGL equation. Some numerical experiments are performed with different parameters. The results are consistent with the physical phenomenon, which verifies the good simulation of the stochastic term.
From Equation to Inequality Using a Function-Based Approach
Verikios, Petros; Farmaki, Vassiliki
2010-01-01
This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to…
From Equation to Inequality Using a Function-Based Approach
Verikios, Petros; Farmaki, Vassiliki
2010-01-01
This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to…
A Boussinesq Equation-Based Model for Nearshore Wave Breaking
Institute of Scientific and Technical Information of China (English)
余建星; 张伟; 王广东; 杨树清
2004-01-01
Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally' s analytical solution to the wave-height decay irstead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.
Comparison of stator-mounted permanent-magnet machines based on a general power equation
DEFF Research Database (Denmark)
Chen, Zhe; Hua, Wei; Cheng, Ming
2009-01-01
The stator-mounted permanent-magnet (SMPM) machines have some advantages compared with its counterparts, such as simple rotor, short winding terminals, and good thermal dissipation conditions for magnets. In this paper, a general power equation for three types of SMPM machine is introduced first......, and then, power equations considering the specific topologies are derived. Based on these power equations, theoretical comparisons are carried out between various types of the SMPM machines. In all, eight topologies have been presented and benchmarked. It reveals that the flux switching permanent......-magnet (PM) machine owns higher power density than the flux reversal PM machine and the doubly salient PM machine under same outer diameter. The comparison based on the power equation has established a foundation for optimizing the SMPM machines....
Xie, Jiaquan; Huang, Qingxue; Yang, Xia
2016-01-01
In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.
Finite difference modeling of sinking stage curved beam based on revised Vlasov equations
Institute of Scientific and Technical Information of China (English)
张磊; 朱真才; 沈刚; 曹国华
2015-01-01
For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.
A Switching Algorithm Based on Modified Quasi-Newton Equation
Institute of Scientific and Technical Information of China (English)
Yueting Yang; Chengxian Xu
2006-01-01
In this paper, a switching method for unconstrained minimization is proposed.The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization.The numerical results are reported and analyzed to show the superiority of the proposed method.
Wavelet-based integral representation for solutions of the wave equation
Energy Technology Data Exchange (ETDEWEB)
Perel, Maria V; Sidorenko, Mikhail S [Department of Mathematical Physics, Physics Faculty, St Petersburg University, Ulyanovskaya 1-1, Petrodvorets, St Petersburg 198904 (Russian Federation)], E-mail: perel@mph.phys.spbu.ru, E-mail: M-Sidorenko@yandex.ru
2009-09-18
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on mathematical techniques of continuous wavelet analysis. The formulae obtained are justified from the point of view of distribution theory. A comparison of the results with those by G Kaiser is carried out. Methods of obtaining physical wavelets are discussed.
Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions
Directory of Open Access Journals (Sweden)
Yeguo Sun
2012-01-01
Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.
A new non-exercise-based Vo2max prediction equation for aerobically trained men.
Malek, Moh H; Housh, Terry J; Berger, Dale E; Coburn, Jared W; Beck, Travis W
2005-08-01
The purposes of the present study were to (a) modify previously published Vo(2)max equations using the constant error (CE = mean difference between actual and predicted Vo(2)max) values from Malek et al. (28); (b) cross-validate the modified equations to determine their accuracy for estimating Vo(2)max in aerobically trained men; (c) derive a new non- exercise-based equation for estimating Vo(2)max in aerobically trained men if the modified equations are not found to be accurate; and (d) cross-validate the new Vo(2)max equation using the predicted residual sum of squares (PRESS) statistic and an independent sample of aerobically trained men. One hundred and fifty-two aerobically trained men (Vo(2)max mean +/- SD = 4,154 +/- 629 ml.min(-1)) performed a maximal incremental test on a cycle ergometer to determine actual Vo(2)max. An aerobically trained man was defined as someone who had participated in continuous aerobic exercise 3 or more sessions per week for a minimum of 1 hour per session for at least the past 18 months. Nine previously published Vo(2)max equations were modified for use with aerobically trained men. The predicted Vo(2)max values from the 9 modified equations were compared to actual Vo(2)max by examining the CE, standard error of estimate (SEE), validity coefficient (r), and total error (TE). Cross-validation of the modified non-exercise-based equations on a random subsample of 50 subjects resulted in a %TE > or = 13% of the mean of actual Vo(2)max. Therefore, the following non-exercise-based Vo(2)max equation was derived from a random subsample of 112 subjects: Vo(2)max (ml.min(-1)) = 27.387(weight in kg) + 26.634(height in cm) - 27.572(age in years) + 26.161(h.wk(-1) of training) + 114.904(intensity of training using the Borg 6-20 scale) + 506.752(natural log of years of training) - 4,609.791 (R = 0.82, R(2) adjusted = 0.65, and SEE = 378 ml.min(-1)). Cross-validation of this equation on the remaining sample of 40 subjects resulted in a %TE of 10
Alirezaei, M.; Kanarachos, S.A.; Scheepers, B.T.M.; Maurice, J.P.
2013-01-01
Development and experimentally evaluation of an optimal Vehicle Dynamic Control (VDC) strategy based on the State Dependent Riccati Equation (SDRE) control technique is presented. The proposed nonlinear controller is based on a nonlinear vehicle model with nonlinear tire characteristics. A novel ext
Alirezaei, M.; Kanarachos, S.A.; Scheepers, B.T.M.; Maurice, J.P.
2013-01-01
Development and experimentally evaluation of an optimal Vehicle Dynamic Control (VDC) strategy based on the State Dependent Riccati Equation (SDRE) control technique is presented. The proposed nonlinear controller is based on a nonlinear vehicle model with nonlinear tire characteristics. A novel
The Effect of Small Calibration Sample Sizes on TOEFL IRT-Based Equating.
Tang, K. Linda; And Others
This study compared the performance of the LOGIST and BILOG computer programs on item response theory (IRT) based scaling and equating for the Test of English as a Foreign Language (TOEFL) using real and simulated data and two calibration structures. Applications of IRT for the TOEFL program are based on the three-parameter logistic (3PL) model.…
A multivariate family-based association test using generalized estimating equations : FBAT-GEE
Lange, C; Silverman, SK; Xu, [No Value; Weiss, ST; Laird, NM
2003-01-01
In this paper we propose a multivariate extension of family-based association tests based on generalized estimating equations. The test can be applied to multiple phenotypes and to phenotypic data obtained in longitudinal studies without making any distributional assumptions for the phenotypic obser
Directory of Open Access Journals (Sweden)
Luning Shi
2014-01-01
Full Text Available A prestress force identification method for externally prestressed concrete uniform beam based on the frequency equation and the measured frequencies is developed. For the purpose of the prestress force identification accuracy, we first look for the appropriate method to solve the free vibration equation of externally prestressed concrete beam and then combine the measured frequencies with frequency equation to identify the prestress force. To obtain the exact solution of the free vibration equation of multispan externally prestressed concrete beam, an analytical model of externally prestressed concrete beam is set up based on the Bernoulli-Euler beam theory and the function relation between prestress variation and vibration displacement is built. The multispan externally prestressed concrete beam is taken as the multiple single-span beams which must meet the bending moment and rotation angle boundary conditions, the free vibration equation is solved using sublevel simultaneous method and the semi-analytical solution of the free vibration equation which considered the influence of prestress on section rigidity and beam length is obtained. Taking simply supported concrete beam and two-span concrete beam with external tendons as examples, frequency function curves are obtained with the measured frequencies into it and the prestress force can be identified using the abscissa of the crosspoint of frequency functions. Identification value of the prestress force is in good agreement with the test results. The method can accurately identify prestress force of externally prestressed concrete beam and trace the trend of effective prestress force.
An adjoint-based approach for finding invariant solutions of Navier-Stokes equations
Farazmand, Mohammad
2015-01-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flo...
Connectivity as an alternative to boundary integral equations: Construction of bases
Herrera, Ismael; Sabina, Federico J.
1978-01-01
In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522
Directory of Open Access Journals (Sweden)
Gülden Gün
2013-01-01
Full Text Available We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.
A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations
Directory of Open Access Journals (Sweden)
Xiaomin Wang
2014-01-01
Full Text Available A wavelet iterative method based on a numerical integration by using the Coiflets orthogonal wavelets for a nonlinear fractional differential equation is proposed. With the help of Laplace transform, the fractional differential equation was converted into equivalent integral equation of convolution type. By using the wavelet approximate scheme of a function, the undesired jump or wiggle phenomenon near the boundary points was avoided and the expansion constants in the approximation of arbitrary nonlinear term of the unknown function can be explicitly expressed in finite terms of the expansion ones of the approximation of the unknown function. Then a numerical integration method for the convolution is presented. As an example, an iterative method which can solve the singular nonlinear fractional Riccati equations is proposed. Numerical results are performed to show the efficiency of the method proposed.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solution problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACO algorithm. Finally, the ACO with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.
Directory of Open Access Journals (Sweden)
Yaodeng Chen
2014-01-01
Full Text Available There are two different approaches on how to formulate adjoint numerical model (ANM. Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper.
A simple and accurate model for Love wave based sensors: Dispersion equation and mass sensitivity
Directory of Open Access Journals (Sweden)
Jiansheng Liu
2014-07-01
Full Text Available Dispersion equation is an important tool for analyzing propagation properties of acoustic waves in layered structures. For Love wave (LW sensors, the dispersion equation with an isotropic-considered substrate is too rough to get accurate solutions; the full dispersion equation with a piezoelectric-considered substrate is too complicated to get simple and practical expressions for optimizing LW-based sensors. In this work, a dispersion equation is introduced for Love waves in a layered structure with an anisotropic-considered substrate and an isotropic guiding layer; an intuitive expression for mass sensitivity is also derived based on the dispersion equation. The new equations are in simple forms similar to the previously reported simplified model with an isotropic substrate. By introducing the Maxwell-Weichert model, these equations are also applicable to the LW device incorporating a viscoelastic guiding layer; the mass velocity sensitivity and the mass propagation loss sensitivity are obtained from the real part and the imaginary part of the complex mass sensitivity, respectively. With Love waves in an elastic SiO2 layer on an ST-90°X quartz structure, for example, comparisons are carried out between the velocities and normalized sensitivities calculated by using different dispersion equations and corresponding mass sensitivities. Numerical results of the method presented in this work are very close to those of the method with a piezoelectric-considered substrate. Another numerical calculation is carried out for the case of a LW sensor with a viscoelastic guiding layer. If the viscosity of the layer is not too big, the effect on the real part of the velocity and the mass velocity sensitivity is relatively small; the propagation loss and the mass loss sensitivity are proportional to the viscosity of the guiding layer.
Barakat, A. R.; Schunk, R. W.
1982-01-01
A wide variety of plasma flow conditions is found in aeronomy and space plasma physics. Transport equations based on an isotropic Maxwellian vilecity distribution function can be used to describe plasma flows which contain 'small' temperature anisotropies. However, for plasma flows characterized by large temperature anisotropies, transport equations based on an anisotropic bi-Maxwellian (or two-temperature) velocity distribution function are expected to provide a much better description of the plasma transport properties. The present investigation is concerned with the extent to which transport equations based on both Maxwellian and bi-Maxwellian series expansions can describe plasma flows characterized by non-Maxwellian velocity distributions, giving particular attention to a modelling of the anisotropic character of the distribution function. The obtained results should provide clues as to the extent to which a given series expansion can account for the anisotropic character of a plasma.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
Zhou, Yanjun; Yin, Cangtao
2016-12-01
The Fokker-Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The memory effect, taken into transition probability, is relevant and important for lots of anomalous phenomena. The Taylor expansion for large volume is applied to derive the power-law FPE. The steady-state solution of FPE and microscopic dynamics Ito-Langevin equation of concentration variables are therefore obtained and discussed. Two unimolecular reactions are taken as examples and the concentration distributions with different power-law parameters are analyzed, which may imply strong memory effect of hopping process.
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
A set of microstructure-based constitutive equations in hot forming of a titanium alloy
Institute of Scientific and Technical Information of China (English)
Xiaoli Li; Miaoquan Li
2006-01-01
A physical model of microstructure evolution including dislocation density rate and grain growth rate was established based on the deformation mechanism for the hot forming of a class of two-phase titanium alloys. Further, a set of mechanism-based constitutive equations were proposed, in which the microstructure variables such as grain size and dislocation density were taken as internal state variables for characterizing the current material state. In the set of constitutive equations, the contributions of different mechanisms and individual phase to the deformation behavior were analyzed. The present equations have been applied to describe a correlation of the flow stress with the microstructure evolution of the TC6 alloy in hot forming.
An Improved Nearshore Wave Breaking Model Based on the Fully Nonlinear Boussinesq Equations
Institute of Scientific and Technical Information of China (English)
LI Shao-wu; LI Chun-ying; SHI Zhong; GU Han-bin
2005-01-01
This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.
Fan, Zongwei; Mei, Deqing; Yang, Keji; Chen, Zichen
2014-12-01
To eliminate the limitations of the conventional sound field separation methods which are only applicable to regular surfaces, a sound field separation method based on combined integral equations is proposed to separate sound fields directly in the spatial domain. In virtue of the Helmholtz integral equations for the incident and scattering fields outside a sound scatterer, combined integral equations are derived for sound field separation, which build the quantitative relationship between the sound fields on two arbitrary separation surfaces enclosing the sound scatterer. Through boundary element discretization of the two surfaces, corresponding systems of linear equations are obtained for practical application. Numerical simulations are performed for sound field separation on different shaped surfaces. The influences induced by the aspect ratio of the separation surfaces and the signal noise in the measurement data are also investigated. The separated incident and scattering sound fields agree well with the original corresponding fields described by analytical expressions, which validates the effectiveness and accuracy of the combined integral equations based separation method. Copyright © 2014 Elsevier B.V. All rights reserved.
A Nitsche-based domain decomposition method for hypersingular integral equations
Chouly, Franz
2011-01-01
We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as opposed to the traditional mortar method. We prove its almost quasi-optimal convergence and underline the theory by a numerical experiment.
A meshless based method for solution of integral equations: Improving the error analysis
Mirzaei, Davoud
2015-01-01
This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian of some parts of Chapter 2 of the author's PhD thesis in 2011.
Standards-Based Evaluation and Teacher Career Satisfaction: A Structural Equation Modeling Analysis
Conley, Sharon; Muncey, Donna E.; You, Sukkyung
2005-01-01
Structural equation modeling was used to assess the plausibility of a conceptual model specifying hypothesized linkages among perceptions of characteristics of standards-based evaluation, work environment mediators, and career satisfaction and other outcomes. Four comprehensive high schools located in two neighboring counties in southern…
Directory of Open Access Journals (Sweden)
Qin Ma
2008-05-01
Full Text Available Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.
Institute of Scientific and Technical Information of China (English)
Fang Zhang; Wenyao Liu; Lin Xia; Jinjiang Wang; Yue Zhu
2009-01-01
Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.
Numerical Simulation of Breaking Wave Based on Higher-Order Mild Slope Equation
Institute of Scientific and Technical Information of China (English)
陶建华; 韩光
2001-01-01
The "surface roller" to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation including diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circularshoal, and the numerical results of random wave breaking model agree with the experimental data very well. This modelcan be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natural topography.
Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots
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Ching-Long Shih
2012-08-01
Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on-line numerical computations. Based on the decomposition approach and cross-product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on-line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed-chain robot systems.
Tang, Chen; Zhang, Fang; Yan, Haiqing; Chen, Zhanqing
2006-04-01
Denoising in electronic speckle pattern interferometry fringes is the key problem in electronic speckle pattern interferometry. We present the new filtering method based on partial differential equations (called PDE filtering method) to electronic speckle pattern interferometry fringes. The PDE filtering method transforms the image processing to solving the partial differential equations. We test the proposed method on experimentally obtained electronic speckle pattern interferometry fringes, and compare with traditional mean filtering and low-pass Fourier filtering methods. The experimental results show that the technique is capable of effectively removing noise. The PDE filtering method is flexible and has fast computational speed and stable results.
On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations
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Abdeslem Hafid Bentbib
2017-03-01
Full Text Available In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments.
Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots
Directory of Open Access Journals (Sweden)
Ching-Long Shih
2012-08-01
Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton‐Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on‐line numerical computations. Based on the decomposition approach and cross‐product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on‐line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed‐chain robot systems.
Ortiz-Hernández, Luis; Vega López, A Valeria; Ramos-Ibáñez, Norma; Cázares Lara, L Joana; Medina Gómez, R Joab; Pérez-Salgado, Diana
To develop and validate equations to estimate the percentage of body fat of children and adolescents from Mexico using anthropometric measurements. A cross-sectional study was carried out with 601 children and adolescents from Mexico aged 5-19 years. The participants were randomly divided into the following two groups: the development sample (n=398) and the validation sample (n=203). The validity of previously published equations (e.g., Slaughter) was also assessed. The percentage of body fat was estimated by dual-energy X-ray absorptiometry. The anthropometric measurements included height, sitting height, weight, waist and arm circumferences, skinfolds (triceps, biceps, subscapular, supra-iliac, and calf), and elbow and bitrochanteric breadth. Linear regression models were estimated with the percentage of body fat as the dependent variable and the anthropometric measurements as the independent variables. Equations were created based on combinations of six to nine anthropometric variables and had coefficients of determination (r(2)) equal to or higher than 92.4% for boys and 85.8% for girls. In the validation sample, the developed equations had high r(2) values (≥85.6% in boys and ≥78.1% in girls) in all age groups, low standard errors (SE≤3.05% in boys and ≤3.52% in girls), and the intercepts were not different from the origin (p>0.050). Using the previously published equations, the coefficients of determination were lower, and/or the intercepts were different from the origin. The equations developed in this study can be used to assess the percentage of body fat of Mexican schoolchildren and adolescents, as they demonstrate greater validity and lower error compared with previously published equations. Copyright © 2017 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Asiri, Sharefa M.
2013-05-25
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Bai, Shirong; Skodje, Rex T
2017-08-17
A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H2 combustion model.
Furtmaier, Oliver
2016-01-01
Inspired by the idea of mimicking the measurement on a quantum system through a decoherence process to target specific eigenstates based on Born's law instead of the hierarchy of eigenvalues, we transform a Lindblad equation for the reduced density operator into a nonlinear Schr\\"odinger equation to obtain a computationally feasible simulation of the decoherent dynamics in the open quantum system. The method shows an exponential convergence and its computational costs scale linear for sparse matrix representations of the involved Hermitian operators. Symmetries of the problem can be incorporated either in the initial state of the dynamics or explicitly using the symmetry operators in the evolution equation. As an application of the method we discuss \\textit{eigenstate towing}, which relies on the perturbation theory to follow the progression of an arbitrary subset of eigenstates along a sum of perturbation operators with the intention to explore for instance the effect of interactions on these eigenstates.
Institute of Scientific and Technical Information of China (English)
2008-01-01
A discrete ordinates method for a threedimensional first-order neutron transport equation based on unstructured-meshes that avoids the singularity of the second-order neutron transport equation in void regions was derived.The finite element variation equation was obtained using the least-squares method.A three-dimensional transport calculation code was developed.Both the triangular-z and the tetrahedron elements were included.The numerical results of some benchmark problems demonstrated that this method can solve neutron transport problems in unstructuredmeshes very well.For most problems,the error of the eigenvalue and the angular flux is less than 0.3% and 3.0% respectively.
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2015-04-01
This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.
Xu, Ling; Cheng, Xuan; Dai, Chao-Qing
2015-12-01
Although the mapping method based on Riccati equation was proposed to obtain variable separation solutions many years ago, two important problems have not been studied: i) the equivalence of variable separation solutions by means of the mapping method based on Riccati equation with the radical sign combined ansatz; and ii) lack of physical meanings for some localized structures constructed by variable separation solutions. In this paper, we re-study the (2+1)-dimensional Boiti-Leon-Pempinelli equation via the mapping method based on Riccati equation and prove that nine types of variable separation solutions are actually equivalent to each other. Moreover, we also re-study localized structures constructed by variable separation solutions. Results indicate that some localized structures reported in the literature are lacking real values due to the appearance of the divergent and un-physical phenomenon for the initial field. Therefore, we must be careful with the initial field to avoid the appearance of some un-physical or even divergent structures in it when we construct localized structures for the potential field.
A quadrature based method of moments for nonlinear Fokker-Planck equations
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Noise Analysis of Common-Base Amplifier using Stochastic Differential Equation
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Dushyant Kumar Shukla
2014-03-01
Full Text Available In this paper, we analyse the effect of noise in a common-base amplifier working at high frequencies. Extrinsic noise is analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications for improved noise characteristics of the common-base amplifier
Estimation of Velocity Profile Based on Chiu’s Equation in Width of Channels
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Saman Nikmehr
2010-08-01
Full Text Available Distribution of velocity in channel is one of the most parameters for solution of hydraulic problems. Determination of energy coefficient, momentum and distribution of sediment concentration depend on distribution of velocity profile. The entropy parameter of a channel section can be determined from the relation between the mean and maximum velocities. A technique has been developed to determine a velocity profile on a single vertical passing through the point of maximum velocity in a channel cross section. This method is a way in order to quick and cheap estimating of velocity distribution with high accuracy in channels. So that in this research the power estimation of Chiu method base on entropy concept was determined. Also Chiu’s equation that is based on entropy concept and probability domain, has compared with logarithmic and exponential equations to estimation of velocity profile in width of channel in various depths. The results show that Chiu’s equation better than logarithmic and exponential equations to estimation of velocity profile in width of channel.
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
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Vladimir P. Gerdt
2006-05-01
Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.
Institute of Scientific and Technical Information of China (English)
ZHANG Suying; DENG Zichen
2005-01-01
Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.
Institute of Scientific and Technical Information of China (English)
QIU Ling; GONG XueDong; JU XueHai; XIAO HeMing
2008-01-01
Density functional theory (DFT) method has been employed to study the effect of nitroamino group as a substituent in cyclopentane and cyclohexane, which usually construct the polycyclic or caged nitra-mines. Molecular structures were investigated at the B3LYP/6-31G** level, and isodesmic reactions were designed for calculating the group interactions. The results show that the group interactions ac-cord with the group additivity, increasing with the increasing number of nitroamino groups. The distance between substituents influences the interactions. Detonation performances were evaluated by the Kamlet-Jacobs equations based on the predicted densities and heats of formation, while thermal stability and pyrolysis mechanism were studied by the computations of bond dissociation energy (BDE). It is found that the contributions of nitroamino groups to the detonation heat, detonation velocity, detonation pressure, and stability all deviate from the group additivity. Only 3a, 3b, and 9a-9c may be novel potential candidates of high energy density materials (HEDMs) according to the quantitative cri-teria of HEDM (ρ≈1.9 g/cm3, D≈9.0 km/s, P≈40.0 GPa). Stability decreases with the increasing number of N-NO2 groups, and homolysis of N-NO2 bond is the initial step in the thermolysis of the title com-pounds. Coupled with the demand of thermal stability (BDE > 20 kcal/mol), only 1,2,4-trinitrotriazacy-clohexane and 1,2,4,5-tetranitrotetraazacyclohexane are suggested as feasible energetic materials.These results may provide basic information for the molecular design of HEDMs.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Density functional theory (DFT) method has been employed to study the effect of nitroamino group as a substituent in cyclopentane and cyclohexane, which usually construct the polycyclic or caged nitra-mines. Molecular structures were investigated at the B3LYP/6-31G** level, and isodesmic reactions were designed for calculating the group interactions. The results show that the group interactions ac-cord with the group additivity, increasing with the increasing number of nitroamino groups. The dis-tance between substituents influences the interactions. Detonation performances were evaluated by the Kamlet-Jacobs equations based on the predicted densities and heats of formation, while thermal stability and pyrolysis mechanism were studied by the computations of bond dissociation energy (BDE). It is found that the contributions of nitroamino groups to the detonation heat, detonation velocity, detonation pressure, and stability all deviate from the group additivity. Only 3a, 3b, and 9a-9c may be novel potential candidates of high energy density materials (HEDMs) according to the quantitative cri-teria of HEDM (ρ≈ 1.9 g/cm3, D ≈ 9.0 km/s, P ≈ 40.0 GPa). Stability decreases with the increasing number of N-NO2 groups, and homolysis of N-NO2 bond is the initial step in the thermolysis of the title com-pounds. Coupled with the demand of thermal stability (BDE > 20 kcal/mol), only 1,2,4-trinitrotriazacy-clohexane and 1,2,4,5-tetranitrotetraazacyclohexane are suggested as feasible energetic materials. These results may provide basic information for the molecular design of HEDMs.
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.
Institute of Scientific and Technical Information of China (English)
FENG Jie; XU WenCheng; LI ShuXian; LIU SongHao
2008-01-01
Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduc-tion algorithm.The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper.And these theoretical results are consistent with the numerical simulations.
INVESTIGATION ON KANE DYNAMIC EQUATIONS BASED ON SCREW THEORY FOR OPENCHAIN MANIPULATORS
Institute of Scientific and Technical Information of China (English)
LIU Wu-fa; GONG Zhen-bang; WANG Qin-que
2005-01-01
First, screw theory, product of exponential formulas and Jacobian matrix are introduced. Then definitions are given about active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force according to screw theory. After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising
2014-01-01
Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient s...
A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
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Mustafa Inc
2013-01-01
Full Text Available We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.
Green, B. I.; Vedula, Prakash
2013-07-01
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework.
[New topics regarding equations for GFR estimation based on serum creatinine and cystatin C].
Horio, Masaru
2014-02-01
Japanese GFR equations and CKD-EPI equations based on standardized serum creatinine and standardized cystatin C are recommended in recent Japanese CKD guides and KDIGO guidelines for CKD management, respectively. CKD-EPIcreat overestimates GFR in Japanese subjects, probably due to the difference in muscle mass between Japanese and Caucasians. Unlike CKD-EPIcreat, CKD-EPIcys performs well in Japanese subjects, indicating the advantages of using cystatin C as a GFR marker. KDIGO guidelines suggest measuring eGFRcys in adults with eGFRcreat of 45-59 ml/min/1.73 m2 who do not have markers of kidney damage if confirmation of CKD is required. Creatinine is excreted by glomerular filtration, but also secreted by the tubules. Alteration of the tubular secretion of creatinine may influence the performance of GFR equations based on serum creatinine. Multivariate analysis showed that GFR and serum albumin levels were independent parameters affecting the fractional excretion of creatinine (FE-Cr). Alteration of FE-Cr according to the serum albumin levels may be one of the reasons for the bias of GFR equations based on serum creatinine. Low GFR is a risk factor for all-cause and cardiovascular mortality in a general population. However, the relationship between eGFR and the hazard risk of events is different depending on whether cystatin C or creatinine is used to calculate eGFR. The association between eGFRcys and the hazard risk is much stronger compared with eGFRcreat. Cystatin C may be a useful alternative to creatinine for detecting a high risk of complications in a general population and subjects with CKD.
Polynomial-based approximate solutions to the Boussinesq equation near a well
Telyakovskiy, Aleksey S.; Kurita, Satoko; Allen, Myron B.
2016-10-01
This paper presents a method for constructing polynomial-based approximate solutions to the Boussinesq equation with cylindrical symmetry. This equation models water injection at a single well in an unconfined aquifer; as a sample problem we examine recharge of an initially empty aquifer. For certain injection regimes it is possible to introduce similarity variables, reducing the original problem to a boundary-value problem for an ordinary differential equation. The approximate solutions introduced here incorporate both a singular part to model the behavior near the well and a polynomial part to model the behavior in the far field. Although the nonlinearity of the problem prevents decoupling of the singular and polynomial parts, the paper presents an approach for calculating the solution based on its spatial moments. This approach yields closed-form expressions for the position of the wetting front and for the form of the phreatic surface. Comparison with a highly accurate numerical solution verifies the accuracy of the newly derived approximate solutions.
GENERAL CONSTITUTIVE EQUATIONS OF AN ER SUSPENSION BASED ON THE INTERNAL VARIABLE THEORY
Institute of Scientific and Technical Information of China (English)
王彪; 肖忠民
2001-01-01
A microstructural constitutive theory of ER suspensions was formulated in this investigation. The framework was based on the internal variable theory and the mechanism analysis. The ER suspension consists of fine particles with high dielectric constant and the supporting fluid. Under the action of the electric field, the polarized particles will aggregate together to form the chain-like structures along the direction of the electric field.As the size and orientation of the particle aggregates are volatile, and they adjust according to the applied electric field and strain rate, the energy conservation equation and the force equilibrium equation were thus established to determine the orientation and size of the aggregates. Following that, a three-dimensional, explicit form of the constitutive equation was derived based on the interaction energy and the dissipation function of the system. The response of the system under the action of a simple shearing load was considered and discussed in detail. It is found that the shear-thinning viscosity of an ER suspension is well approximated by the power-law ∞ (Mn) -0.82
Directory of Open Access Journals (Sweden)
Kanittha Yimnak
2014-01-01
Full Text Available The meshless local Pretrov-Galerkin method (MLPG with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.
Directory of Open Access Journals (Sweden)
F. P. Santos
2013-09-01
Full Text Available Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0,∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.
Tang, Chen; Wang, Linlin; Yan, Haiqing
2012-07-10
In this paper, we first present the general description for partial differential equations (PDEs) based image processing methods, including the basic idea, the main advantages and disadvantages, a few representative PDE models, and the derivation of PDE models. Then we review our contributions on PDE-based anisotropic filtering methods for electronic speckle pattern interferometry, including the second-order, fourth-order, and coupled nonoriented PDE filtering models and the second-order and coupled nonlinear oriented PDE filtering models. We have summarized the features of each model.
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Hamid A. Jalab
2014-01-01
Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.
Institute of Scientific and Technical Information of China (English)
Guo Yushun
2001-01-01
A new transient analysis method for the transmission line circuits is presented in this paper. Based on the semidiscretization of the telegraph equations, a discretized time domain companion models for the transmission lines which can be conveniently implemented in a general circuit simulator such as SPICE is derived. The computation required for the model is linear with time, equivalent to the recursive convolution-based method. The formulations for both single and coupled lossy transmission lines are given. Numerical experiments are carried out to demonstrate the validity of the method.
Institute of Scientific and Technical Information of China (English)
TAO Wen-peng; DONG Shou-hua; LI Yang
2008-01-01
In seismic exploration for coal, seismic waves are very difficult to transmit downward because of high velocity protec-tive layers, making the reflection information very hard to receive above ground. Based on the Snell law and the Zoeppritz equation, we studied the relationship between the incidence angle and reflection seismic wave energy using a forward model of level media. The result shows that the seismic wave energy has a sudden increase at the critical angle. Based on the energy propagation rule, using big offset to receive the seismic wave energy under a protective layer can effectively reduce its protection effect.
2014-06-01
3D Euler Equations of Moist Atmospheric Convection 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...STABILIZATION OF SPECTRAL ELEMENTS FOR THE 3D EULER EQUATIONS OF MOIST ATMOSPHERIC CONVECTION SIMONE MARRAS, ANDREAS MÜLLER, FRANCIS X. GIRALDO Dept. Appl...spectral elements, we introduce a dissipative scheme based on the solution of the compressible Euler equations that are regularized through the addi
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
Zhang, Fang; Wang, Danyu; Xiao, Zhitao; Geng, Lei; Wu, Jun; Xu, Zhenbei; Sun, Jiao; Wang, Jinjiang; Xi, Jiangtao
2015-11-16
A novel phase extraction method for single electronic speckle pattern interferometry (ESPI) fringes is proposed. The partial differential equations (PDEs) are used to extract the skeletons of the gray-scale fringe and to interpolate the whole-field phase values based on skeleton map. Firstly, the gradient vector field (GVF) of the initial fringe is adjusted by an anisotropic PDE. Secondly, the skeletons of the fringe are extracted combining the divergence property of the adjusted GVF. After assigning skeleton orders, the whole-field phase information is interpolated by the heat conduction equation. The validity of the proposed method is verified by computer-simulated and experimentally obtained poor-quality ESPI fringe patterns.
A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhendong LUO; Lei LI; Ping SUN
2013-01-01
In this paper, we extend the applications of proper orthogonal decomposition (POD) method, i.e., apply POD method to a mixed finite element (MFE) formulation naturally satisfied Brezz-Babu˘ska for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and suﬃciently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis-tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and eﬃcient for solving MFE formulation for parabolic equations.
Modeling the Heating of Biological Tissue based on the Hyperbolic Heat Transfer Equation
Tung, M M; Molina, J A Lopez; Rivera, M J; Berjano, E J
2008-01-01
In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled by the bioheat equation introduced by Pennes, who considers Fourier's theory of heat conduction. We present an alternative and more realistic model established by the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the obtained results to different types of tissue heating with high energy fluxes, in particular radiofrequency heating and pulsed laser treatment of the cornea to correct refractive errors. Hopefully, the results of our approach help to refine surgical interventions in this novel field of medical treatment.
A multi-dimensional kinetic-based upwind solver for the Euler equations
Eppard, W. M.; Grossman, B.
1993-01-01
A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.
An unstructured grid, three-dimensional model based on the shallow water equations
Casulli, V.; Walters, R.A.
2000-01-01
A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
A simple numerical method for snowmelt simulation based on the equation of heat energy.
Stojković, Milan; Jaćimović, Nenad
2016-01-01
This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events.
UNIFIED MODELS OF ELEMENTS OF POWER SUPPLY SYSTEMS BASED ON EQUATIONS IN PHASE COORDINATES
Directory of Open Access Journals (Sweden)
Yu.N. Vepryk
2015-12-01
Full Text Available Purpose. The models of electrical machines in the phase coordinates, the universal algorithm for the simulation of separate elements in a d-q coordinates system and in a phase-coordinates system are proposed. Methodology. Computer methods of investigation of transients in electrical systems are based on a compilation of systems of differential equations and their numerical integration solution methods. To solve differential equations an implicit method of numerical integration was chosen. Because it provides to complete structural simulation possibility: firstly developing models of separate elements and then forming a model of the complex system. For the mathematical simulation of electromagnetic transients in the elements of the electrical systems has been accepted the implicit Euler-Cauchy method, because it provides a higher precision and stability of the computing processes. Results. In developing the model elements identified two groups of elements: - Static elements and electrical machines in the d-q coordinates; - Rotating electrical machines in phase coordinates. As an example, the paper provides a model of synchronous and asynchronous electric machines in the d-q coordinates system and the phase coordinate system. The generalization algorithm and the unified notation form of equations of elements of an electrical system are obtained. It provides the possibility of using structural methods to develop a mathematical model of power systems under transient conditions. Practical value. In addition, the using of a computer model allows to implement multivariant calculations for research and study of factors affecting the quantitative characteristics of the transients.
The adjoint method for general EEG and MEG sensor-based lead field equations
Energy Technology Data Exchange (ETDEWEB)
Vallaghe, Sylvain; Papadopoulo, Theodore; Clerc, Maureen [INRIA, Projet Odyssee, Sophia Antipolis (France)], E-mail: Sylvain.Vallaghe@sophia.inria.fr
2009-01-07
Most of the methods for the inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) use a lead field as an input. The lead field is the function which relates any source in the brain to its measurements at the sensors. For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles), and the computation can be expensive for as much as 10 000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. In this paper, we use the adjoint method to derive general EEG and MEG sensor-based lead field equations. Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-pointlike sensors.
HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation
Directory of Open Access Journals (Sweden)
Shu-Li Mei
2014-01-01
Full Text Available The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j from O(43J, (j≪J. The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods.
HPM-based dynamic sparse grid approach for Perona-Malik equation.
Mei, Shu-Li; Zhu, De-Hai
2014-01-01
The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4 (J+2j)) from O(4(3J)), (j ≪ J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods.
Numerical simulation for the Gross-Pitaevskii equation based on the lattice Boltzmann method
Wang, Huimin
2017-09-01
A lattice Boltzmann model for the Gross-Pitaevskii equation is proposed in this paper. Some numerical tests for one- and two-dimensional Gross-Pitaevskii equation have been conducted. The waves of the Gross-Pitaevskii equation are simulated. Numerical results show that the lattice Boltzmann method is an effective method for the wave of the Gross-Pitaevskii equation.
LANDSLIDE-TYPE TSUNAMI MODELLING BASED ON THE NAVIER - STOKES EQUATIONS
Directory of Open Access Journals (Sweden)
A.S. Kozelkov
2016-11-01
Full Text Available The paper presents a unified computing technology for all stages of landslide-type tsunami. The computing technology is based on the numerical solution of the Navier – Stokes equations for multiphase flows. The method of numerical solution of the Navier – Stokes equations uses a fully implicit algorithm. This algorithm removes stiff restrictions on the time steps and allows simulating a tsunami propagation in arbitrarily large water basins. The basic sampling equation formulas, coefficient types as well as the basic steps of the computational procedure are presented. The landslide is modeled by a single phase with its density and viscosity, which is separated by the interface from water and air phases. A parallel algorithm of the method implementation based on an algebraic multigrid method is proposed for the effective usage of the method to calculate the tsunami in large water areas. The multigrid method of implementation is based on algorithms of global level and cascading collection. These algorithms do not impose restrictions on the scale parallelization and allow the use of the proposed technology in petaflop class systems. It shows the possibility ofsimulating all the stages of the landslide-type tsunamis: generation, propagation and runup. The verification of the method is carried out by using the tests provided by the experimental data. The mechanism of bathymetric data accounting and the technology of constructing three-dimensional grid models are described. The results of the comparison with the non-linear dispersion theory are presented for the historical tsunami that resulted from a volcanic eruption on the island of Montserrat, the Caribbean. The results of this comparison are in good agreement.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Self-tuning decoupled fusion Kalman filter based on the Riccati equation
Institute of Scientific and Technical Information of China (English)
Xiaojun SUN; Peng ZHANG; Zili DENG
2008-01-01
An online noise variance estimator for multi-sensor systems with unknown noise variances is proposed by using the correlation method. Based on the Riccati equa-tion and optimal fusion rule "weighted by scalars for state components, a self-tuning component decoupled informa-tion fusion Kalman filter is presented. It is proved that the filter converges to the optimal fusion Kalman filter in a realization by dynamic error system analysis method, so that it has asymptotic optimality. Its effectiveness is demon-strated by simulation for a tracking system with 3 sensors.
Partial-differential-equation-based coherence-enhancing denoising for fringe patterns
Wang, Haixia; Qian, Kemao; Gao, Wenjing; Lin, Feng; Seah, Hock Soon
2008-11-01
Fringe patterns produced by electronic speckle pattern interferometry (ESPI) are evaluated to measure the deformation on object surfaces. Noise is one of the key problems affecting further processing of the fringe patterns and reduces the final measurement quality. This paper presents a partial differential equations (PDEs) based coherence enhancing denoising model to reduce the noise, enhance the flow-like structure and improve the image quality of fringe patterns. Experimental results show that this filter is flexible and capable of removing most of the noise in ESPI fringe patterns.
Image restoration with surface-based fourth-order partial differential equation
Lu, Bibo; Liu, Qiang
2010-07-01
This paper presents an edge-preserving fourth order partial differential equation (PDE) for image restoration derived from a new surface-based energy functional. The corresponding fourth order PDE can preserve edges and avoid the staircase effect. The proposed model contains a function of gradient norm as an edge detector, which controls the diffusion speed according to the local structure of the image and preserves more details. Denoising results are given and we have also compared our method with some related PDE models.
Image Denoising based on Fourth-Order Partial Differential Equations: A Survey
Directory of Open Access Journals (Sweden)
Anand Swaroop Khare
2013-03-01
Full Text Available Reduction of noise is essential especially in the field of image processing. Several researchers are continuously working in this direction and provide some good insights, but still there are lot of scope in this field. Noise mixed with image is harmful for image processing. In this paper we survey several aspects of image denoising and fourth-order partial differential equation. We also discuss several traditional methodology used with their advantages and disadvantages. We also provide a deep analysis based on the literature work from the previous research.
DEFF Research Database (Denmark)
Nadernejad, Ehsan; Nikpour, Mohsen
2012-01-01
In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential...... equations (PDEs) are applied on the pixonal image for noise removing. The proposed algorithm has been examined on variety of standard images and their performance compared with the existing algorithms. Experimental results show that in comparison with the other existing methods, the proposed algorithm has...... a better performance in denoising and preserving image edges....
Hussain, Nur Farahin Mee; Zahid, Zalina
2014-12-01
Nowadays, in the job market demand, graduates are expected not only to have higher performance in academic but they must also be excellent in soft skill. Problem-Based Learning (PBL) has a number of distinct advantages as a learning method as it can deliver graduates that will be highly prized by industry. This study attempts to determine the satisfaction level of engineering students on the PBL Approach and to evaluate their determinant factors. The Structural Equation Modeling (SEM) was used to investigate how the factors of Good Teaching Scale, Clear Goals, Student Assessment and Levels of Workload affected the student satisfaction towards PBL approach.
An equation of state for polyurea aerogel based on multi-shock response
Aslam, T. D.; Gustavsen, R. L.; Bartram, B. D.
2014-05-01
The equation of state (EOS) of polyurea aerogel (PUA) is examined through both single shock Hugoniot data as well as more recent multi-shock compression experiments performed on the LANL 2-stage gas gun. A simple conservative Lagrangian numerical scheme, utilizing total variation diminishing (TVD) interpolation and an approximate Riemann solver, will be presented as well as the methodology of calibration. It will been demonstrated that a p-a model based on a Mie-Gruneisen fitting form for the solid material can reasonably replicate multi-shock compression response at a variety of initial densities; such a methodology will be presented for a commercially available polyurea aerogel.
New bolting structure of fractured roof based on the Bossinesq equations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Present support theories contain a number of shortcomings in the designation of fractured roof bolt parameters of rectangular or trapezoidal coal roadways.Roof fall accidents occur easily in this kind of roadway.Based on the Bossinesq equations and the Mohr strength theory,we propose a theory of an anchored cluster structure for fractured roofs and have investigated the formation of such an anchored cluster structure,its self stability mechanism and mechanical properties.The results show that an anchor and ...
信息动态%Midcourse trajectory correction based on orbital motion equation linearization
Institute of Scientific and Technical Information of China (English)
2011-01-01
Midcourse trajectory correction is an essential technique to ensure the completion of long-time midcourse coasting missions, such as deep space exploration, long-distance rendezvous, and approaching observation.Based on perturbation guidance theory, this paper presents a correction strategy by linearizing the orbital motion equations about the nominal orbit. Orbital perturbations have an obvious effect on the spacecraft undertaking mission near the earth space, especially the J2 perturbation. Therefore, a modified method is proposed by adding correction terms onto the two-body matrices to reduce errors caused by perturbations. Finally, numerical simulations are conducted to verify the validity of the methods addressed herein.
Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law
Institute of Scientific and Technical Information of China (English)
Liu Changmao
2005-01-01
The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codifferential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, respectively. The definitions of the divergence and the curl of a 2D surface flux of a tensor are obtained.Maxwell's equations, namely, the construction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field ( or its composition). By the feature of central field ( or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple basing no effect on the sum of forces) are presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.
Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation
Almubarak, Mohammed S.
2013-05-01
The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.
Huang, Guanghui; Wan, Jianping; Chen, Hui
2013-02-01
Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.
Mechanical Analogy-based Iterative Method for Solving a System of Linear Equations
Directory of Open Access Journals (Sweden)
Yu. V. Berchun
2015-01-01
Full Text Available The paper reviews prerequisites to creating a variety of the iterative methods to solve a system of linear equations (SLE. It considers the splitting methods, variation-type methods, projection-type methods, and the methods of relaxation.A new iterative method based on mechanical analogy (the movement without resistance of a material point, that is connected by ideal elastically-linear constraints with unending guides defined by equations of solved SLE. The mechanical system has the unique position of stable equilibrium, the coordinates of which correspond to the solution of linear algebraic equation. The model of the mechanical system is a system of ordinary differential equations of the second order, integration of which allows you to define the point trajectory. In contrast to the classical methods of relaxation the proposed method does not ensure a trajectory passage through the equilibrium position. Thus the convergence of the method is achieved through the iterative stop of a material point at the moment it passes through the next (from the beginning of the given iteration minimum of potential energy. After that the next iteration (with changed initial coordinates starts.A resource-intensive process of numerical integration of differential equations in order to obtain a precise law of motion (at each iteration is replaced by defining its approximation. The coefficients of the approximating polynomial of the fourth order are calculated from the initial conditions, including higher-order derivatives. The resulting approximation enables you to evaluate the kinetic energy of a material point to calculate approximately the moment of time to reach the maximum kinetic energy (and minimum of the potential one, i.e. the end of the iteration.The software implementation is done. The problems with symmetric positive definite matrix, generated as a result of using finite element method, allowed us to examine a convergence rate of the proposed method
Majeed, Muhammad Usman
2017-07-19
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
Meng, Xin; Huang, Huachuan; Yan, Keding; Tian, Xiaolin; Yu, Wei; Cui, Haoyang; Kong, Yan; Xue, Liang; Liu, Cheng; Wang, Shouyu
2016-12-20
In order to realize high contrast imaging with portable devices for potential mobile healthcare, we demonstrate a hand-held smartphone based quantitative phase microscope using the transport of intensity equation method. With a cost-effective illumination source and compact microscope system, multi-focal images of samples can be captured by the smartphone's camera via manual focusing. Phase retrieval is performed using a self-developed Android application, which calculates sample phases from multi-plane intensities via solving the Poisson equation. We test the portable microscope using a random phase plate with known phases, and to further demonstrate its performance, a red blood cell smear, a Pap smear and monocot root and broad bean epidermis sections are also successfully imaged. Considering its advantages as an accurate, high-contrast, cost-effective and field-portable device, the smartphone based hand-held quantitative phase microscope is a promising tool which can be adopted in the future in remote healthcare and medical diagnosis.
Mehralizadeh, Semira; Dehdashti, Alireza; Kashani, Masoud Motalebi
2017-07-26
Evaluating educational program can improve the quality of education that learners receive. The present study evaluated undergraduate occupational health educational program at Medical sciences university of Semnan, Iran, focused on the associations between alumni perceptions of learning environment and outcomes in occupational health program. cross-sectional questionnaire survey was carried out among alumni of occupational health enrolled in an undergraduate program. We asked alumni to rate their perceptions of the items based on a Likert four-point scale. The associations between alumni perceptions of educational program and curriculum, faculty, institutional resources and learning outcomes were modeled and described using structural equation modeling procedures. Descriptive perception indicated low evaluations for administration systems, practical and research based courses and the number of faculty members. Results indicated a structural model of the evaluation variables of curriculum, faculty qualification, and institutional resources significantly predict undergraduate educational program outcomes. Curriculum had direct and indirect effects on learning outcomes mediated by faculty. study findings highlight the usefulness of structural equation modeling approach with which to examine linking between variables of learning process and learning outcomes. Surveys among alumni permit to provide data to reassess the learning environment in the light of professional competencies needed for occupational health graduates.
Fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation
Directory of Open Access Journals (Sweden)
Eckart eMarsch
2015-10-01
Full Text Available A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1 and the SU(3 groups, corresponding to quantum electrodynamics (QED based on electric charge and chromodynamics (QCD based on colour charge. In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac representations of the Dirac equation. This yields the SU(2 symmetry of the weak interaction, which can be married to U(1 to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8, which can accommodate and unify the observed eight basic stable fermions.
Elasto-capillarity Simulations based on the Navier-Stokes-Cahn-Hilliard Equations
van Brummelen, E H; van Zwieten, G J
2015-01-01
We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the incompressible Navier-Stokes-Cahn-Hilliard equations with preferential-wetting boundary conditions at the fluid-solid interface. The corresponding fluid traction on the interface includes a capillary-stress contribution, and the dynamic interface condition comprises the traction exerted by the non-uniform fluid-solid surface tension. We present a weak formulation of the aggregated complex-fluid-solid-interaction problem, based on an Arbitrary-Lagrangian-Eulerian formulation of the Navier-Stokes-Cahn-Hilliard equations and a proper reformulation of the complex-fluid traction and the fluid-solid surface tension. To validate the presented complex-fluid-solid-interaction model, we present numerical results and conduct a comparison to experimental data for a droplet on a soft subs...
Asiri, Sharefa M.
2016-10-20
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
Toporkov, Jakov V.
1998-01-01
A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects o...
Zhang, Jialin; Chen, Qian; Li, Jiaji; Zuo, Chao
2017-02-01
The transport of intensity equation (TIE) is a powerful tool for direct quantitative phase retrieval in microscopy imaging. However, there may be some problems when dealing with the boundary condition of the TIE. The previous work introduces a hard-edged aperture to the camera port of the traditional bright field microscope to generate the boundary signal for the TIE solver. Under this Neumann boundary condition, we can obtain the quantitative phase without any assumption or prior knowledge about the test object and the setup. In this paper, we will demonstrate the effectiveness of this method based on some experiments in practice. The micro lens array will be used for the comparison of two TIE solvers results based on introducing the aperture or not and this accurate quantitative phase imaging technique allows measuring cell dry mass which is used in biology to follow cell cycle, to investigate cell metabolism, or to address effects of drugs.
High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method
Kruglyakov, Mikhail
2015-01-01
A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: 1) the reduction of the memory usage in half, compared to analogous IE based algorithms, without additional restriction on the background media; 2) accurate and stable method to compute matrix coefficients corresponding to the IE; 3) high degree of parallelism. The solver's computational efficiency is shown on a problem of magnetotelluric sounding of the high conductivity contrast media. A good agreement with the results obtained with the second order finite element method is demonstrated. Due to effective approach to parallelization and distributed data storage the program exhibits perfect scalability on different hardware platforms.
Prestack migration velocity analysis based on simplifi ed two-parameter moveout equation
Institute of Scientific and Technical Information of China (English)
Chen Hai-Feng; Li Xiang-Yang; Qian Zhong-Ping; Song Jian-Jun; Zhao Gui-Ling
2016-01-01
Stacking velocityVC2, vertical velocity ratioγ0, effective velocity ratioγef, and anisotropic parameterχef are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity VC2 and anisotropic parameterkef) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocityVC2, vertical velocity ratioγ0, effective velocity ratioγef, and anisotropic parameterkef) PS-wave anisotropic PKTM velocity model updating and processfl ow based on the simplifi ed two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratioγ0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratioγef is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratioγef is obtained by percentage scanning migration. This method simplifi es the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice.
Optimum plane selection for transport-of-intensity-equation-based solvers.
Martinez-Carranza, J; Falaggis, K; Kozacki, T
2014-10-20
Deterministic single beam phase retrieval techniques based on the transport of intensity equation (TIE) use the axial intensity derivative obtained from a series of intensities recorded along the propagation axis as an input to the TIE-based solver. The common belief is that, when reducing the error present in the axial intensity derivative, there will be minimal error in the retrieved phase. Thus, reported optimization schemes of measurement condition focuses on the minimization of error in the axial intensity derivative. As it is shown in this contribution, this assumption is not correct and leads to underestimating the value of plane separation, which increases the phase retrieval errors and sensitivity to noise of the TIE-based measurement system. Therefore, in this paper, a detailed analysis that shows the existence of an optimal separation that minimizes the error in the retrieved phase for a given TIE-based solver is carried out. The developed model is used to derive analytical expressions that provide an optimal plane separation for a given number of planes and level of noise for the case of equidistant plane separation. The obtained results are derived for the widely used Fourier-transform-based TIE solver, but it is shown that they can also be applied to multigrid-based techniques.
Asiri, Sharefa M.
2017-10-08
Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions\\' parameters. (iii) Propose an effective algorithm for selecting the method\\'s design parameters
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
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......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...
Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots
National Research Council Canada - National Science Library
Ching-Long Shih; Wen-Yo Lee; Chia-Pin Wu
2012-01-01
This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method...
Simulation of a fast diffuse optical tomography system based on radiative transfer equation
Motevalli, S. M.; Payani, A.
2016-12-01
Studies show that near-infrared (NIR) light (light with wavelength between 700nm and 1300nm) undergoes two interactions, absorption and scattering, when it penetrates a tissue. Since scattering is the predominant interaction, the calculation of light distribution in the tissue and the image reconstruction of absorption and scattering coefficients are very complicated. Some analytical and numerical methods, such as radiative transport equation and Monte Carlo method, have been used for the simulation of light penetration in tissue. Recently, some investigators in the world have tried to develop a diffuse optical tomography system. In these systems, NIR light penetrates the tissue and passes through the tissue. Then, light exiting the tissue is measured by NIR detectors placed around the tissue. These data are collected from all the detectors and transferred to the computational parts (including hardware and software), which make a cross-sectional image of the tissue after performing some computational processes. In this paper, the results of the simulation of an optical diffuse tomography system are presented. This simulation involves two stages: a) Simulation of the forward problem (or light penetration in the tissue), which is performed by solving the diffusion approximation equation in the stationary state using FEM. b) Simulation of the inverse problem (or image reconstruction), which is performed by the optimization algorithm called Broyden quasi-Newton. This method of image reconstruction is faster compared to the other Newton-based optimization algorithms, such as the Levenberg-Marquardt one.
Li, Jie; Dault, Daniel; Liu, Beibei; Tong, Yiying; Shanker, Balasubramaniam
2016-08-01
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but not differentiable. The need to define physical quantities on this geometric representation has led to development of sets of basis functions that need to satisfy constraints at the boundaries of the elements/tessellations (viz., continuity of normal or tangential components across element boundaries). For electromagnetics, these result in either curl/div-conforming basis sets. The geometric representation used for analysis is in stark contrast with that used for design, wherein the surface representation is higher order differentiable. Using this representation for both geometry and physics on geometry has several advantages, and is elucidated in Hughes et al. (2005) [7]. Until now, a bulk of the literature on isogeometric methods have been limited to solid mechanics, with some effort to create NURBS based basis functions for electromagnetic analysis. In this paper, we present the first complete isogeometry solution methodology for the electric field integral equation as applied to simply connected structures. This paper systematically proceeds through surface representation using subdivision, definition of vector basis functions on this surface, to fidelity in the solution of integral equations. We also present techniques to stabilize the solution at low frequencies, and impose a Calderón preconditioner. Several results presented serve to validate the proposed approach as well as demonstrate some of its capabilities.
Master equation-based analysis of a motor-clutch model for cell traction force.
Bangasser, Benjamin L; Odde, David J
2013-12-01
Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.
Targeting eigenstates using a decoherence-based nonlinear Schrödinger equation
Furtmaier, O.; Mendoza, M.
2017-08-01
Inspired by the idea of mimicking the measurement on a quantum system through a decoherence process to target specific eigenstates based on Born's law, i.e., the hierarchy of probabilities instead of the hierarchy of eigenvalues, we transform a Lindblad equation for the reduced density operator into a nonlinear Schrödinger equation to obtain a computationally feasible simulation of the decoherent dynamics in the open quantum system. This gives the opportunity to target the eigenstates which have the largest L2 overlap with an initial superposition state and hence more flexibility in the selection criteria. One can use this feature, for instance, to approximate eigenstates with certain localization or symmetry properties. As an application of the theory we discuss eigenstate towing, which relies on the perturbation theory to follow the progression of an arbitrary subset of eigenstates along a sum of perturbation operators with the intention to explore, for example, the effect of interactions on these eigenstates. The easily parallelizable numerical method shows an exponential convergence and its computational costs scale linearly for sparse matrix representations of the involved Hermitian operators.
Use of chemistry software to teach and assess model-based reaction and equation knowledge
Directory of Open Access Journals (Sweden)
Kevin Pyatt
2014-12-01
Full Text Available This study investigated the challenges students face when learning chemical reactions in a first-year chemistry course and the effectiveness of a curriculum and software implementation that was used to teach and assess student understanding of chemical reactions and equations. This study took place over a two year period in a public suburban high-school, in southwestern USA. Two advanced placement (AP chemistry classes participated, referred to here as study group A (year 1, N = 14; and study group B (year 2, N = 21. The curriculum for a first-year chemistry course (group A was revised to include instruction on reaction-types. The second year of the study involved the creation and implementation of a software solution which promoted mastery learning of reaction-types. Students in both groups benefited from the reaction-type curriculum and achieved proficiency in chemical reactions and equations. The findings suggest there was an added learning benefit to using the reaction-type software solution. This study also found that reaction knowledge was a moderate to strong predictor of chemistry achievement. Based on regression analysis, reaction knowledge significantly predicted chemistry achievement for both groups.
Na, Seong-Won; Kallivokas, Loukas F.
2008-03-01
In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush-Kuhn-Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1-4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries.
Three new branched chain equations of state based on Wertheim's perturbation theory.
Marshall, Bennett D; Chapman, Walter G
2013-05-07
In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.
Age- and height-based prediction bias in spirometry reference equations
P.H. Quanjer (Philip); G.L. Hall (G. L.); S. Stanojevic (Sanja); T.J. Cole (Tim); J. Stocks (Janet)
2012-01-01
textabstractPrediction bias in spirometry reference equations can arise from combining equations for different age groups, rounding age or height to integers or using self-reported height. To assess the bias arising from these sources, the fit of 13 prediction equations was tested against the Global
Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques
2012-09-01
The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.
Directory of Open Access Journals (Sweden)
Qingxue Huang
2017-01-01
Full Text Available In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.
Phase retrieval based on cosine grating modulation and transport of intensity equation
Chen, Ya-ping; Zhang, Quan-bing; Cheng, Hong; Qian, Yi; Lv, Qian-qian
2016-10-01
In order to calculate the lost phase from the intensity information effectively, a new method of phase retrieval which based on cosine grating modulation and transport of intensity equation is proposed. Firstly, the cosine grating is loaded on the spatial light modulator in the horizontal and vertical direction respectively, and the corresponding amplitude of the light field is modulated. Then the phase is calculated by its gradient which is extracted from different direction modulation light illumination. The capability of phase recovery of the proposed method in the presence of noise is tested by simulation experiments. And the results show that the proposed algorithm has a better resilience than the traditional Fourier transform algorithm at low frequency noise. Furthermore, the phase object of different scales can be retrieved using the proposed algorithm effectively by changing the frequency of cosine grating, which can control the imaging motion expediently.
Xu, Mingdong; Wu, Fan; Leung, Henry
2009-09-01
Based on the stochastic delay differential equation (SDDE) modeling of neural networks, we propose an effective signal transmission approach along the neurons in such a network. Utilizing the linear relationship between the delay time and the variance of the SDDE system output, the transmitting side encodes a message as a modulation of the delay time and the receiving end decodes the message by tracking the delay time, which is equivalent to estimating the variance of the received signal. This signal transmission approach turns out to follow the principle of the spread spectrum technique used in wireless and wireline wideband communications but in the analog domain rather than digital. We hope the proposed method might help to explain some activities in biological systems. The idea can further be extended to engineering applications. The error performance of the communication scheme is also evaluated here.
Second-Order Polynomial Equation-Based Block Adjustment for Orthorectification of DISP Imagery
Directory of Open Access Journals (Sweden)
Guoqing Zhou
2016-08-01
Full Text Available Due to the lack of ground control points (GCPs and parameters of satellite orbits, as well as the interior and exterior orientation parameters of cameras in historical declassified intelligence satellite photography (DISP imagery, a second order polynomial equation-based block adjustment model is proposed for orthorectification of DISP imagery. With the proposed model, 355 DISP images from four missions and five orbits are orthorectified, with an approximate accuracy of 2.0–3.0 m. The 355 orthorectified images are assembled into a seamless, full-coverage mosaic image map of the karst area of Guangxi, China. The accuracy of the mosaicked image map is within 2.0–4.0 m when compared to 78 checkpoints measured by Real–Time Kinematic (RTK GPS surveys. The assembled image map will be delivered to the Guangxi Geological Library and released to the public domain and the research community.
An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising.
Khanian, Maryam; Feizi, Awat; Davari, Ali
2014-01-01
Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient stopping criterion is presented. In this regard, the current paper introduces two strategies: utilizing the efficient explicit method due to its advantages with presenting impressive software technique to effectively solve the anisotropic diffusion filter which is mathematically unstable, proposing an automatic stopping criterion, that takes into consideration just input image, as opposed to other stopping criteria, besides the quality of denoised image, easiness and time. Various medical images are examined to confirm the claim.
Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Institute of Scientific and Technical Information of China (English)
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
Pacheco-Vega, Arturo
2016-09-01
In this work a new set of correlation equations is developed and introduced to accurately describe the thermal performance of compact heat exchangers with possible condensation. The feasible operating conditions for the thermal system correspond to dry- surface, dropwise condensation, and film condensation. Using a prescribed form for each condition, a global regression analysis for the best-fit correlation to experimental data is carried out with a simulated annealing optimization technique. The experimental data were taken from the literature and algorithmically classified into three groups -related to the possible operating conditions- with a previously-introduced Gaussian-mixture-based methodology. Prior to their use in the analysis, the correct data classification was assessed and confirmed via artificial neural networks. Predictions from the correlations obtained for the different conditions are within the uncertainty of the experiments and substantially more accurate than those commonly used.
An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising
Khanian, Maryam; Feizi, Awat; Davari, Ali
2014-01-01
Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient stopping criterion is presented. In this regard, the current paper introduces two strategies: utilizing the efficient explicit method due to its advantages with presenting impressive software technique to effectively solve the anisotropic diffusion filter which is mathematically unstable, proposing an automatic stopping criterion, that takes into consideration just input image, as opposed to other stopping criteria, besides the quality of denoised image, easiness and time. Various medical images are examined to confirm the claim. PMID:24696809
Shin, Jaemin; Lee, Hyun Geun; Lee, June-Yub
2016-12-01
The phase-field crystal equation derived from the Swift-Hohenberg energy functional is a sixth order nonlinear equation. We propose numerical methods based on a new convex splitting for the phase-field crystal equation. The first order convex splitting method based on the proposed splitting is unconditionally gradient stable, which means that the discrete energy is non-increasing for any time step. The second order scheme is unconditionally weakly energy stable, which means that the discrete energy is bounded by its initial value for any time step. We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods. Numerical experiments are presented to show the accuracy and stability of the proposed splitting methods compared to the existing other splitting methods. Numerical tests indicate that the proposed convex splitting is a good choice for numerical methods of the phase-field crystal equation.
Equation-free analysis of agent-based models and systematic parameter determination
Thomas, Spencer A.; Lloyd, David J. B.; Skeldon, Anne C.
2016-12-01
Agent based models (ABM)s are increasingly used in social science, economics, mathematics, biology and computer science to describe time dependent systems in circumstances where a description in terms of equations is difficult. Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a well-established tool for the study of deterministic systems. Recently, equation-free (EF) methods have been developed to extend numerical continuation techniques to systems where the dynamics are described at a microscopic scale and continuation of a macroscopic property of the system is considered. To date, the practical use of EF methods has been limited by; (1) the over-head of application-specific implementation; (2) the laborious configuration of problem-specific parameters; and (3) large ensemble sizes (potentially) leading to computationally restrictive run-times. In this paper we address these issues with our tool for the EF continuation of stochastic systems, which includes algorithms to systematically configuration problem specific parameters and enhance robustness to noise. Our tool is generic and can be applied to any 'black-box' simulator and determines the essential EF parameters prior to EF analysis. Robustness is significantly improved using our convergence-constraint with a corrector-repeat (C3R) method. This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels of noise than classical approaches. We demonstrate our method with application to several ABM models, revealing parameter dependence, bifurcation and stability analysis of these complex systems giving a deep understanding of the dynamical behaviour of the models in a way that is not otherwise easily obtainable. In each case we demonstrate our systematic parameter determination stage for
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
Directory of Open Access Journals (Sweden)
Yaoyu Hu
2015-09-01
Full Text Available The solution of the energy equation of thermo-elasto-hydrodynamic analysis for bearings by the finite element method usually leads to convergence difficulties due to the presence of convection terms inherited from the Navier–Stokes equations. In this work, the numerical analysis is performed with finite element method universally by adopting the characteristic-based split method to solve the energy equation. Five case studies of fixed pad thrust bearings have been set up with different geometries, loads, and lubricants. The two-dimensional film pressure is obtained by solving the Reynolds equation with pre-defined axial load on the pad. The energy equation of the lubricant film and the heat transfer equation of the bearing pad are handled by characteristic-based split method and conventional finite element method in three-dimensional space, respectively. Hot oil carry-over effect and variable lubricant viscosity are considered in the simulations. The results of the temperature distributions in the lubricant film and the bearing pad are presented. The possible usability of characteristic-based split method for future thermo-elasto-hydrodynamic analysis is discussed.
Dynamic modeling of dual-arm cooperating manipulators based on Udwadia–Kalaba equation
Directory of Open Access Journals (Sweden)
Jia Liu
2016-07-01
Full Text Available Dual-arm cooperating manipulators subject to a certain constraint brought about by the desired trajectory and geometric constraint show high nonlinearity and coupling in their dynamic characteristic. Therefore, it is hard to build dynamical equation with traditional Lagrange equation. The Udwadia–Kalaba equation presents a new idea of dynamic modeling of multi-body systems. However, the dynamic modeling of the unconstrained systems still depends on the traditional Lagrange equation and is quite tedious for dual-arm cooperating manipulators. A generalized dynamical equation of multi-link planar manipulators is thus presented and proven to make modeling conveniently. The constraint relationship is established from a new perspective, and the dynamical equation of dual-arm cooperating manipulator subject to the desired trajectory is acquired with the Udwadia–Kalaba equation. The simple approach overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The simulation results of varying law of the joint angles and the motion path of the bar prove that the dynamical equation established by this method conforms to reality.
Directory of Open Access Journals (Sweden)
Jinping Tang
2017-01-01
Full Text Available Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE. It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.
Yuan, Zhengwen; Xiao, Hong; Xie, Hongbiao
2014-02-01
Precise strip-shape control theory is significant to improve rolled strip quality, and roll flattening theory is a primary part of the strip-shape theory. To improve the accuracy of roll flattening calculation based on semi-infinite body model, a new and more accurate roll flattening model is proposed in this paper, which is derived based on boundary integral equation method. The displacement fields of the finite length semi-infinite body on left and right sides are simulated by using finite element method (FEM) and displacement decay functions on left and right sides are established. Based on the new roll flattening model, a new 4Hi mill deformation model is established and verified by FEM. The new model is compared with Foppl formula and semi-infinite body model in different strip width, roll shifting value and bending force. The results show that the pressure and flattening between rolls calculated by the new model are more precise than other two models, especially near the two roll barrel edges.
Krishnaswami, G S
2006-01-01
Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren't differential equations as they involve left annihilation, which doesn't satisfy the Leibnitz rule with concatenation. But left annihilation is a derivation of the commutative shuffle product. Moreover shuffle and concatenation combine to define a bialgebra. Motivated by deformation quantization, we expand concatenation around shuffle in powers of q, whose physical value is 1. At zeroth order the loop equations become quadratic PDEs in the shuffle algebra. If the variation of the action is linear in iterated commutators of left annihilations, these quadratic PDEs linearize by passage to shuffle reciprocal of correlations. Remarkably, this is true for r...
Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M
2008-10-01
A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.
Expansion of Edlen Equation based on cascade-correlation learning architecture
Institute of Scientific and Technical Information of China (English)
张琢; 陈中; 钟丽
2004-01-01
Due to the limitation of Edlen Equation to compensate for air refractivity in ordinary air pressure, an experiment to study the relationship between air refractivity and temperature, along with its pressure, is designed and carried out from ordinary pressure to low pressure. The expansion of Edlen Equation is achieved by using the cascade-Correlation learning method, and a neural network architecture model. The applied accuracy of neural network is the same as that of Edlen Equation in an ordinary pressure zone.
Harko, Tiberiu; Mak, M K
2014-01-01
Gravitationally coupled scalar fields $\\phi $, distinguished by the choice of an effective self-interaction potential $V(\\phi )$, simulating a temporarily non-vanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation, and their cosmological properties are investigated in detail.
Figueredo, Grazziela P; Siebers, Peer-Olaf; Owen, Markus R; Reps, Jenna; Aickelin, Uwe
2014-01-01
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
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Grazziela P Figueredo
Full Text Available There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1 Does this new stochastic formulation produce similar results to the agent-based version? (2 Can these methods be used interchangeably? (3 Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
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Ye XS
2014-09-01
Full Text Available Xiaoshuang Ye,1 Lu Wei,1 Xiaohua Pei,1 Bei Zhu,1 Jianqing Wu,2 Weihong Zhao1 1Division of Nephrology, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China; 2Division of Respiration, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China Background: No conventional creatinine- or cystatin C-based glomerular filtration rate (GFR estimation equation performed consistently outstandingly in elderly Chinese in our previous studies. This research aimed to further evaluate the performance of some recently proposed estimation equations based on creatinine and cystatin C, alone or combined, in this specific population. Materials and methods: The equations were validated in a population totaling 419 participants (median age 68 [range 60–94] years. The estimated GFR (eGFR calculated separately by ten equations was compared with the reference GFR (rGFR measured by the 99mTc-DTPA renal dynamic imaging method. Results: Median serum creatinine, cystatin C, and rGFR levels were 0.93 mg/L, 1.13 mg/L, and 74.20 mL/min/1.73 m2, respectively. The Chinese population-developed creatinine- and cystatin C-based (Cscr-cys equation yielded the least median absolute difference (8.81 vs range 9.53–16.32, P<0.05, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, the highest proportion of eGFR within 15% and 30% of rGFR (P15 and P30, 55.13 and 85.44, P<0.05 and P<0.01, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, and the lowest root mean square error (14.87 vs range 15.30–22.45 in the whole cohort. A substantial agreement of diagnostic consistency between eGFR and rGFR (with a kappa 0.61–0.80 was also observed with the Cscr-cys equation. Moreover, measures of performance in the Cscr-cys equation were consistent across normal to mildly
Zhao, GuoZheng; Lu, Ming
2012-06-01
The nitramine compounds containing benzene ring were optimized to obtain their molecular geometries and electronic structures at DFT-B3LYP/6-31+G(d) level. The theoretical molecular density (ρ), heat of formation (HOF), energy gap (ΔE(LUMO-HOMO)), charge on the nitro group (-Q(NO2)), detonation velocity (D) and detonation pressure (P), estimated using Kamlet-Jacobs equations, showed that the detonation properties of these compounds were excellent. It is found that there are good linear relationships between density, heat of formation, detonation velocity, detonation pressure and the number of nitro group. The simulation results reveal that molecule G performs similarly to famous explosive HMX, and molecule H outperforms HMX. According to the quantitative standard of energetics as an HEDC (high energy density compound), molecule H essentially satisfies this requirement. These results provide basic information for molecular design of novel high energetic density compounds.
Validity Of Bmi-Based Body Fat Equations In Men And Women: A Four-Compartment Model Comparison.
Nickerson, Brett S; Esco, Michael R; Bishop, Phillip A; Fedewa, Michael V; Snarr, Ronald L; Kliszczewicz, Brian M; Park, Kyung-Shin
2016-12-20
The purpose of this study was to compare body mass index (BMI)-based body fat percentage (BF%) equations and skinfolds to a four-compartment (4C) model in men and women. One hundred and thirty adults (63 women and 67 men) volunteered to participate (age = 23±5 years). BMI was calculated as weight (kg) divided by height squared (m). BF% was predicted with the BMI-based equations of Jackson et al. (BMIJA), Deurenberg et al. (BMIDE), Gallagher et al. (BMIGA), Zanovec et al. (BMIZA), Womersley and Durnin (BMIWO) and from 7-site skinfolds using the generalized skinfold equation of Jackson et al. (SF7JP). 4C model BF% was the criterion and derived from underwater weighing for body volume, dual energy X-ray absorptiometry for bone mineral content, and bioimpedance spectroscopy for total body water. The constant error (CE) was not significantly different for BMIZA compared to the 4C model (p=0.74; CE = -0.2%). However, BMIJA, BMIDE, BMIGA, and BMIWO produced significantly higher mean values than the 4C model (all pBMI-based equations produced similar group mean values as the 4C model, SF7JP produced the smallest individual errors. Therefore, SF7JP is recommended over the BMI-based equations, but practitioners should consider the associated CE.
Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji
2015-09-01
We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state.
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Yunjiao Bai
2015-01-01
Full Text Available The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.
Local algorithm for computing complex travel time based on the complex eikonal equation.
Huang, Xingguo; Sun, Jianguo; Sun, Zhangqing
2016-04-01
The traditional algorithm for computing the complex travel time, e.g., dynamic ray tracing method, is based on the paraxial ray approximation, which exploits the second-order Taylor expansion. Consequently, the computed results are strongly dependent on the width of the ray tube and, in regions with dramatic velocity variations, it is difficult for the method to account for the velocity variations. When solving the complex eikonal equation, the paraxial ray approximation can be avoided and no second-order Taylor expansion is required. However, this process is time consuming. In this case, we may replace the global computation of the whole model with local computation by taking both sides of the ray as curved boundaries of the evanescent wave. For a given ray, the imaginary part of the complex travel time should be zero on the central ray. To satisfy this condition, the central ray should be taken as a curved boundary. We propose a nonuniform grid-based finite difference scheme to solve the curved boundary problem. In addition, we apply the limited-memory Broyden-Fletcher-Goldfarb-Shanno technology for obtaining the imaginary slowness used to compute the complex travel time. The numerical experiments show that the proposed method is accurate. We examine the effectiveness of the algorithm for the complex travel time by comparing the results with those from the dynamic ray tracing method and the Gauss-Newton Conjugate Gradient fast marching method.
Li, Xujing; Zheng, Weiying
2016-10-01
A new parallel code based on discontinuous Galerkin (DG) method for hyperbolic conservation laws on three dimensional unstructured meshes is developed recently. This code can be used for simulations of MHD equations, which are very important in magnetic confined plasma research. The main challenges in MHD simulations in fusion include the complex geometry of the configurations, such as plasma in tokamaks, the possibly discontinuous solutions and large scale computing. Our new developed code is based on three dimensional unstructured meshes, i.e. tetrahedron. This makes the code flexible to arbitrary geometries. Second order polynomials are used on each element and HWENO type limiter are applied. The accuracy tests show that our scheme reaches the desired three order accuracy and the nonlinear shock test demonstrate that our code can capture the sharp shock transitions. Moreover, One of the advantages of DG compared with the classical finite element methods is that the matrices solved are localized on each element, making it easy for parallelization. Several simulations including the kink instabilities in toroidal geometry will be present here. Chinese National Magnetic Confinement Fusion Science Program 2015GB110003.
Local algorithm for computing complex travel time based on the complex eikonal equation
Huang, Xingguo; Sun, Jianguo; Sun, Zhangqing
2016-04-01
The traditional algorithm for computing the complex travel time, e.g., dynamic ray tracing method, is based on the paraxial ray approximation, which exploits the second-order Taylor expansion. Consequently, the computed results are strongly dependent on the width of the ray tube and, in regions with dramatic velocity variations, it is difficult for the method to account for the velocity variations. When solving the complex eikonal equation, the paraxial ray approximation can be avoided and no second-order Taylor expansion is required. However, this process is time consuming. In this case, we may replace the global computation of the whole model with local computation by taking both sides of the ray as curved boundaries of the evanescent wave. For a given ray, the imaginary part of the complex travel time should be zero on the central ray. To satisfy this condition, the central ray should be taken as a curved boundary. We propose a nonuniform grid-based finite difference scheme to solve the curved boundary problem. In addition, we apply the limited-memory Broyden-Fletcher-Goldfarb-Shanno technology for obtaining the imaginary slowness used to compute the complex travel time. The numerical experiments show that the proposed method is accurate. We examine the effectiveness of the algorithm for the complex travel time by comparing the results with those from the dynamic ray tracing method and the Gauss-Newton Conjugate Gradient fast marching method.
Erban, R; Othmer, H G; Erban, Radek; Kevrekidis, Ioannis G.; Othmer, Hans G.
2005-01-01
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging from ecology to medicine involve large collections of individuals, and a further intellectual challenge is to model population-level behavior based on a detailed individual-level model. Because of the large number of interacting individuals and because the individual-level model is complex, classical direct Monte Carlo simulations can be very slow, and often of little practical use. In this case, an equation-free approach may provide effective methods for the analysis and simulation of individual-based models. In this paper we analyze equation-free coarse projective integration. For analytical purposes, we start with known partial differential equations describing biological rando...
Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations
Bhowmik, S.K.; Stolk, C.C.
2011-01-01
We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given
Validation of a New Skinfold Prediction Equation Based on Dual-Energy X-Ray Absorptiometry
Ball, Stephen; Cowan, Celsi; Thyfault, John; LaFontaine, Tom
2014-01-01
Skinfold prediction equations recommended by the American College of Sports Medicine underestimate body fat percentage. The purpose of this research was to validate an alternative equation for men created from dual energy x-ray absorptiometry. Two hundred ninety-seven males, aged 18-65, completed a skinfold assessment and dual energy x-ray…
Tian, Jianxiang; Mulero, A
2016-01-01
Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...
SDP-based approximation of stabilising solutions for periodic matrix Riccati differential equations
Gusev, Sergei V.; Shiriaev, Anton S.; Freidovich, Leonid B.
2016-07-01
Numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions. The most successful method requires solving matrix differential Riccati equations with periodic coefficients. All previously proposed techniques for solving such equations involve numerical integration of unstable differential equations and consequently fail whenever the period is too large or the coefficients vary too much. Here, a new method for numerical computation of stabilising solutions for matrix differential Riccati equations with periodic coefficients is proposed. Our approach does not involve numerical solution of any differential equations. The approximation for a stabilising solution is found in the form of a trigonometric polynomial, matrix coefficients of which are found solving a specially constructed finite-dimensional semidefinite programming (SDP) problem. This problem is obtained using maximality property of the stabilising solution of the Riccati equation for the associated Riccati inequality and sampling technique. Our previously published numerical comparisons with other methods shows that for a class of problems only this technique provides a working solution. Asymptotic convergence of the computed approximations to the stabilising solution is proved below under the assumption that certain combinations of the key parameters are sufficiently large. Although the rate of convergence is not analysed, it appeared to be exponential in our numerical studies.
Wang, Dongdong; Li, Xiwei; Pan, Feixu
2016-11-01
A simple and unified finite element formulation is presented for superconvergent eigenvalue computation of wave equations ranging from 1D to 3D. In this framework, a general method based upon the so called α mass matrix formulation is first proposed to effectively construct 1D higher order mass matrices for arbitrary order elements. The finite elements discussed herein refer to the Lagrangian type of Lobatto elements that take the Lobatto points as nodes. Subsequently a set of quadrature rules that exactly integrate the 1D higher order mass matrices are rationally derived, which are termed as the superconvergent quadrature rules. More importantly, in 2D and 3D cases, it is found that the employment of these quadrature rules via tensor product simultaneously for the mass and stiffness matrix integrations of Lobatto elements produces a unified superconvergent formulation for the eigenvalue or frequency computation without wave propagation direction dependence, which usually is a critical issue for the multidimensional higher order mass matrix formulation. Consequently the proposed approach is capable of computing arbitrary frequencies in a superconvergent fashion. Meanwhile, numerical implementation of the proposed method for multidimensional problems is trivial. The effectiveness of the proposed methodology is systematically demonstrated by a series of numerical examples. Numerical results revealed that a superconvergence with 2(p+1)th order of frequency accuracy is achieved by the present unified formulation for the pth order Lobatto element.
A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.
Harrison, Jonathan U; Yates, Christian A
2016-09-01
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time.
Evaluating Fit Indices for Multivariate t-Based Structural Equation Modeling with Data Contamination
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Mark H. C. Lai
2017-07-01
Full Text Available In conventional structural equation modeling (SEM, with the presence of even a tiny amount of data contamination due to outliers or influential observations, normal-theory maximum likelihood (ML-Normal is not efficient and can be severely biased. The multivariate-t-based SEM, which recently got implemented in Mplus as an approach for mixture modeling, represents a robust estimation alternative to downweigh the impact of outliers and influential observations. To our knowledge, the use of maximum likelihood estimation with a multivariate-t model (ML-t to handle outliers has not been shown in SEM literature. In this paper we demonstrate the use of ML-t using the classic Holzinger and Swineford (1939 data set with a few observations modified as outliers or influential observations. A simulation study is then conducted to examine the performance of fit indices and information criteria under ML-Normal and ML-t in the presence of outliers. Results showed that whereas all fit indices got worse for ML-Normal with increasing amount of outliers and influential observations, their values were relatively stable with ML-t, and the use of information criteria was effective in selecting ML-normal without data contamination and selecting ML-t with data contamination, especially when the sample size was at least 200.
Wave equation-based reflection tomography of the 1992 Landers earthquake area
Huang, Xueyuan; Yang, Dinghui; Tong, Ping; Badal, José; Liu, Qinya
2016-03-01
In the framework of a recent wave equation-based traveltime seismic tomography, we show that incorporating Moho-reflected phases (PmP and SmS) in addition to the direct P and S phases can significantly increase tomography resolution in the lower crust and this may provide additional evidence to resolve important tectonic issues. To highlight the resolving power of the new strategy, we apply it in the region around the 1992 Landers earthquake (Mw = 7.3) in Southern California using seismic arrivals from local earthquakes, obtaining 3-D high-resolution P and S wave crustal velocity models and Poisson's ratio structures. In the upper crust, our method confirmed features that had been previously found. However, in the middle-to-lower crust, we found low-velocity anomalies on the southeastern section of the San Jacinto Fault and high Vp and low Vs structures to the west of the Big Bear earthquake, which may be related to upwelling of partial melt from the mantle.
DAE Tools: equation-based object-oriented modelling, simulation and optimisation software
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Dragan D. Nikolić
2016-04-01
Full Text Available In this work, DAE Tools modelling, simulation and optimisation software, its programming paradigms and main features are presented. The current approaches to mathematical modelling such as the use of modelling languages and general-purpose programming languages are analysed. The common set of capabilities required by the typical simulation software are discussed, and the shortcomings of the current approaches recognised. A new hybrid approach is introduced, and the modelling languages and the hybrid approach are compared in terms of the grammar, compiler, parser and interpreter requirements, maintainability and portability. The most important characteristics of the new approach are discussed, such as: (1 support for the runtime model generation; (2 support for the runtime simulation set-up; (3 support for complex runtime operating procedures; (4 interoperability with the third party software packages (i.e. NumPy/SciPy; (5 suitability for embedding and use as a web application or software as a service; and (6 code-generation, model exchange and co-simulation capabilities. The benefits of an equation-based approach to modelling, implemented in a fourth generation object-oriented general purpose programming language such as Python are discussed. The architecture and the software implementation details as well as the type of problems that can be solved using DAE Tools software are described. Finally, some applications of the software at different levels of abstraction are presented, and its embedding capabilities and suitability for use as a software as a service is demonstrated.
Fox, Zachary; Neuert, Gregor; Munsky, Brian
2016-08-01
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
Adaptive change of basis in entropy-based moment closures for linear kinetic equations
Alldredge, Graham W; O'Leary, Dianne P; Tits, André L
2013-01-01
Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes th...
New Kohn-Sham density functional based on microscopic nuclear and neutron matter equations of state
Baldo, M.; Robledo, L. M.; Schuck, P.; Viñas, X.
2013-06-01
A new version of the Barcelona-Catania-Paris energy functional is applied to a study of nuclear masses and other properties. The functional is largely based on calculated ab initio nuclear and neutron matter equations of state. Compared to typical Skyrme functionals having 10-12 parameters apart from spin-orbit and pairing terms, the new functional has only 2 or 3 adjusted parameters, fine tuning the nuclear matter binding energy and fixing the surface energy of finite nuclei. An energy rms value of 1.58 MeV is obtained from a fit of these three parameters to the 579 measured masses reported in the Audi and Wapstra [Nucl. Phys. ANUPABL0375-947410.1016/j.nuclphysa.2003.11.003 729, 337 (2003)] compilation. This rms value compares favorably with the one obtained using other successful mean field theories, which range from 1.5 to 3.0 MeV for optimized Skyrme functionals and 0.7 to 3.0 for the Gogny functionals. The other properties that have been calculated and compared to experiment are nuclear radii, the giant monopole resonance, and spontaneous fission lifetimes.
Daphnias: from the individual based model to the large population equation
Metz, J A J
2012-01-01
The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approxima...
Study of carbon dioxide gas treatment based on equations of kinetics in plasma discharge reactor
Abedi-Varaki, Mehdi
2017-08-01
Carbon dioxide (CO2) as the primary greenhouse gas, is the main pollutant that is warming earth. CO2 is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO2 emission. To this end, this study investigates the behavior of CO2 in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO2 density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO2 decreases and very low concentration of CO2 molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.
A spatial discretization of the MHD equations based on the finite volume - spectral method
Energy Technology Data Exchange (ETDEWEB)
Miyoshi, Takahiro [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA{sub {phi}}, is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
The rate equation based optical model for phosphor-converted white light-emitting diodes
Du, Kang; Li, Haokai; Guo, Keqin; Wang, Heng; Li, Dacheng; Zhang, Wending; Mei, Ting; Chua, Soo Jin
2017-03-01
An optical model based on the rate equation was developed to calculate the emission spectrum of a phosphor-converted white light-emitting diode (pc-WLED) taking into consideration the phosphor weight percentage, film thickness, and optical properties of phosphor, viz. absorption spectrum, quantum efficiency spectrum and fluorescent emission spectrum. Films containing a mixture of phosphor and silicone elastomer encapsulant were investigated using this model. A linear relationship was found between the peak absorption coefficient and the phosphor weight percentage with slopes of 66.76 ± 0.52 mm‑1 and 29.66 ± 2.05 mm‑1 for a red phosphor CaAlSiN3:Eu2+ and a yellow phosphor Y3Al5O12:Ce3+, respectively. With these parameters, the model predicted emission spectra which are in good agreement with measurement, thus verifying the validity of the model. The model correctly predicts redshift and spectral width reduction of the emission peak for increasing phosphor weight percentage or film thickness, as expected from the phenomenon of photon reabsorption by the phosphors. This model does not require the use of Monte Carlo simulation and Mie theory.
Institute of Scientific and Technical Information of China (English)
Zhongxiao Jia; Yuquan Sun
2007-01-01
Based on the generalized minimal residual(GMRES)principle,Hu and Reichel proposed a minimal residual algorithm for the Sylvester equation.The algorithm requires the solution of a structured least squares problem.They form the normal equations of the least squares problem and then solve it by a direct solver,so it is susceptible to instability.In this paper,by exploiting the special structure of the least squares problem and working on the problem directly,a numerically stable QR decomposition based algorithm is presented for the problem.The new algorithm is more stable than the normal equations algorithm of Hu and Reichel.Numerical experiments are reported to confirm the superior stability of the new algorithm.
Grossman, Bernard
1999-01-01
The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based
Direct Numerical Simulation of Interaction Between Wave and Porous Breakwater Based on N-S Equation
Institute of Scientific and Technical Information of China (English)
WANG Deng-ting
2012-01-01
In this paper,a numerical model is established.A modified N-S equation is used as a control equation for the wave field and porous flow area.The control equations are discreted and solved by the finite difference method.The free surface is tracked by the VOF method.The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method.Finally,compared with the physical model test results of wave flume,the numerical model established in the present study is validated.
Golden, R. L.; Badhwar, G. D.; Stephens, S. A.
1975-01-01
The continuity equation for cosmic ray propagation is used to derive a set of linear equations interrelating the fluxes of multiply charged nuclei as observed at any particular part of the galaxy. The derivation leads to model independent definitions for cosmic ray storage time, mean density of target nuclei and effective mass traversed. The set of equations form a common framework for comparisons of theories and observations. As an illustration, it is shown that there exists a large class of propagation models which give the same result as the exponential path length model. The formalism is shown to accommodate dynamic as well as equilibrium models of production and propagation.
A delay differential equation solver based on the parallel Adams algorithms
Institute of Scientific and Technical Information of China (English)
ChengjianZHANG; HongbingYU
2001-01-01
This paper constructs a class of parallel Adams algorithms for the systems of delay differential equations.The results on convergence and stability are given.The theoretical analysis and numerical test shows that this algorithm is effect and comparable.
Directory of Open Access Journals (Sweden)
Di Zhang
2016-01-01
Full Text Available The present paper proposes a new unconditionally stable method to solve telegraph equation by using associated Hermite (AH orthogonal functions. Unlike other numerical approaches, the time variables in the given equation can be handled analytically by AH basis functions. By using the Galerkin’s method, one can eliminate the time variables from calculations, which results in a series of implicit equations. And the coefficients of results for all orders can then be obtained by the expanded equations and the numerical results can be reconstructed during the computing process. The precision and stability of the proposed method are proved by some examples, which show the numerical solution acquired is acceptable when compared with some existing methods.
High tip angle approximation based on a modified Bloch-Riccati equation.
Boulant, Nicolas; Hoult, David I
2012-02-01
When designing a radio-frequency pulse to produce a desired dependence of magnetization on frequency or position, the small flip angle approximation is often used as a first step, and a Fourier relation between pulse and transverse magnetization is then invoked. However, common intuition often leads to linear scaling of the resulting pulse so as to produce a larger flip angle than the approximation warrants--with surprisingly good results. Starting from a modified version of the Bloch-Riccati equation, a differential equation in the flip angle itself, rather than in magnetization, is derived. As this equation has a substantial linear component that is an instance of Fourier's equation, the intuitive approach is seen to be justified. Examples of the accuracy of this higher tip angle approximation are given for both constant- and variable-phase pulses.
Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces
Directory of Open Access Journals (Sweden)
Paul Bracken
2009-01-01
Full Text Available The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric for the space. The manifolds of interest are surfaces and higher-dimensional Riemannian spaces. Methods for specifying integrable evolutions of surfaces by means of these equations will also be presented.
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2015-05-01
Full Text Available In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.
Growth Process of Eucalyptus urophylla × E.grandis Stand Based on Logistic Equation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Eucalyptus is the most valuable cultivated forest genus in the tropical and subtropical areas nowadays. It has been a challenge for foresters to model growth due to the genetic variations, management regimes, and multiple products generated from the plantations. In this paper, Logistic equation was used to study the stock growth process of E. urophylla × E. grandis plantation at age of 14 with 6 spacing treatments. And the biological interpretation of the parameters of Logistic equation was analyzed. The re...
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
Estimating equations for biomarker based exposure estimation under non-steady-state conditions.
Bartell, Scott M; Johnson, Wesley O
2011-06-13
Unrealistic steady-state assumptions are often used to estimate toxicant exposure rates from biomarkers. A biomarker may instead be modeled as a weighted sum of historical time-varying exposures. Estimating equations are derived for a zero-inflated gamma distribution for daily exposures with a known exposure frequency. Simulation studies suggest that the estimating equations can provide accurate estimates of exposure magnitude at any reasonable sample size, and reasonable estimates of the exposure variance at larger sample sizes.
Directory of Open Access Journals (Sweden)
Yi-Fei Pu
2013-01-01
Full Text Available The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.
DEFF Research Database (Denmark)
D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar
2012-01-01
and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...
Institute of Scientific and Technical Information of China (English)
I. M. STAMOVA; T. G. STAMOV
2014-01-01
Sufficient conditions are investigated for the global stability of the solu-tions to models based on nonlinear impulsive differential equations with“supremum”and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu-mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
McRae, Andrew T T
2013-01-01
This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods, and hence, unlike some finite difference methods, do not require an orthogonal grid. Numerical verification of the aforementioned properties is also provided.
DEFF Research Database (Denmark)
Pandey, Bishwajeet; Pandey, Sujeet; Sharma, Shivani
2016-01-01
In this paper, we are integrating clock gating in design of energy efficient equation solver circuits based on Vedic mathematics. Clock gating is one of the best energy efficient techniques. The Sutra 'SunyamSamyasamuccaye' says thatif sum of numerator and sum of denominator is same then we can e...
Directory of Open Access Journals (Sweden)
Vasyl Kushnir
2015-10-01
Full Text Available The problems of training basics of binary technology creation while teaching differential equations and information-communication technology (ICT based on the Maple-technology are researched. The relevance of the study is resulted from the basic contradiction between the latest opportunities of modern ICT, in particular Maple-technology and traditional methods of teaching mathematical disciplines, including differential equations. It is not enough only occasional applications of Maple-technology while conducting the lessons of mathematics. Maple-technology opportunities allow to teach such differential equations by means of ICT. Thus it is necessary to solve the problem of the organic connection of traditional methods for solving differential equations and possibilities of Maple-technology regarding to the solving the generalization of high level. These actions include the simplification of the expression, solution of algebraic equations and systems, determining of eigenvalues and eigenvectors of matrices, differentiation and integration of scalar functions, vector functions and matrix functions, multiplication of matrix and matrix-vectors, the finding of the inverse matrix, etc. Binary classes are designed to teach mathematics and Computer science at the same time. Therefore, the creation of binary training technology is rather complicated problem. First of all, the teacher needs to develop an algorithm for determining the method for solving differential equations or systems of differential equations. This algorithm must consist of activities that can be automated in Maple-technology. Such actions are of a technical nature and do not have meaning-forming actions of a method of solving problems. Then efforts and attention to the subjects of the teaching will be directed to a method of solving the problem, the establishment of an appropriate algorithm and program in Maple-technology. The creation and set-up of the program algorithm, is carried
Bartels, Robert E.
2002-01-01
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo
2007-01-01
A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.
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.
Institute of Scientific and Technical Information of China (English)
ZHU Limin; HE Gaiyun; SONG Zhanjie
2016-01-01
Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process (MMP). However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.
A Forward GPS Multipath Simulator Based on the Vegetation Radiative Transfer Equation Model.
Wu, Xuerui; Jin, Shuanggen; Xia, Junming
2017-06-05
Global Navigation Satellite Systems (GNSS) have been widely used in navigation, positioning and timing. Nowadays, the multipath errors may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), i.e., GPS-Multipath Reflectometry (GPS-MR). However, bistatic scattering properties and the relation between GPS observables and geophysical parameters are not clear, e.g., vegetation. In this paper, a new element on bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that the wheat will decrease the amplitudes of GPS multipath observables (SNR, phase and code), if we increase the vegetation moisture contents or the scatters sizes (stem or leaf). Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with previous results for environmental parameter detections by GPS-MR.
Energy Technology Data Exchange (ETDEWEB)
Siewert, C.E. [North Carolina State Univ., Dept. Mathematics, Raleigh, NC (United States)
2002-10-01
A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model. (author)
Laryunin, O. A.
2016-09-01
The goal of this work is to solve Maxwell equations analytically and numerically in a one-dimensional case under the conditions of a nonstationary medium. Analytical solutions to the Maxwell equations have been obtained in two partial cases of the linear and quadratic time dependence of medium permittivity. Since the number of models for which the wave equation can be solved analytically is limited, it becomes also necessary to apply numerical methods, specifically the method of finite differences, in a time domain Finite Difference Time Domain method. The effects of the decameter wave dynamic reflection from structures with considerable spatial gradients (the scales of which are comparable with the sounding pulse wavelength) have been studied based on this method. It has been shown that the spectrum can broaden and a Doppler frequency shift of a reflected signal can originate can take place.
Naz, Hafeeza; Mushtaq, Kinza; Butt, Bilal Azeem; Khawaja, Khadija Irfan
2017-01-01
To compare three different body fats estimation equations using skin fold measurements with bioelectrical impedance analysis. A total of 130 subjects were included from Department of Endocrinology and Metabolism, Services Hospital, Lahore from 1(st) April 2016 to 30(th) Sep. 2016. The triceps, biceps, subscapular, chest, thigh, abdominal, suprailiac skinfold thickness of the subjects was measured with skin-fold calipers (Harpenden) on non-dominant side. The percentage fat mass (%FM) predicted by using each skin-fold-thickness equations namely Durnin & Womersley, Jackson & Pollock and Sloan was compared with %FM measured using a bioelectrical impedance analyzer (BIA). The mean age of subjects was 48.75±10.7 years, mean BMI was 29.08±6.09 kg/m(2). The mean %FM calculated by Durnin & Womersley (32.408±0.584), Jackson & Pollock (24.658±0.527), Sloan (20.40±0.545). The %FM by BIA was 38.182±0.529. All three equations showed positive correlation but underestimated %FM as compared to BIA. All three BF estimation equations underestimate body fat percentage compared to BIA. Among the three, Durnin & Womersley equation shows best positive correlation and hence it can be used for estimation of percentage fat mass as an alternate to BIA.
Mae, H.
2006-08-01
The strong strain-rate dependence, neck propagation and craze evolution characterize the large plastic deformation and fracture behavior of polymer. In the latest study, Kobayashi, Tomii and Shizawa suggested the elastoviscoplastic constitutive equation based on craze evolution and annihilation and then applied it to the plane strain issue of polymer. In the previous study, the author applied their suggested elastoviscoplastic constitutive equation with craze effect to the three dimensional shell and then showed that the load displacement history was in good agreement with the experimental result including only microscopic crack such as crazes. For the future industrial applications, the macroscopic crack has to be taken into account. Thus, the main objective of this study is to propose the tensile softening equation and then add it to the elastoviscoplastic constitutive equation with craze effect so that the load displacement history can be roughly simulated during the macroscopic crack propagation. The tested material in this study is the elastomer blended polypropylene used in the interior and exterior of automobiles. First, the material properties are obtained based on the tensile test results at wide range of strain rates: 10 - 4-102 (1/sec). Next, the compact tension test is conducted and then the tensile softening parameters are fixed. Then, the dart impact test is carried out in order to obtain the load displacement history and also observe the macroscopic crack propagation at high strain rate. Finally, the fracture behavior is simulated and then compared with the experimental results. It is shown that the predictions of the constitutive equation with the proposed tensile softening equation are in good agreement with the experimental results for the future industrial applications.
A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation
Plante, Ianik; Wu, Honglu
2014-01-01
Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the
Norman, Matthew Ross
The social need for realistic atmospheric simulation in weather prediction, climate change attribution, seasonal forecasting, and climate projection is great. To obtain realistic simulations, we need more physical processes included in the model with greater fidelity and finer spatial resolution. Spatial resolution primarily drives the need for computational resources because reducing the model grid spacing by a factor f requires f 4 times more computation (assuming 3-D refinement). This compute power comes from large parallel machines with 10,000s of separate nodes and accelerators such as graphics processing units (GPUs) making efficiency a complicated problem. Efficiency parallel integration algorithms need low internode communication, minimal synchronization, large time steps, and clustered computation. To this end, we propose new characteristics-based methods for the atmospheric dynamical equations with these properties in mind. These schemes are capable of simulating at a large CFL time step in only one stage of computations, needing only one copy of the state variables. They are implemented in a 2-D non-hydrostatic compressible equation set in an x-z (horizontal-vertical) Cartesian plane to simulate buoyancy-driven flows such as rising thermals and internal gravity waves. The schemes are implemented to run on CPU and multi-GPU architectures using Nvidia's CUDA (Compute Unified Device Architecture) language to test relative efficiency. Even with- out memory tuning, the GPU code showed roughly 2.5x (5x) better performance per Watt. With optimization, this could increase by an order of magnitude. The methods can use any spatial interpolant, so two major formulations are proposed and tested. One uses WENO interpolants which are pre-computed, and the other uses standard polynomials and computes them on-the-fly. The advantage of on-the-fly calculations is a significant reduction in the volume of data communicated to and from the GPU's slow global memory. In some
An integral equation-based numerical solver for Taylor states in toroidal geometries
O'Neil, Michael
2016-01-01
We develop an algorithm for the numerical calculation of Taylor states (also known as Beltrami, or force-free fields) in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. The scheme relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter $\\lambda$ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking in the plasma. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Zheng, Lin; Zhai, Qinglan
2014-01-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface fore (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter visa Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is also solved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and a two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then ...
Equation of State of Al Based on Quantum Molecular Dynamics Calculations
Minakov, Dmitry V.; Levashov, Pavel R.; Khishchenko, Konstantin V.
2011-06-01
In this work, we present quantum molecular dynamics calculations of the shock Hugoniots of solid and porous samples as well as release isentropes and values of isentropic sound velocity behind the shock front for aluminum. We use the VASP code with an ultrasoft pseudopotential and GGA exchange-correlation functional. Up to 108 particles have been used in calculations. For the Hugoniots of Al we solve the Hugoniot equation numerically. To calculate release isentropes, we use Zel'dovich's approach and integrate an ordinary differential equation for the temperature thus restoring all thermodynamic parameters. Isentropic sound velocity is calculated by differentiation along isentropes. The results of our calculations are in good agreement with experimental data. Thus, quantum molecular dynamics results can be effectively used for verification or calibration of semiempirical equations of state under conditions of lack of experimental information at high energy densities. This work is supported by RFBR, grants 09-08-01129 and 11-08-01225.
Simulation of quantum dynamics based on the quantum stochastic differential equation.
Li, Ming
2013-01-01
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.
2015-08-31
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
Space-Like Particle Production: an Interpretation Based on the Majorana Equation
Nanni, Luca
2016-01-01
This study reconsiders the decay of an ordinary particle in bradyons, tachyons and luxons in the field of the relativistic quantum mechanics. Lemke already investigated this from the perspective of covariant kinematics. Since the decay involves both spacelike and timelike particles, the study uses the Majorana equation for particles with an arbitrary spin. The equation describes the tachyonic and bradyonic realms of massive particles, and approaches the problem of how spacelike particles might develop. This method confirms the kinematic constraints that Lemke theory provided and proves that some possible decays are more favourable than others are.
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
A unified model for informetrics based on the wave and heat equations
Ye, Fred Y
2010-01-01
The function g(r,t) = p(r+q)^(-{\\beta}). e^(kt) is introduced as a basic informetric function describing the classical informetric laws (through its Mandelbrot part) and a time evolution. It is shown that this function is a solution of a wave-type and of a heat-type partial differential equation. It is suggested that our approach may lead to a description of informetrics in a partial differential equation setting, formally similar to that for well-known physical laws.
Chen, Xueli; Zhang, Qitan; Yang, Defu; Liang, Jimin
2014-01-01
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP3) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.
Jungemann, C.; Pham, A. T.; Meinerzhagen, B.; Ringhofer, C.; Bollhöfer, M.
2006-07-01
The Boltzmann equation for transport in semiconductors is projected onto spherical harmonics in such a way that the resultant balance equations for the coefficients of the distribution function times the generalized density of states can be discretized over energy and real spaces by box integration. This ensures exact current continuity for the discrete equations. Spurious oscillations of the distribution function are suppressed by stabilization based on a maximum entropy dissipation principle avoiding the H transformation. The derived formulation can be used on arbitrary grids as long as box integration is possible. The approach works not only with analytical bands but also with full band structures in the case of holes. Results are presented for holes in bulk silicon based on a full band structure and electrons in a Si NPN bipolar junction transistor. The convergence of the spherical harmonics expansion is shown for a device, and it is found that the quasiballistic transport in nanoscale devices requires an expansion of considerably higher order than the usual first one. The stability of the discretization is demonstrated for a range of grid spacings in the real space and bias points which produce huge gradients in the electron density and electric field. It is shown that the resultant large linear system of equations can be solved in a memory efficient way by the numerically robust package ILUPACK.
Schmuck, Markus; Pradas, Marc; Pavliotis, Grigorios A.; Kalliadasis, Serafim
2014-11-01
Based on thermodynamic and variational principles we formulate novel equations for mixtures of incompressible fluids in strongly heterogeneous domains, such as composites and porous media, using elements from the regular solution theory. Starting with equations that fully resolve the pores of a porous medium, represented as a periodic covering of a single reference pore, we rigorously derive effective macroscopic phase field equations under the assumption of periodic and strongly convective flow. Our derivation is based on the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations. We discover systematically diffusion-dispersion relations (including Taylor-Aris-dispersion) as in classical convection-diffusion problems. Our results represent a systematic and efficient computational strategy to macroscopically track interfaces in heterogeneous media which together with the well-known versatility of phase field models forms a promising basis for the analysis of a wide spectrum of engineering and scientific applications such as oil recovery, for instance.
Accelerating 3D Elastic Wave Equations on Knights Landing based Intel Xeon Phi processors
Sourouri, Mohammed; Birger Raknes, Espen
2017-04-01
In advanced imaging methods like reverse-time migration (RTM) and full waveform inversion (FWI) the elastic wave equation (EWE) is numerically solved many times to create the seismic image or the elastic parameter model update. Thus, it is essential to optimize the solution time for solving the EWE as this will have a major impact on the total computational cost in running RTM or FWI. From a computational point of view applications implementing EWEs are associated with two major challenges. The first challenge is the amount of memory-bound computations involved, while the second challenge is the execution of such computations over very large datasets. So far, multi-core processors have not been able to tackle these two challenges, which eventually led to the adoption of accelerators such as Graphics Processing Units (GPUs). Compared to conventional CPUs, GPUs are densely populated with many floating-point units and fast memory, a type of architecture that has proven to map well to many scientific computations. Despite its architectural advantages, full-scale adoption of accelerators has yet to materialize. First, accelerators require a significant programming effort imposed by programming models such as CUDA or OpenCL. Second, accelerators come with a limited amount of memory, which also require explicit data transfers between the CPU and the accelerator over the slow PCI bus. The second generation of the Xeon Phi processor based on the Knights Landing (KNL) architecture, promises the computational capabilities of an accelerator but require the same programming effort as traditional multi-core processors. The high computational performance is realized through many integrated cores (number of cores and tiles and memory varies with the model) organized in tiles that are connected via a 2D mesh based interconnect. In contrary to accelerators, KNL is a self-hosted system, meaning explicit data transfers over the PCI bus are no longer required. However, like most
Crossvalidation of two heart rate-based equations for predicting VO2max in white and black men.
Esco, Michael R; Olson, Michele S; Williford, Henry N; Mugu, Emmanuel M; Bloomquist, Barbara E; McHugh, Aindrea N
2012-07-01
The purpose of this investigation was to crossvalidate 2 equations that use the ratio of maximal heart rate (HRmax) to resting HR (HRrest) for predicting maximal oxygen consumption (VO2max) in white and black men. One hundred and nine white (n = 51) and black (n = 58) men completed a maximal exercise test on a treadmill to determine VO2max. The HRrest and HRmax were used to predict VO2max via the HRindex and HRratio equations. Validity statistics were done to compare the criterion versus predicted VO2max values across the entire cohort and within each race separately. For the entire group, VO2max was significantly overestimated with the HRindex equation, but the HRratio equation yielded no significant difference compared with the criterion. In addition, there were no significant differences shown between VO2max and either HR-based prediction equation for the white subgroup. However, both equations significantly overestimated VO2max in the black group. Furthermore, large standard error of estimates (ranging from 6.92 to 7.90 ml·kg(-1)·min(-1)), total errors (ranging from 8.30 to 8.62 ml·kg(-1)·min(-1)), and limits of agreement (ranging from upper limits of 16.65 to lower limits of -18.25 ml·kg(-1)·min(-1)) were revealed when comparing the predicted to criterion VO2max for both the groups. Considering the results of this investigation, the HRratio and HRindex methods appear to crossvalidate and prove useful for estimating the mean VO2max in white men as a group but not for an age-matched group of black men. However, because of inflated values for error, caution should be exercised when using these methods to predict individual VO2max.
Equations of State of Elements Based on the Generalized Fermi-Thomas Theory
Feynman, R. P.; Metropolis, N.; Teller, E.
1947-04-28
The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z-values.
New dielectric mixture equation for porous materials based on depolarization factors
Hilhorst, M.A.; Dirksen, C.; Kampers, F.W.H.; Feddes, R.A.
2001-01-01
A change in the relative proportions of the constituents of a porous material like soil will cause a change in its electrical permittivity. The measured permittivity reflects the impact of the permittivities of the individual material constituents. Numerous dielectric mixture equations are
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
DEFF Research Database (Denmark)
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi;
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser charact...
TRANSMISSION MOMENTARY EFFICIENCY BASED ON THE D'ALEMBERT-LAGRANGE EQUATION FOR INVOLUTES GEARS
Institute of Scientific and Technical Information of China (English)
Liang Yi; Lai Changying
2004-01-01
The D'Alembert-Lagrange equation is introduced and used to derive the formulas of momentary efficiency for external gearing of standard involutes spur gears.The gearings with correct and increased center distance are discussed.The momentary efficiency formula is calculated and analyzed using software Matlab.The derived formula of momentary efficiency is also compared with the traditional formula.
The Equation Based on the Rotational and Orbital Motion of the Planets
Directory of Open Access Journals (Sweden)
G.A. Korablev
2017-03-01
Full Text Available Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data.
Is classical mechanics based on Newton's laws or Eulers analytical equations?
Directory of Open Access Journals (Sweden)
H.Iro
2005-01-01
Full Text Available In an example I illustrate how my picture of physics is enriched due to my frequent conversations with Reinhard Folk. The subject is: Who wrote down the basic equations of motion of classical mechanics for the first time? (To be sure, it was not Newton.
Is classical mechanics based on Newton's laws or Eulers analytical equations?
Iro, H
2005-01-01
In an example I illustrate how my picture of physics is enriched due to my frequent conversations with Reinhard Folk. The subject is: Who wrote down the basic equations of motion of classical mechanics for the first time? (To be sure, it was not Newton.)
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
Aktaa, J
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.
Magnitude Estimation for the 2011 Tohoku-Oki Earthquake Based on Ground Motion Prediction Equations
Eshaghi, Attieh; Tiampo, Kristy F.; Ghofrani, Hadi; Atkinson, Gail M.
2015-08-01
This study investigates whether real-time strong ground motion data from seismic stations could have been used to provide an accurate estimate of the magnitude of the 2011 Tohoku-Oki earthquake in Japan. Ultimately, such an estimate could be used as input data for a tsunami forecast and would lead to more robust earthquake and tsunami early warning. We collected the strong motion accelerograms recorded by borehole and free-field (surface) Kiban Kyoshin network stations that registered this mega-thrust earthquake in order to perform an off-line test to estimate the magnitude based on ground motion prediction equations (GMPEs). GMPEs for peak ground acceleration and peak ground velocity (PGV) from a previous study by Eshaghi et al. in the Bulletin of the Seismological Society of America 103. (2013) derived using events with moment magnitude ( M) ≥ 5.0, 1998-2010, were used to estimate the magnitude of this event. We developed new GMPEs using a more complete database (1998-2011), which added only 1 year but approximately twice as much data to the initial catalog (including important large events), to improve the determination of attenuation parameters and magnitude scaling. These new GMPEs were used to estimate the magnitude of the Tohoku-Oki event. The estimates obtained were compared with real time magnitude estimates provided by the existing earthquake early warning system in Japan. Unlike the current operational magnitude estimation methods, our method did not saturate and can provide robust estimates of moment magnitude within ~100 s after earthquake onset for both catalogs. It was found that correcting for average shear-wave velocity in the uppermost 30 m () improved the accuracy of magnitude estimates from surface recordings, particularly for magnitude estimates of PGV (Mpgv). The new GMPEs also were used to estimate the magnitude of all earthquakes in the new catalog with at least 20 records. Results show that the magnitude estimate from PGV values using
Ion strength limit of computed excess functions based on the linearized Poisson-Boltzmann equation.
Fraenkel, Dan
2015-12-05
The linearized Poisson-Boltzmann (L-PB) equation is examined for its κ-range of validity (κ, Debye reciprocal length). This is done for the Debye-Hückel (DH) theory, i.e., using a single ion size, and for the SiS treatment (D. Fraenkel, Mol. Phys. 2010, 108, 1435), which extends the DH theory to the case of ion-size dissimilarity (therefore dubbed DH-SiS). The linearization of the PB equation has been claimed responsible for the DH theory's failure to fit with experiment at > 0.1 m; but DH-SiS fits with data of the mean ionic activity coefficient, γ± (molal), against m, even at m > 1 (κ > 0.33 Å(-1) ). The SiS expressions combine the overall extra-electrostatic potential energy of the smaller ion, as central ion-Ψa>b (κ), with that of the larger ion, as central ion-Ψb>a (κ); a and b are, respectively, the counterion and co-ion distances of closest approach. Ψa>b and Ψb>a are derived from the L-PB equation, which appears to conflict with their being effective up to moderate electrolyte concentrations (≈1 m). However, the L-PB equation can be valid up to κ ≥ 1.3 Å(-1) if one abandons the 1/κ criterion for its effectiveness and, instead, use, as criterion, the mean-field electrostatic interaction potential of the central ion with its ion cloud, at a radial distance dividing the cloud charge into two equal parts. The DH theory's failure is, thus, not because of using the L-PB equation; the lethal approximation is assigning a single size to the positive and negative ions. © 2015 Wiley Periodicals, Inc.
Reference equations for the six-minute walk distance based on a Brazilian multicenter study.
Britto, Raquel R; Probst, Vanessa S; de Andrade, Armele F Dornelas; Samora, Giane A R; Hernandes, Nidia A; Marinho, Patrícia E M; Karsten, Marlus; Pitta, Fabio; Parreira, Veronica F
2013-01-01
It is important to include large sample sizes and different factors that influence the six-minute walking distance (6MWD) in order to propose reference equations for the six-minute walking test (6 MWT). To evaluate the influence of anthropometric, demographic, and physiologic variables on the 6 MWD of healthy subjects from different regions of Brazil to establish a reference equation for the Brazilian population. In a multicenter study, 617 healthy subjects performed two 6 MWTs and had their weight, height, and body mass index (BMI) measured, as well as their physiologic responses to the test. Delta heart rate (∆HR), perceived effort, and peripheral oxygen saturation were calculated by the difference between the respective values at the end of the test minus the baseline value. Walking distance averaged 586 ± 106 m, 54 m greater in male compared to female subjects (p<0.001). No differences were observed among the 6 MWD from different regions. The quadratic regression analysis considering only anthropometric and demographic data explained 46% of the variability in the 6 MWT (p<0.001) and derived the equation: 6 MWD(pred)=890.46-(6.11 × age)+(0.0345 × age(2))+(48.87 × gender)-(4.87 × BMI). A second model of stepwise multiple regression including ∆HR explained 62% of the variability (p<0.0001) and derived the equation: 6 MWD(pred)=356.658-(2.303 × age)+(36.648 × gender)+(1.704 × height)+(1.365×∆HR). The equations proposed in this study, especially the second one, seem adequate to accurately predict the 6 MWD for Brazilians.
Energy Technology Data Exchange (ETDEWEB)
Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)
2015-10-15
In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the
Peng, NaiFu; Guan, Hui; Wu, ChuiJie
2016-11-01
In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level.
A Partially-ordered-set Based Approach to the Dirac Equation in 3+1 space-time
Earle, Keith; Knuth, Kevin
2012-02-01
Recent work by Knuth and co-workers has shown how insights into Einstein's Theory of Special Relativity may be obtained by careful reasoning about consistent quantification of a poset. The Feynman Chessboard problem in 1+1 spacetime can be treated from this perspective, for example. Alternative methods of solution based on techniques borrowed from statistical mechanics have also been developed over the years to solve the Feynman Chessboard model in 1+1 spacetime. One particularly intriguing solution is based on a master-equation approach developed by McKeon and Ord for 1+1 spacetime. We will show how this model may be extended to 3+1 spacetime using techniques developed by Bialynicki-Birula, thus providing an alternative derivation of the Dirac equation. An external electromagnetic field can be accommodated very naturally in the formalism from which a pleasing pictorial representation of electromagnetic interactions in the lattice picture emerges.
Ibáñez, Javier; Hernández, Vicente
2011-03-01
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.
Reche-López, Pedro; Hernández, Erwin
2014-01-01
In the context of wave-like phenomena, Fourier pseudospectral time-domain (PSTD) algorithms are some of the most efficient time-domain numerical methods for engineering applications. One important drawback of these methods is the so-called Gibbs phenomenon. This error can be avoided by using absorbing boundary conditions (ABC) at the end of the simulations. However, there is an important lack of ABC using a PSTD methods on a wave equation. In this paper, we present an ABC model based on a PSTD damped wave equation with an absorption parameter that depends on the position. Some examples of optimum variation profiles are studied analytically and numerically. Finally, the results of this model are also compared to another ABC model based on an hybrid formulation of the scalar perfectly matched layer. PMID:24737966
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Viscosity is an important physical parameter of fluid,and the Eyring viscosity equation is a popular viscosity theory.Based on the Eyring reaction rate equation and Boltzmann statistical theory,and including the probabilities of creating a hole in liquid and the transition to the neighboring hole,a modified Eyring viscosity equation was proposed.According to the structural characteristics of short-range order,liquid is treated as a quasi-lattice structure in a small region.The activation energy,which is the minimum energy needed for the molecule to jump to its neighboring hole because of the restriction of other molecules around it,was analytically calculated from an intermolecular Lennard-Jones potential function and a Stockmayer potential function.The viscosity values of 37 kinds of typical liquids at 25°C and the dependence of viscosity of three kinds of liquids on temperatures were calculated with this modified viscosity equation,and the calculated results agree with the experimental values to some extent.This work not only enriches the understanding of the mechanism of liquid viscosity,but also could provide some theoretical guides for the relevant studies and applications.
Chen, Xueli; Sun, Fangfang; Yang, Defu; Liang, Jimin
2015-09-01
For fluorescence tomographic imaging of small animals, the liver is usually regarded as a low-scattering tissue and is surrounded by adipose, kidneys, and heart, all of which have a high scattering property. This leads to a breakdown of the diffusion equation (DE)-based reconstruction method as well as a heavy computational burden for the simplified spherical harmonics equation (SPN). Coupling the SPN and DE provides a perfect balance between the imaging accuracy and computational burden. The coupled third-order SPN and DE (CSDE)-based reconstruction method is developed for fluorescence tomographic imaging. This is achieved by doubly using the CSDE for the excitation and emission processes of the fluorescence propagation. At the same time, the finite-element method and hybrid multilevel regularization strategy are incorporated in inverse reconstruction. The CSDE-based reconstruction method is first demonstrated with a digital mouse-based liver cancer simulation, which reveals superior performance compared with the SPN and DE-based methods. It is more accurate than the DE-based method and has lesser computational burden than the SPN-based method. The feasibility of the proposed approach in applications of in vivo studies is also illustrated with a liver cancer mouse-based in situ experiment, revealing its potential application in whole-body imaging of small animals.
Pauwels, Valentijn R. N.; Verhoest, Niko E. C.; de Troch, FrançOis P.
2002-12-01
In hydrology the slow, subsurface component of the discharge is usually referred to as base flow. One method to model base flow is the conceptual approach, in which the complex physical reality is simplified using hypotheses and assumptions, and the various physical processes are described mathematically. The purpose of this paper is to develop and validate a conceptual method, based on hydraulic theory, to calculate the base flow of a catchment, under observed precipitation rates. The governing groundwater equation, the Boussinesq equation, valid for a unit width sloping aquifer, is linearized and solved for a temporally variable recharge rate. The solution allows the calculation of the transient water table profile in and the outflow from an aquifer under temporally variable recharge rates. When a catchment is considered a metahillslope, the solution can be used, when coupled to a routing model, to calculate the catchment base flow. The model is applied to the Zwalm catchment and four subcatchments in Belgium. The results suggest that it is possible to model base flow at the catchment scale, using a Boussinesq-based metahillslope model. The results further indicate that it is sufficient to use a relatively simple formulation of the infiltration, overland flow, and base flow processes to obtain reasonable estimates of the total catchment discharge.
Galka, Andreas; Ozaki, Tohru; Muhle, Hiltrud; Stephani, Ulrich; Siniatchkin, Michael
2008-01-01
We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to the electric potentials at the surface of the head, the model can be put into relation with recordings of the electroencephalogram (EEG). Through ...
Modelling solar cycle length based on Poincaré maps for Lorenz-type equations
Directory of Open Access Journals (Sweden)
H. Lundstedt
2010-04-01
Full Text Available Two systems of Lorenz-type equations modelling solar magnetic activity are studied: Firstly a low order dynamic system in which the toroidal and poloidal fields are represented by x- and y-coordinates respectively, and the hydrodynamical information is given by the z coordinate. Secondly a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements.
Campbell, D A; Chkrebtii, O
2013-12-01
Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories.
Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation.
Wei, Qi; Dobigeon, Nicolas; Tourneret, Jean-Yves
2015-11-01
This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.
Spectral methods based on new formulations for coupled Stokes and Darcy equations
Wang, Weiwei; Xu, Chuanju
2014-01-01
In this paper we consider the numerical solution of the Stokes and Darcy coupled equations, which frequently appears in porous media modeling. The main contribution of this work is as follows: First, we introduce a new formulation for the Stokes/Darcy coupled equations, subject respectively to the Beavers-Joseph-Saffman interface condition and an alternative matching interface condition. Secondly, we prove the well-posedness of these weak problems by using the classical saddle point theory. Thirdly, some spectral approximations to the weak problems are proposed and analyzed, and some error estimates are provided. It is found that the new formulations significantly simplify the error analysis and numerical implementation. Finally, some two-dimensional spectral and spectral element numerical examples are provided to demonstrate the efficiency of our methods.
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
Dantas, Christine C
2016-01-01
We consider an integrable, nonlocal and nonlinear, Schr\\"odinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.
Directory of Open Access Journals (Sweden)
Sankar Prasad Mondal
Full Text Available In this paper the First Order Linear Ordinary Differential Equations (FOLODE are described in fuzzy environment. Here coefficients and /or initial condition of FOLODE are taken as Generalized Triangular Fuzzy Numbers (GTFNs.The solution procedure of the FOLODE is developed by Laplace transform. It is illustrated by numerical examples. Finally imprecise bank account problem and concentration of drug in blood problem are described.
Image Denoising based on Fourth-Order Partial Differential Equations: A Survey
Directory of Open Access Journals (Sweden)
Anand Swaroop Khare,
2013-04-01
Full Text Available Reduction of noise is essential especially in the fieldof image processing. Several researchers arecontinuously working in this direction and providesome good insights, but still there are lot of scope inthis field.Noise mixed with image is harmful forimage processing. Inthis paper we survey severalaspects of image denoising and fourth-order partialdifferential equation.We also discuss severaltraditional methodology used with their advantagesand disadvantages. We also provide a deep analysisbased on the literature work from the previousresearch.
Finite element formulation based on proper orthogonal decomposition for parabolic equations
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.
Filters in topology optimization based on Helmholtz‐type differential equations
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Sigmund, Ole
2011-01-01
The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimizat......The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology...... optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non‐overlapping partitions. Obtaining information...... from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation...
Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation
Ren, Feng; Song, Baowei; Sukop, Michael C.; Hu, Haibao
2016-08-01
The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015), 10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014), 10.1103/PhysRevE.89.053320]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Zheng, Lin; Zheng, Song; Zhai, Qinglan
2016-02-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Energy Technology Data Exchange (ETDEWEB)
Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)
2016-02-05
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Esco, Michael R; Nickerson, Brett S; Bicard, Sara C; Russell, Angela R; Bishop, Phillip A
2016-01-01
The purpose of this investigation was to evaluate measurements of body-fat percentage (BF%) in 4 body-mass-index- (BMI) -based equations and dual-energy X-ray absorptiometry (DXA) in individuals with Down syndrome (DS). Ten male and 10 female adults with DS volunteered for this study. Four regression equations for estimating BF% based on BMI previously developed by Deurenberg et al. (DE(BMI-BF%)), Gallagher et al. (GA(BMI-BF%)), Womersley & Durnin (WO(BMI-BF%)), and Jackson et al. (JA(BMI-BF%)) were compared with DXA. There was no significant difference (p = .659) in mean BF% values between JA(BMI-BF%) (BF% = 40.80% ± 6.3%) and DXA (39.90% ± 11.1%), while DE(BMI-BF%) (34.40% ± 9.0%), WO(BMI-BF%) (35.10% ± 9.4%), and GA(BMI-BF%) (35.10% ± 9.4%) were significantly (p BMI-based BF% equations should not be used in individuals with DS.
Directory of Open Access Journals (Sweden)
Jing Yin
2015-07-01
Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.
Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
Directory of Open Access Journals (Sweden)
Zainab T. Baqer
2010-01-01
Full Text Available Computer models are used in the study of electrocardiography to provide insight into physiological phenomena that are difficult to measure in the lab or in a clinical environment. The electrocardiogram is an important tool for the clinician in that it changes characteristically in a number of pathological conditions. Many illnesses can be detected by this measurement. By simulating the electrical activity of the heart one obtains a quantitative relationship between the electrocardiogram and different anomalies. Because of the inhomogeneous fibrous structure of the heart and the irregular geometries of the body, finite element method is used for studying the electrical properties of the heart. This work describes the implementation of the Conjugate Gradient iterative method for the solution of large linear equation systems resulting from the finite element method. A diagonal Jacobi preconditioner is used in order to accelerate the convergence. Gaussian elimination is also implemented and compared with the Precondition Conjugate Gradient (PCG method and with the iterative method. Different types of matrix storage schemes are implemented such as the Compressed Sparse Row (CSR to achieve better performance. In order to demonstrate the validity of the finite element analysis, the technique is adopted to solve Laplace's equation that describes the electrical activity of the human body with Dirichlet and Neumann boundary conditions. An automatic mesh generator is built using C++ programming language. Initially a complete finite element program is built to solve Laplace's equation. The same accuracy is obtained using these methods. The results show that the CSR format reduces computation time compared to the order format. The PCG method is better for the solution of large linear system (sparse matrices than the Gaussian Elimination and back substitution method, while Gaussian elimination is better than iterative method.
Prestack AVA inversion of exact Zoeppritz equations based on modified Trivariate Cauchy distribution
Zhou, Lin; Li, Jingye; Chen, Xiaohong; Liu, Xingye; Chen, Li
2017-03-01
Obtaining interlayer weak reflection information that helps identify properties and accurate density information from complex and elusive reservoirs is particularly important for reservoir characterization and detection. However, conventional prestack amplitude variation with incidence angle inversion method is strongly influenced by the accuracy of the approximate Zoeppritz equations, which suppresses weak reflections coming from the commonly used prior distribution. In this paper, we address these problems by using exact Zoeppritz equations. First, the objective function of the inverse problem was constructed and the modified Cauchy distribution was introduced as the prior information by utilizing Bayes' theorem. In the complicated objective function, the forward operators are the sophisticated and nonlinear Zoeppritz equations with respect to estimate parameters. We then combined the idea of generalized linear inversion with iterative reweighed least-squares algorithm in order to solve the problem. Generalized linear inversion was used to solve the objective function, from which a nonlinear solution of the model parameters' perturbations can be calculated. The iterative reweighed least-squares algorithm was applied to solve the nonlinear expression in an attempt to obtain an updated iterative formula of the model parameters. Therefore the prestack amplitude variation with incidence angle inversion was able to be performed in order to better characterize a reservoir. Both synthetic and field data examples show that the new method can not only directly inverse P-wave velocity, S-wave velocity and density, but also provides accurate estimation results, particularly for density. The introduction of the modified Trivariate Cauchy prior constraints effectively estimated and inverted elastic parameters of weak reflections. Both examples demonstrated the feasibility and effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Ming-Lu Wu
2013-12-01
Full Text Available This paper links professional service firms’ resource-based strategies to their customer-focused performance for formulating service quality improvement priorities. The research applies the structural equation modelling approach to survey data from Hong Kong construction consultants to test some hypotheses. The study validates the various measures of firms’ resource-based strategies and customer-focused performance and bridges the gaps in firms’ organizational learning, core competences and customer-focused performance mediated by their strategic flexibility. The research results have practical implications for professional service firms to deploy resources appropriately to first enhance different competences and then improve customerfocused performance using their different competences.
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Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
A mesh deformation technique based on two-step solution of the elasticity equations
Huang, Guo; Huang, Haiming; Guo, Jin
2016-12-01
In the computation of fluid mechanics problems with moving boundaries, including fluid-structure interaction, fluid mesh deformation is a common problem to be solved. An automatic mesh deformation technique for large deformations of the fluid mesh is presented on the basis of a pseudo-solid method in which the fluid mesh motion is governed by the equations of elasticity. A two-dimensional mathematical model of a linear elastic body is built by using the finite element method. The numerical result shows that the proposed method has a better performance in moving the fluid mesh without producing distorted elements than that of the classic one-step methods.
A Fast Mixed-Precision Strategy for Iterative GPU-Based Solution of the Laplace Equation
DEFF Research Database (Denmark)
Our work is concerned with the development of a generic high-performance library for scientific computing. The library is targeted for assembling flexible-order finite-difference solvers for PDEs. Our goal is to enable fast solution of large PDE systems, fully exploiting the massively parallel...... architecture of Graphics Processing Units. We will detail a strategy for an iterative mixed-precision defect correction method, with p-multigrid preconditioning. We present a case study of the fully nonlinear potential flow equations, in which the bottleneck problem is finding the solution of a Laplace...
Numerical modeling of photon migration in human neck based on the radiative transport equation
Fujii, Hiroyuki; Nadamoto, Ken; Okada, Eiji; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao
2016-01-01
Biomedical optical imaging has a possibility of a comprehensive diagnosis of thyroid cancer in conjunction with ultrasound imaging. For improvement of the optical imaging, this study develops a higher order scheme for solving the time-dependent radiative transport equation (RTE) by use of the finite-difference and discrete-ordinate methods. The accuracy and efficiency of the developed scheme are examined by comparison with the analytical solutions of the RTE in homogeneous media. Then, the developed scheme is applied to describing photon migration in the human neck model. The numerical simulations show complex behaviors of photon migration in the human neck model due to multiple diffusive reflection near the trachea.
Directory of Open Access Journals (Sweden)
Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
Energy Technology Data Exchange (ETDEWEB)
Furuya, Atsushi [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan); Yagi, Masatoshi; Itoh, Sanae-I. [Kyushu Univ., Research Institute for Applied Mechanics, Kasuga, Fukuoka (Japan)
2003-02-01
The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if {delta}' > 0. (author)
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Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
A mesh deformation technique based on two-step solution of the elasticity equations
Huang, Guo; Huang, Haiming; Guo, Jin
2017-04-01
In the computation of fluid mechanics problems with moving boundaries, including fluid-structure interaction, fluid mesh deformation is a common problem to be solved. An automatic mesh deformation technique for large deformations of the fluid mesh is presented on the basis of a pseudo-solid method in which the fluid mesh motion is governed by the equations of elasticity. A two-dimensional mathematical model of a linear elastic body is built by using the finite element method. The numerical result shows that the proposed method has a better performance in moving the fluid mesh without producing distorted elements than that of the classic one-step methods.
Areias, P.; Rabczuk, T.; de Sá, J. César
2016-12-01
We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved.
Berardi, Marco; Andrisani, Andrea; Lopez, Luciano; Vurro, Michele
2016-11-01
In this paper a new data assimilation technique is proposed which is based on the ensemble Kalman filter (EnKF). Such a technique will be effective if few observations of a dynamical system are available and a large model error occurs. The idea is to acquire a fine grid of synthetic observations in two steps: (1) first we interpolate the real observations with suitable polynomial curves; (2) then we estimate the relative measurement errors by means of Brownian bridges. This technique has been tested on the Richards' equation, which governs the water flow in unsaturated soils, where a large model error has been introduced by solving the Richards' equation by means of an explicit numerical scheme. The application of this technique to some synthetic experiments has shown improvements with respect to the classical ensemble Kalman filter, in particular for problems with a large model error.
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches.
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Mikell, Justin K. [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas (United States); Klopp, Ann H. [Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Gonzalez, Graciela M.N. [Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Kisling, Kelly D. [Department of Radiation Physics-Patient Care, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas (United States); Price, Michael J. [Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, Baton Rouge, Louisiana, and Mary Bird Perkins Cancer Center, Baton Rouge, Louisiana (United States); Berner, Paula A. [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Eifel, Patricia J. [Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Mourtada, Firas, E-mail: fmourtad@christianacare.org [Department of Radiation Physics-Patient Care, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Department of Experimental Diagnostic Imaging, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Department of Radiation Oncology, Helen F. Graham Cancer Center, Newark, Delaware (United States)
2012-07-01
Purpose: To investigate the dosimetric impact of the heterogeneity dose calculation Acuros (Transpire Inc., Gig Harbor, WA), a grid-based Boltzmann equation solver (GBBS), for brachytherapy in a cohort of cervical cancer patients. Methods and Materials: The impact of heterogeneities was retrospectively assessed in treatment plans for 26 patients who had previously received {sup 192}Ir intracavitary brachytherapy for cervical cancer with computed tomography (CT)/magnetic resonance-compatible tandems and unshielded colpostats. The GBBS models sources, patient boundaries, applicators, and tissue heterogeneities. Multiple GBBS calculations were performed with and without solid model applicator, with and without overriding the patient contour to 1 g/cm{sup 3} muscle, and with and without overriding contrast materials to muscle or 2.25 g/cm{sup 3} bone. Impact of source and boundary modeling, applicator, tissue heterogeneities, and sensitivity of CT-to-material mapping of contrast were derived from the multiple calculations. American Association of Physicists in Medicine Task Group 43 (TG-43) guidelines and the GBBS were compared for the following clinical dosimetric parameters: Manchester points A and B, International Commission on Radiation Units and Measurements (ICRU) report 38 rectal and bladder points, three and nine o'clock, and {sub D2cm3} to the bladder, rectum, and sigmoid. Results: Points A and B, D{sub 2} cm{sup 3} bladder, ICRU bladder, and three and nine o'clock were within 5% of TG-43 for all GBBS calculations. The source and boundary and applicator account for most of the differences between the GBBS and TG-43 guidelines. The D{sub 2cm3} rectum (n = 3), D{sub 2cm3} sigmoid (n = 1), and ICRU rectum (n = 6) had differences of >5% from TG-43 for the worst case incorrect mapping of contrast to bone. Clinical dosimetric parameters were within 5% of TG-43 when rectal and balloon contrast were mapped to bone and radiopaque packing was not overridden
Greuell, W.; Oerlemans, J.
2004-01-01
In this paper, we propose equations for narrowband-to-broadband (NTB) albedo conversion for glacier ice and snow for four types of satellite sensors: thematic mapper (TM), advanced very high resolution radiometer (AVHRR), moderate resolution imaging spectroradiometer (MODIS), and multi-angle imaging
A CNN-based approach to integrate the 3-D turbolent diffusion equation
Nunnari, G.
2003-04-01
The paper deals with the integration of the 3-D turbulent diffusion equation. This problem is relevant in several application fields including fluid dynamics, air/water pollution, volcanic ash emissions and industrial hazard assessment. As it is well known numerical solution of such a kind of equation is very time consuming even by using modern digital computers and this represents a short-coming for on-line applications. To overcome this drawback a Cellular Neural Network Approach is proposed in this paper. CNN's proposed by Chua and Yang in 1988 are massive parallel analog non-linear circuits with local interconnections between the computing elements that allow very fast distributed computations. Nowadays several producers of semiconductors such as SGS-Thomson are producing on chip CNN's so that their massive use for heavy computing applications is expected in the near future. In the paper the methodological background of the proposed approach will be outlined. Further some results both in terms of accuracy and computation time will be presented also in comparison with traditional three-dimensional computation schemes. Some results obtained to model 3-D pollution problems in the industrial area of Siracusa (Italy), characterised by a large concentration of petrol-chemical plants, will be presented.
Planar diffusions with rank-based characteristics and perturbed Tanaka equations
Fernholz, E Robert; Karatzas, Ioannis; Prokaj, Vilmos
2011-01-01
For given non negative constants $g$, $h$, $\\rho$, $\\sigma$ with $\\rho^2+\\sigma^2 =1$ and $g+h>0$, we construct a diffusion process $(X_1, X_2)$ with values in the plane and infinitesimal generator $L = 1_{x_1>x_2} p(\\partial_{x_1},\\partial_{x_2}) + 1_{x_2>x_1} p(\\partial_{x_2},\\partial_{x_1}), $ where $ p(x,y)= \\frac{\\rho^2}2 x^2 + \\frac{\\sigma^2}2 y^2 - h x + g y. $ We compute the transition probabilities of this process, discuss its realization in terms of appropriate systems of stochastic differential equations, study its dynamics under a time reversal, and note that these involve singularly continuous components governed by local time. Crucial in our analysis are properties of Brownian and semimartingale local time; properties of the generalized perturbed Tanaka equation $dZ(t) = f(Z(t)) dM(t) + dN(t)$, $Z(0)=\\xi $$ driven by suitable continuous, orthogonal semimartingales $M$ and $N$ and with $f$ of bounded variation, which we study here in detail; and those of a one-dimensional diffusion $Y$ with bang-...
Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
Directory of Open Access Journals (Sweden)
Ana M. Martín-Caraballo
2015-08-01
Full Text Available but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position method and the tangent (or Newton-Raphson method, this last as example of fixed-point methods.
Papas, Brian N; Schuurman, Michael S; Yarkony, David R
2008-09-28
A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.
Aczél, J
1987-01-01
Recently I taught short courses on functional equations at several universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My aim was to introduce the most important equations and methods of solution through actual (not artifi cial) applications which were recent and with which I had something to do. Most of them happened to be related to the social or behavioral sciences. All were originally answers to questions posed by specialists in the respective applied fields. Here I give a somewhat extended version of these lectures, with more recent results and applications included. As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula tions are set in fine print. I am grateful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for critical remarks and to Mrs. Brenda Law for care ful computer-typing of the manuscript (in several versions). A...
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
基于偏微分方程的图像去噪算法%Image denoising algorithms based on partial differential equation
Institute of Scientific and Technical Information of China (English)
武伟; 王宏志; 宋宇
2011-01-01
介绍了3种常见的偏微分方程去噪模型：热扩散方程、P-M扩散方程、TV扩散方程,并结合实验分析了它们在图像去噪中的优缺点。%Three image denoising models based on partial differential equation,hot diffusion equation,P-M diffusion equation and TV diffusion equation are introduced.By means of experimental analysis,the advantages and disadvantages are listed for image denoising.
Foucart, F.; Desai, D.; Brege, W.; Duez, M. D.; Kasen, D.; Hemberger, D. A.; Kidder, L. E.; Pfeiffer, H. P.; Scheel, M. A.
2017-02-01
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about the composition of low-density, cold material in the different equations of state, and propose an updated estimate for the ejecta velocity which takes those effects into account. We also present an updated mesh-refinement algorithm which allows us to improve the numerical resolution used to evolve neutron star-black hole mergers.
von Kármán–Howarth and Corrsin equations closure based on Lagrangian description of the fluid motion
Energy Technology Data Exchange (ETDEWEB)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
2016-05-15
A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarth and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.
Lee, Yongjin; Shin, Moon Sam; Kim, Hwayong
2008-12-01
In this study, a new crossover sine model (CSM) n was developed from a trigonometric model [M. E. Fisher, S. Zinn, and P. J. Upton, Phys. Rev. B 59, 14533 (1999)]. The trigonometric model is a parametric formulation model that is used to represent the thermodynamic variables near a critical point. Although there are other crossover models based on this trigonometric model, such as the CSM and the analytical sine model, which is an analytic formulation of the CSM, the new sine model (NSM) employs a different approach from these two models in terms of the connections between the parametric variables of the trigonometric model and thermodynamic variables. In order to test the performance of the NSM, the crossover lattice equation of state [M. S. Shin, Y. Lee, and H. Kim, J. Chem. Thermodyn. 40, 174 (2008)] was applied using the NSM for correlations of various pure fluids and fluid mixtures. The results showed that over a wide range of states, the crossover lattice fluid (xLF)/NSM yields the saturated properties of pure fluids and the phase behavior of binary mixtures more accurately than the original lattice equation of state. Moreover, a comparison with the crossover lattice equation of state using the CSM (xLF/CSM) showed that the new model presents good correlation results that are comparable to the xLF/CSM.
Zeng, Zhaoyuanling; Wang, Xiaowan; Wang, Zengwu; Guo, Rui; Feng, Ruihua
2017-02-28
To analyze the relationship among hypertension-relevant knowledge, attitude and behavior and to provide evidence for prevention of hypertension. Methods: A total of 5 861 employees with hypertension from 10 provinces were selected, and their data were collected by uniform questionnaires. The structural equation model was established by using LISREL version 8.7. Knowledge, attitude and behavior was set as latent variables, and the observed variables corresponding to latent variables served as explicit variables. The parametric estimation of the structural equation model is based on polyserial correlation coefficients and asymptotical covariance matrix. Results: Knowledge directly affected attitude, and the impact coefficient was 0.84; attitude directly affect behavior, and the impact coefficient was 0.38; knowledge showed indirect effect on behavior; the structural equation model fitted the data well. Conclusion: Hypertension-related knowledge significantly affect attitude, while knowledge and attitude showed slight effect on behavior. There were other factors that affected the patient's behavior. It was suggested that we should fully consider the factors for behavior in health education, and adopt more appropriate measures in hypertension control.
Bich, Dao Huy; Xuan Nguyen, Nguyen
2012-12-01
In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge-Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency-amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.
Tamellini, L.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Institute of Scientific and Technical Information of China (English)
Naman; YANG
2015-01-01
Using the method of structural equation and balanced scorecard,this paper establishes the evaluation indicators and evaluation model for the performance of 21 rural cooperative economic organizations in X City of Hunan Province,and analyzes the relationship between indicators and dimensions of performance evaluation indicators,in order to find the influencing factors,obstacles and successful experience concerning the development of rural cooperative economic organizations. According to model analysis and conclusions,this paper sets forth the recommendations for promoting the development of rural cooperative economic organizations in Hunan Province,in order to provide a scientific basis for the institutional design and mechanism innovation of rural cooperative economic organizations in Hunan Province.
Zalys-Geller, E.; Hatridge, M.; Silveri, M.; Narla, A.; Sliwa, K. M.; Shankar, S.; Girvin, S. M.; Devoret, M. H.
2015-03-01
Remote entanglement of two superconducting qubits may be accomplished by first entangling them with flying coherent microwave pulses, and then erasing the which-path information of these pulses by using a non-degenerate parametric amplifier such as the Josephson Parametric Converter (JPC). Crucially, this process requires no direct interaction between the two qubits. The JPC, however, will fail to completely erase the which-path information if the flying microwave pulses encode any difference in dynamics of the two qubit-cavity systems. This which-path information can easily arise from mismatches in the cavity linewidths and the cavity dispersive shifts from their respective qubits. Through analysis of the Stochastic Master Equation for this system, we have found a strategy for shaping the measurement pulses to eliminate the effect of these mismatches on the entangling measurement. We have then confirmed the effectiveness of this strategy by numerical simulation. Work supported by: IARPA, ARO, and NSF.
Solution of N-S equations based on the quadtree cut cell method
Institute of Scientific and Technical Information of China (English)
KASE; Kiwamu
2009-01-01
With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.
MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS
Institute of Scientific and Technical Information of China (English)
Qing-ping Deng; Xiao-ping Feng
2002-01-01
Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion.To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
Experimental confirmation of tissue liquidity based on the exact solution of the Laplace equation
Norotte, Cyrille; Neagu, Adrian; Kosztin, Ioan; Forgacs, Gabor
2007-01-01
The notion of tissue surface tension has provided a physical understanding of morphogenetic phenomena such as tissue spreading or cell sorting. The measurement of tissue surface tension so far relied on strong approximations on the geometric profile of a spherical droplet compressed between parallel plates. We solved the Laplace equation for this geometry and tested its solution on true liquids and embryonic tissue fragments as well as multicellular aggregates. The analytic solution provides the surface tension in terms of easily and accurately measurable geometric parameters. Experimental results show that the various tissues and multicellular aggregates studied here are incompressible and, similarly to true liquids, possess effective surface tensions that are independent of the magnitude of the compressive force and the volume of the droplet.
Norotte, C.; Marga, F.; Neagu, A.; Kosztin, I.; Forgacs, G.
2008-02-01
The notion of apparent tissue surface tension offered a systematic way to interpret certain morphogenetic processes in early development. It also allowed deducing quantitative information on cellular and molecular parameters that is otherwise difficult to obtain. To accurately determine such tensions we combined novel experiments with the exact solution of the Laplace equation for the profile of a liquid drop under the employed experimental conditions and used the exact solution to evaluate data collected on tissues. Our results confirm that tissues composed of adhesive and motile cells indeed can be characterized in terms of well-defined apparent surface tension. Our experimental technique presents a way to measure liquid interfacial tensions under conditions when known methods fail.
The intrinsic periodic fluctuation of forest: a theoretical model based on diffusion equation
Zhou, J.; Lin, G., Sr.
2015-12-01
Most forest dynamic models predict the stable state of size structure as well as the total basal area and biomass in mature forest, the variation of forest stands are mainly driven by environmental factors after the equilibrium has been reached. However, although the predicted power-law size-frequency distribution does exist in analysis of many forest inventory data sets, the estimated distribution exponents are always shifting between -2 and -4, and has a positive correlation with the mean value of DBH. This regular pattern can not be explained by the effects of stochastic disturbances on forest stands. Here, we adopted the partial differential equation (PDE) approach to deduce the systematic behavior of an ideal forest, by solving the diffusion equation under the restricted condition of invariable resource occupation, a periodic solution was gotten to meet the variable performance of forest size structure while the former models with stable performance were just a special case of the periodic solution when the fluctuation frequency equals zero. In our results, the number of individuals in each size class was the function of individual growth rate(G), mortality(M), size(D) and time(T), by borrowing the conclusion of allometric theory on these parameters, the results perfectly reflected the observed "exponent-mean DBH" relationship and also gave a logically complete description to the time varying form of forest size-frequency distribution. Our model implies that the total biomass of a forest can never reach a stable equilibrium state even in the absence of disturbances and climate regime shift, we propose the idea of intrinsic fluctuation property of forest and hope to provide a new perspective on forest dynamics and carbon cycle research.
Liang, Jie; Qian, Hong
2010-01-01
Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.
Directory of Open Access Journals (Sweden)
A. A. Shevtsov
2015-01-01
Full Text Available Spray drying of solutions and suspensions is among the most common methods of producing a wide range of powdered products in chemical, food and pharmaceutical industries. For the drying of heat-sensitive materials, which is fully applicable to the distillery stillage filtrate continuous-flow type of contact of drying agent and the solution droplets is examined. Two-phase simulation method of computational hydrodynamics in a stationary state for studying the process of drying of the distillery stillage filtrate in the pilot spray dryer under the following assumptions was used. The components form an ideal mixture, the properties of which are calculated directly from the properties of the components and their proportions. The droplets were presented in spherical form. The density and specific heat of the solution and the coefficient of vapors diffusion in the gas phase remained unchanged. To solve the heat exchange equations between the drying agent and the drops by the finite volume method the software package ANSYS CFX was used. The bind between the two phases was established by Navier-Stokes equations. The continuous phase (droplets of the distillery stillage filtrate was described by the k-ε turbulence model. The results obtained showed that the interaction of "drop-wall" causes a significant change of velocity, temperature and humidity both of a drying agent and the product particles. The behavior of the particles by spraying, collision with walls and deposition of the finished product allowed to determine the dependence of physical parameters of the drying process, of the geometric dimensions of the dryer. Comparison of simulation results with experimental data showed satisfactory convergence of the results: for the temperature of the powder 10% its humidity of 12% and temperature of the spent drying agent at the outlet from the drier of 13%. The possibility of using the model in the spray dryers designing, and control of the drying process
Koda, Shin-ichi
2015-12-28
We formulate various semiclassical propagators for the Wigner phase space representation from a unified point of view. As is shown in several studies, the Moyal equation, which is an equation of motion for the Wigner distribution function, can be regarded as the Schrödinger equation of an extended Hamiltonian system where its "position" and "momentum" correspond to the middle point of two points of the original phase space and the difference between them, respectively. Then we show that various phase-space semiclassical propagators can be formulated just by applying existing semiclassical propagators to the extended system. As a result, a phase space version of the Van Vleck propagator, the initial-value Van Vleck propagator, the Herman-Kluk propagator, and the thawed Gaussian approximation are obtained. In addition, we numerically compare the initial-value phase-space Van Vleck propagator, the phase-space Herman-Kluk propagator, and the classical mechanical propagation as approximation methods for the time propagation of the Wigner distribution function in terms of both accuracy and convergence speed. As a result, we find that the convergence speed of the Van Vleck propagator is far slower than others as is the case of the Hilbert space, and the Herman-Kluk propagator keeps its accuracy for a long period compared with the classical mechanical propagation while the convergence speed of the latter is faster than the former.
Raychaudhuri, Debasree
2013-12-01
There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following question. Who succeeds at making the leap and can we describe the attributes that set them apart from the ones that do not? In this article, we offer a framework to categorize students as learners based on their individual approaches towards learning concepts in differential equations and related concepts - as demonstrated by their efforts to resolve a conflict, conserve and rebuild their cognitive structures.
Steady-state equation of water vapor sorption for CaCl2-based chemical sorbents and its application
Zhang, Haiquan; Yuan, Yanping; Sun, Qingrong; Cao, Xiaoling; Sun, Liangliang
2016-09-01
Green CaCl2-based chemical sorbent has been widely used in sorption refrigeration, air purification and air desiccation. Methods to improve the sorption rate have been extensively investigated, but the corresponding theoretical formulations have not been reported. In this paper, a sorption system of solid-liquid coexistence is established based on the hypothesis of steady-state sorption. The combination of theoretical analysis and experimental results indicates that the system can be described by steady-state sorption process. The steady-state sorption equation, μ = (η - γT) , was obtained in consideration of humidity, temperature and the surface area. Based on engineering applications and this equation, two methods including an increase of specific surface area and adjustment of the critical relative humidity (γ) for chemical sorbents, have been proposed to increase the sorption rate. The results indicate that the CaCl2/CNTs composite with a large specific surface area can be obtained by coating CaCl2 powder on the surface of carbon nanotubes (CNTs). The composite reached sorption equilibrium within only 4 h, and the sorption capacity was improved by 75% compared with pure CaCl2 powder. Furthermore, the addition of NaCl powder to saturated CaCl2 solution could significantly lower the solution’s γ. The sorption rate was improved by 30% under the same environment.
Steady-state equation of water vapor sorption for CaCl2-based chemical sorbents and its application
Zhang, Haiquan; Yuan, Yanping; Sun, Qingrong; Cao, Xiaoling; Sun, Liangliang
2016-01-01
Green CaCl2-based chemical sorbent has been widely used in sorption refrigeration, air purification and air desiccation. Methods to improve the sorption rate have been extensively investigated, but the corresponding theoretical formulations have not been reported. In this paper, a sorption system of solid-liquid coexistence is established based on the hypothesis of steady-state sorption. The combination of theoretical analysis and experimental results indicates that the system can be described by steady-state sorption process. The steady-state sorption equation, μ = (η − γT) , was obtained in consideration of humidity, temperature and the surface area. Based on engineering applications and this equation, two methods including an increase of specific surface area and adjustment of the critical relative humidity (γ) for chemical sorbents, have been proposed to increase the sorption rate. The results indicate that the CaCl2/CNTs composite with a large specific surface area can be obtained by coating CaCl2 powder on the surface of carbon nanotubes (CNTs). The composite reached sorption equilibrium within only 4 h, and the sorption capacity was improved by 75% compared with pure CaCl2 powder. Furthermore, the addition of NaCl powder to saturated CaCl2 solution could significantly lower the solution’s γ. The sorption rate was improved by 30% under the same environment. PMID:27682811
Nonlinear Second-Order Partial Differential Equation-Based Image Smoothing Technique
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Tudor Barbu
2016-09-01
Full Text Available A second-order nonlinear parabolic PDE-based restoration model is provided in this article. The proposed anisotropic diffusion-based denoising approach is based on some robust versions of the edge-stopping function and of the conductance parameter. Two stable and consistent approximation schemes are then developed for this differential model. Our PDE-based filtering technique achieves an efficient noise removal while preserving the edges and other image features. It outperforms both the conventional filters and also many PDE-based denoising approaches, as it results from the successful experiments and method comparison applied.
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
Directory of Open Access Journals (Sweden)
Norman W.H. Mason
2014-02-01
Full Text Available Many studies have quantified uncertainty in forest carbon (C storage estimation, but there is little work examining the degree of uncertainty in shrubland C storage estimates. We used field data to simulate uncertainty in carbon storage estimates from three error sources: (1 allometric biomass equations; (2 measurement errors of shrubs harvested for the allometry; and (3 measurement errors of shrubs in survey plots. We also assessed uncertainty for all possible combinations of these error sources. Allometric uncertainty had the greatest independent effect on C storage estimates for individual plots. The largest error arose when all three error sources were included in simulations (where the 95% confidence interval spanned a range equivalent to 40% of mean C storage. Mean C sequestration (1.73 Mg C ha–1 year–1 exceeded the margin of error produced by the simulated sources of uncertainty. This demonstrates that, even when the major sources of uncertainty were accounted for, we were able to detect relatively modest gains in shrubland C storage.
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S. Mattedi
2000-12-01
Full Text Available A modified form of the Hicks and Young algorithm was used with the Mattedi-Tavares-Castier lattice equation of state (MTC lattice EOS to calculate critical points of binary mixtures that exhibit several types of critical behavior. Several qualitative aspects of the critical curves, such as maxima and minima in critical pressure, and minima in critical temperature, could be predicted using the MTC lattice EOS. These results were in agreement with experimental information available in the literature, illustrating the flexibility of the functional form of the MTC lattice EOS. We observed however that the MTC lattice EOS failed to predict maxima in pressure for two of the studied systems: ethane + ethanol and methane + n-hexane. We also observed that the agreement between the calculated and experimental critical properties was at most semi-quantitative in some examples. Despite these limitations, in many ways similar to those of other EOS in common use when applied to critical point calculations, we can conclude that the MTC lattice EOS has the ability to predict several types of critical curves of complex shape.
Tang, Min; Wang, Yihong
2017-02-01
In magnetized plasma, the magnetic field confines the particles around the field lines. The anisotropy intensity in the viscosity and heat conduction may reach the order of 1012. When the boundary conditions are periodic or Neumann, the strong diffusion leads to an ill-posed limiting problem. To remove the ill-conditionedness in the highly anisotropic diffusion equations, we introduce a simple but very efficient asymptotic preserving reformulation in this paper. The key idea is that, instead of discretizing the Neumann boundary conditions locally, we replace one of the Neumann boundary condition by the integration of the original problem along the field line, the singular 1 / ɛ terms can be replaced by O (1) terms after the integration, which yields a well-posed problem. Small modifications to the original code are required and no change of coordinates nor mesh adaptation are needed. Uniform convergence with respect to the anisotropy strength 1 / ɛ can be observed numerically and the condition number does not scale with the anisotropy.
A Fourier transform method for powder diffraction based on the Debye scattering equation.
Thomas, Noel William
2011-11-01
A fast Fourier transform algorithm is introduced into the method recently defined for calculating powder diffraction patterns by means of the Debye scattering equation (DSE) [Thomas (2010). Acta Cryst. A66, 64-77]. For this purpose, conventionally used histograms of interatomic distances are replaced by compound transmittance functions. These may be Fourier transformed to partial diffraction patterns, which sum to give the complete diffraction pattern. They also lead to an alternative analytical expression for the DSE sum, which reveals its convergence behaviour. A means of embedding the DSE approach within the reciprocal-lattice-structure-factor method is indicated, with interpolation methods for deriving the peak profiles of nanocrystalline materials outlined. Efficient calculation of transmittance functions for larger crystallites requires the Patterson group symmetry of the crystals to be taken into account, as shown for α- and β-quartz. The capability of the transmittance functions to accommodate stacking disorder is demonstrated by reference to kaolinite, with a fully analytical treatment of disorder described. Areas of future work brought about by these developments are discussed, specifically the handling of anisotropic atomic displacement parameters, inverse Fourier transformation and the incorporation of instrumental (diffractometer) parameters.
Chen, G; de Figueiredo, R P
1993-01-01
The unified approach to optimal image interpolation problems presented provides a constructive procedure for finding explicit and closed-form optimal solutions to image interpolation problems when the type of interpolation can be either spatial or temporal-spatial. The unknown image is reconstructed from a finite set of sampled data in such a way that a mean-square error is minimized by first expressing the solution in terms of the reproducing kernel of a related Hilbert space, and then constructing this kernel using the fundamental solution of an induced linear partial differential equation, or the Green's function of the corresponding self-adjoint operator. It is proved that in most cases, closed-form fundamental solutions (or Green's functions) for the corresponding linear partial differential operators can be found in the general image reconstruction problem described by a first- or second-order linear partial differential operator. An efficient method for obtaining the corresponding closed-form fundamental solutions (or Green's functions) of the operators is presented. A computer simulation demonstrates the reconstruction procedure.
Scour depth estimation using an equation based on wind tunnel experiments
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Tsutsui Takayuki
2016-01-01
Full Text Available Scour is the result of degradation and aggradation by wind or moving fluid in the front and back of a pole standing in sand, respectively, and is often observed at the bottom of bridge piers in rivers. In this study, we propose a method of estimating the scour depth around a cylindrical structure standing in sand. The relationships among the depth of the scour, the aspect ratio of the structure (= height/diameter, the fluid velocity, and the sand properties (particle size and density were determined experimentally using a wind tunnel. The experiments were carried out under clear-water scour conditions. In the experiments, the aspect ratio of the cylindrical structure, the fluid velocity, and the sand particle size were varied systematically. The diameters of the structure were 20, 40, and 60 mm, and the aspect ratio was varied from 0.25 to 3.0. Sand particles of four sizes (200, 275, 475, and 600 μm were used in the experiment, and the velocity was varied from 4 to 11 m/s. The depth and radius of the scour were measured. As a result, we have developed an equation for estimating the scour depth that uses the aspect ratio, fluid velocity, and sand particle size as parameters.
Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation
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Michael S. Hughes
2015-05-01
Full Text Available Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information”, as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined as the mean variation (i.e., observed change divided by mean variance (i.e., noise. Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an “optimal” reference for the joint entropy emerges, which also has been validated in several studies.
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes.
Circular economy development phase research based on the IPAT equation: The case Shaanxi
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Fang Ying
2015-04-01
Full Text Available In recent years, the worsening of the quality of the air has urged more people to attach great importance to circular economy. Shaanxi, abundant in natural resources, maintained the GDP growth rate of 14.9% during the period of the twelfth five-year plan. However, the fast economic growth under the extensive traditional economic growth mode renders Shaanxi inadequate in resources supply and noticeably worse in ecological environment issues. With the method of the IPAT equation, this paper quantitatively analyzes the developmental stage and the developmental level of the circular economy of Shaanxi to cover the shortage of the previous studies having only been focused on the policy study and the practice mode. The result shows that Shaanxi is in the intermediate stage of circular economy and the advanced stage has an apparent advantage over the intermediate one by comparing their energy consumption and solid pollutant discharge. The development experience of Shaanxi, a typical province of China, has guidance and reference significance to China and other developing countries.
Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I
2016-04-01
Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Equation of teachers primary school course computer with learning method based on imaging
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Елена Сергеевна Пучкова
2011-03-01
Full Text Available The paper considers the possibility of training future teachers with the rate of computer methods of teaching through the creation of visual imagery and operate them, еxamples of practice-oriented assignments, formative professional quality based on explicit and implicit use of a visual image, which decision is based on the cognitive function of visibility.
A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching
Katterbauer, Klemens
2014-12-10
The oil and gas industry has been revolutionized within the last decade, with horizontal drilling and hydraulic fracturing enabling the extraction of huge amounts of shale gas in areas previously considered impossible and the recovering of hydrocarbons in harsh environments like the arctic or in previously unimaginable depths like the off-shore exploration in the South China sea and Gulf of Mexico. With the development of 4D seismic, engineers and scientists have been enabled to map the evolution of fluid fronts within the reservoir and determine the displacement caused by the injected fluids. This in turn has led to enhanced production strategies, cost reduction and increased profits. Conventional approaches to incorporate seismic data into the history matching process have been to invert these data for constraints that are subsequently employed in the history matching process. This approach makes the incorporation computationally expensive and requires a lot of manual processing for obtaining the correct interpretation due to the potential artifacts that are generated by the generally ill-conditioned inversion problems. I have presented here a novel approach via including the time-lapse cross-well seismic survey data directly into the history matching process. The generated time-lapse seismic data are obtained from the full wave 3D viscoelastic acoustic wave equation. Furthermore an extensive analysis has been performed showing the robustness of the method and enhanced forecastability of the critical reservoir parameters, reducing uncertainties and exhibiting the benefits of a full wave 3D seismic approach. Finally, the improved performance has been statistically confirmed. The improvements illustrate the significant improvements in forecasting that are obtained via readily available seismic data without the need for inversion. This further optimizes oil production in addition to increasing return-on-investment on oil & gas field development projects, especially
Institute of Scientific and Technical Information of China (English)
LANG Li-hui; LI Tao; ZHOU Xian-bin; B. E. KRISTENSEN; J. DANCKERT; K. B. NIELSEN
2006-01-01
By using aluminum alloys, the properties of the material in sheet hydroforming were obtained based on the identification of parameters for constitutive models by inverse modeling in which the friction coefficients were also considered in 2D and 3D simulations. With consideration of identified simulation parameters by inverse modeling, some key process parameters including tool dimensions and pre-bulging on the forming processes in sheet hydroforming were investigated and optimized. Based on the optimized parameters, the sheet hydroforming process can be analyzed more accurately to improve the robust design. It proves that the results from simulation based on the identified parameters are in good agreement with those from experiments.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Alrawashdeh, Thamer A; Alqatawnah, Sokyna M
2012-01-01
Advancement in information system leads organizations to apply e-learning system to train their employees in order to enhance its performance. In this respect, applying web based training will enable the organization to train their employees quickly, efficiently and effectively anywhere at any time. This research aims to extend Unified Theory of Acceptance and Use Technology (UTAUT) using some factors such flexibility of web based training system, system interactivity and system enjoyment, in order to explain the employees' intention to use web based training system. A total of 290 employees have participated in this study. The findings of the study revealed that performance expectancy, facilitating conditions, social influence and system flexibility have direct effect on the employees' intention to use web based training system, while effort expectancy, system enjoyment and system interactivity have indirect effect on employees' intention to use the system.
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Donald A. McLaren
2013-04-01
Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Directory of Open Access Journals (Sweden)
Mahmoud M Elnokeety
2017-01-01
In patients with early overt diabetic nephropathy, serum cystatin C showed a significantly stronger correlation than creatinine with isotopically measured GFR, and among the studied equations for GFR estimation the CKD-EPI Cr-Cyst 2012 equation performed best.
Institute of Scientific and Technical Information of China (English)
LI Lian-He; FAN Tian-You
2006-01-01
@@ The stress potential function theory for plane elasticity of icosahedral quasicrystals is developed. By introducing stress functions, huge numbers of basic equations involving elasticity of icosahedral quasicrystals are reduced to a single partial differential equation of the 12th order.
The effect of numerical techniques on differential equation based chaotic generators
Zidan, Mohammed A.
2012-07-29
In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput.
Efficient and spurious-free integral-equation-based optical waveguide mode solver.
Hochman, Amit; Leviatan, Yehuda
2007-10-29
Modal analysis of waveguides and resonators by integra-lequation formulations can be hindered by the existence of spurious solutions. In this paper, spurious solutions are shown to be eliminated by introduction of a Rayleigh-quotient based matrix singularity measure. Once the spurious solutions are eliminated, the true modes may be determined efficiently and reliably, even in the presence of degeneracy, by an adaptive search algorithm. Analysis examples that demonstrate the efficacy of the method include an elliptical dielectric waveguide, two unequal touching dielectric cylinders, a plasmonic waveguide, and a realistic micro-structured optical fiber. A freely downloadable version of an optical waveguide mode solver based on this article is available.
Institute of Scientific and Technical Information of China (English)
SONG Yan; ZHANG Meng; SONG Juan
2011-01-01
Taking spiral chute as example, a method of unfolded drawings and views about irregular spiral surface is introduced. The surface is undevelopable and too complicated to get its views or to draw unfolded drawings by manual method. In this article, a series of the boundary equations of the spiral chute are derived by the movement rule of coal flow, and the solid and views of the spiral chute are generated based on redevelopment of SolidWorks. Unfolded drawing is drawn applying triangular development principle. The views and unfolded drawings not only are produced automatically, precisely and parameterized, but also involve more technological information. So it has an important significance on the irregular spiral surface＇s developments and processing.
A Study of Inverse Problems Based on Two Kinds of Special Matrix Equations in Euclidean Space
Directory of Open Access Journals (Sweden)
Rui Huang
2014-01-01
Full Text Available Two special classes of symmetric coefficient matrices were defined based on characteristics matrix; meanwhile, the expressions of the solution to inverse problems are given and the conditions for the solvability of these problems are studied relying on researching. Finally, the optimal approximation solution of these problems is provided.
Questioning the quantity equation using an agent-based computational model
DEFF Research Database (Denmark)
Bruun, Charlotte
2000-01-01
by Stutzel (1954), argues that the functional relationship may as well be negative. Even focusing the money needed to carry out transactions, there is no immediate answer to the question of the functional relationship between trade turnover and money demand. An agent-based computational model is used...
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Ding, Y. H.; Hu, S. X.
2017-06-01
Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ˜10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ˜20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (˜15%) compared to the simulation using the SESAME 2023 EOS table.
Energy Technology Data Exchange (ETDEWEB)
Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il [Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Lomakin, V., E-mail: vlomakin@eng.ucsd.edu [Department of Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407 (United States)
2016-03-01
Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii) furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.
Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten
2016-08-01
The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.
Foucart, Francois; Brege, Wyatt; Duez, Matthew D; Kasen, Daniel; Hemberger, Daniel A; Kidder, Lawrence E; Pfeiffer, Harald P; Scheel, Mark A
2016-01-01
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about ...
Rijmen, Frank; Manalo, Jonathan R.; von Davier, Alina A.
2009-01-01
This article describes two methods for obtaining the standard errors of two commonly used population invariance measures of equating functions: the root mean square difference of the subpopulation equating functions from the overall equating function and the root expected mean square difference. The delta method relies on an analytical…
Larios, Adam; Titi, Edriss S; Wingate, Beth
2015-01-01
We report the results of a computational investigation of two recently proved blow-up criteria for the 3D incompressible Euler equations. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations. The latter are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter $\\alpha>0$. Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be sufficient criteria for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
SPECIFIC SOLUTIONS GROUNDWATER FLOW EQUATION
Syahruddin, Muhammad Hamzah
2014-01-01
Geophysic publication Groundwater flow under surface, its usually slow moving, so that in laminer flow condition can find analisys using the Darcy???s law. The combination between Darcy law and continuity equation can find differential Laplace equation as general equation groundwater flow in sub surface. Based on Differential Laplace Equation is the equation that can be used to describe hydraulic head and velocity flow distribution in porous media as groundwater. In the modeling Laplace e...
Rizzi, F.
2017-05-25
We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼ 51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.
A Simple Model for Measuring Refractive Index of a Liquid Based upon Fresnel Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Zhi-Wei; WU Zhi-Fang; WEN Ting-Dun
2007-01-01
Due to many experimental data required and a lot of calculations involved, it is very complex and cumbersome to model prism-based liquid-refractive-index-measuring methods. We develop a new method of mathematical modelling for measuring refractive index of a liquid based upon the Fresnel formula and prism internal reflection at an incident angle less than the critical angle. With this method, only two different concentrations measurements for a kind of solution can lead to the determination of computational model. Measurements are performed to examine the validity of the theoretical model. Experimental results indicate the feasibility of the theoretical model with an error of 1%. The method is also capable of measuring even smaller changes in the optical refractive index of the material on a metal surface by the surface plasma resonance sensing techniques.
VIM-based dynamic sparse grid approach to partial differential equations.
Mei, Shu-Li
2014-01-01
Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. In this method, a multilevel interpolation operator is constructed based on the sparse grids theory firstly. The operator is based on the linear combination of the basic functions and independent of them. Second, by means of the precise integration method (PIM), the VIM is developed to solve the nonlinear system of ODEs which is obtained from the discretization of the PDEs. In addition, a dynamic choice scheme on both of the inner and external grid points is proposed. It is different from the traditional interval wavelet collocation method in which the choice of both of the inner and external grid points is dynamic. The numerical experiments show that our method is better than the traditional wavelet collocation method, especially in solving the PDEs with the Nuemann boundary conditions.
Gradient-based estimation of uncertain parameters for elliptic partial differential equations
Borggaard, Jeff; van Wyk, Hans-Werner
2015-06-01
This paper discusses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We treat the parameter identification problem as a variational problem over the appropriate stochastic Sobolev spaces and show that minimizers exist and satisfy a saddle point condition. Although a lack of regularity precludes the direct use of gradient-based optimization techniques, a spectral approximation of the observation field allows us to estimate the original problem by a smooth, albeit high dimensional, deterministic optimization problem, the so-called finite noise problem, which lends itself readily to more traditional optimization approaches. We prove that the finite noise minimizers converge to the appropriate infinite dimensional ones, and devise and analyze a stochastic augmented Lagrangian method for locating these numerically. We also discuss the numerical discretization of the finite noise problem, using sparse grid hierarchical finite elements, and present three numerical examples to illustrate our method.
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
Institute of Scientific and Technical Information of China (English)
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Ignat'ev, Yu G
2015-01-01
The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based on the microscopic dynamics of a particle at presence of scalar fields. The theory is managed to be generalized naturally having strictly reviewed a series of its key positions depending on a sign of particle masses. Thereby, it is possible to remove the artificial restriction contradicting the more fundamental principle of action functional additivity. Additionally, as a condition of internal consistency of the theory, particle effective mass function is found.
Directory of Open Access Journals (Sweden)
Józef DREWNIAK
2016-06-01
Full Text Available Versatile hypotheses of fatigue damage accumulation are utilized in order to determine the fatigue life of particular mechanical elements. Such an approach to an analysis of fatigue processes is recognized as being phenomenological. In the present paper, modifications to the Paris and Foreman laws of fracture mechanics have been proposed. The goal of these modifications is an explicit formulation of crack propagation velocity as a function of crack length. Additionally, the process of crack growth was simulated according to the Palmgren-Miner and Pugno-Ciavarella-Cornetti-Carpinteri fatigue hypotheses. The results of simulation were verified based upon test stand experiments.
Institute of Scientific and Technical Information of China (English)
周文来; 密建国; 贺刚; 于燕梅; 陈健
2003-01-01
The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.
Nayak, B.; Menon, S. V. G.
2017-04-01
A generalized enthalpy-based equation of state, which includes thermal electron excitations and non-equilibrium thermal energies, is formulated for binary solid and porous mixtures. Our approach gives rise to an extra contribution to mixture volume, in addition to those corresponding to average mixture parameters. This excess term involves the difference of thermal enthalpies of the two components, which depend on their individual temperatures. We propose to use the Hugoniot of the components to compute non-equilibrium temperatures in the mixture. These are then compared with the average temperature obtained from the mixture Hugoniot, thereby giving an estimate of non-equilibrium effects. The Birch-Murnaghan model for the zero-temperature isotherm and a linear thermal model are then used for applying the method to several mixtures, including one porous case. Comparison with experimental data on the pressure-volume Hugoniot and shock speed versus particle speed shows good agreement.
Muskingum equation based downstream sediment flow simulation models for a river system
Institute of Scientific and Technical Information of China (English)
Briti Sundar Sil; Parthasarathi Choudhury
2016-01-01
Applications of sediment transport and water flow characteristics based sediment transport simulation models for a river system are presented in this study. An existing water–sediment model and a new sediment–water model are used to formulate the simulation models representing water and sediment movement in a river system. The sediment–water model parameters account for water flow characteristics embodying sediment transport properties of a section. The models are revised formulations of the multiple water inflows model describing water movement through a river system as given by the Muskingum principle. The models are applied to a river system in Mississippi River basin to estimate downstream sediment concentration, sediment discharge, and water discharge. River system and the river section parameters are estimated using a revised and the original multiple water inflows models by applying the genetic algorithm. The models estimate downstream sediment transport rates on the basis of upstream sediment/water flow rates to a system. Model performance is evaluated by using standard statistical criteria;downstream water discharge resulting from the original multiple water inflows model using the estimated river system parameters indicate that the revised models satisfactorily describe water movement through a river system. Results obtained in the study demonstrate the applicability of the sediment transport and water flow characteristics-based simulation models in predicting downstream sediment transport and water flow rates in a river system.
Tutyshkin, Nikolai D.; Lofink, Paul; Müller, Wolfgang H.; Wille, Ralf; Stahn, Oliver
2016-09-01
On the basis of the physical concepts of void formation, nucleation, and growth, generalized constitutive equations are formulated for a tensorial model of plastic damage in metals based on three invariants. The multiplicative decomposition of the metric transformation tensor and a thermodynamically consistent formulation of constitutive relations leads to a symmetric second-order damage tensor with a clear physical meaning. Its first invariant determines the damage related to plastic dilatation of the material due to growth of the voids. The second invariant of the deviatoric damage tensor is related to the change in void shape. The third invariant of the deviatoric tensor describes the impact of the stress state on damage (Lode angle), including the effect of rotating the principal axes of the stress tensor (Lode angle change). The introduction of three measures with related physical meaning allows for the description of kinetic processes of strain-induced damage with an equivalent parameter in a three-dimensional vector space, including the critical condition of ductile failure. Calculations were performed by using experimentally determined material functions for plastic dilatation and deviatoric strain at the mesoscale, as well as three-dimensional graphs for plastic damage of steel DC01. The constitutive parameter was determined from tests in tension, compression, and shear by using scanning electron microscopy, which allowed to vary the Lode angle over the full range of its values [InlineEquation not available: see fulltext.]. In order to construct the three-dimensional plastic damage curve for a range of triaxiality parameters -1 ≤ ST ≤ 1 and of Lode angles [InlineEquation not available: see fulltext.], we used our own, as well as systematized published experimental data. A comparison of calculations shows a significant effect of the third invariant (Lode angle) on equivalent damage. The measure of plastic damage, based on three invariants, can be useful
Tutyshkin, Nikolai D.; Lofink, Paul; Müller, Wolfgang H.; Wille, Ralf; Stahn, Oliver
2017-01-01
On the basis of the physical concepts of void formation, nucleation, and growth, generalized constitutive equations are formulated for a tensorial model of plastic damage in metals based on three invariants. The multiplicative decomposition of the metric transformation tensor and a thermodynamically consistent formulation of constitutive relations leads to a symmetric second-order damage tensor with a clear physical meaning. Its first invariant determines the damage related to plastic dilatation of the material due to growth of the voids. The second invariant of the deviatoric damage tensor is related to the change in void shape. The third invariant of the deviatoric tensor describes the impact of the stress state on damage (Lode angle), including the effect of rotating the principal axes of the stress tensor (Lode angle change). The introduction of three measures with related physical meaning allows for the description of kinetic processes of strain-induced damage with an equivalent parameter in a three-dimensional vector space, including the critical condition of ductile failure. Calculations were performed by using experimentally determined material functions for plastic dilatation and deviatoric strain at the mesoscale, as well as three-dimensional graphs for plastic damage of steel DC01. The constitutive parameter was determined from tests in tension, compression, and shear by using scanning electron microscopy, which allowed to vary the Lode angle over the full range of its values [InlineEquation not available: see fulltext.]. In order to construct the three-dimensional plastic damage curve for a range of triaxiality parameters -1 ≤ ST ≤ 1 and of Lode angles [InlineEquation not available: see fulltext.], we used our own, as well as systematized published experimental data. A comparison of calculations shows a significant effect of the third invariant (Lode angle) on equivalent damage. The measure of plastic damage, based on three invariants, can be useful
Aimran, Ahmad Nazim; Ahmad, Sabri; Afthanorhan, Asyraf; Awang, Zainudin
2017-05-01
Structural equation modeling (SEM) is the second generation statistical analysis technique developed for analyzing the inter-relationships among multiple variables in a model. Previous studies have shown that there seemed to be at least an implicit agreement about the factors that should drive the choice between covariance-based structural equation modeling (CB-SEM) and partial least square path modeling (PLS-PM). PLS-PM appears to be the preferred method by previous scholars because of its less stringent assumption and the need to avoid the perceived difficulties in CB-SEM. Along with this issue has been the increasing debate among researchers on the use of CB-SEM and PLS-PM in studies. The present study intends to assess the performance of CB-SEM and PLS-PM as a confirmatory study in which the findings will contribute to the body of knowledge of SEM. Maximum likelihood (ML) was chosen as the estimator for CB-SEM and was expected to be more powerful than PLS-PM. Based on the balanced experimental design, the multivariate normal data with specified population parameter and sample sizes were generated using Pro-Active Monte Carlo simulation, and the data were analyzed using AMOS for CB-SEM and SmartPLS for PLS-PM. Comparative Bias Index (CBI), construct relationship, average variance extracted (AVE), composite reliability (CR), and Fornell-Larcker criterion were used to study the consequence of each estimator. The findings conclude that CB-SEM performed notably better than PLS-PM in estimation for large sample size (100 and above), particularly in terms of estimations accuracy and consistency.
Crouseilles, Nicolas; Lemou, Mohammed
2016-01-01
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\\em in both space and time}.Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and otherhighly oscillatory waves. Our first main idea is to use the nonlinear geometric optics ansatz, which builds theoscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman-Enskog expansion, for the new model. For a scalar model, we prove that so constructed model will have certain smoothness, and consequently, for a first order approximation scheme we prove uniform error estimates independent of the (possibly small) wave length. The method is extended to systems arising from a semiclassical model for surface hopping, a non-adiabatic quantum dynamic phenomenon. Numerous numerical examples demonstrate that the method has the desired properties...
Contact Angle Adjustment in Equation of States Based Pseudo-Potential Model
Hu, Anjie; Uddin, Rizwan
2015-01-01
Single component pseudo-potential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many research, it has been claimed that this model can be stable for density ratios larger than 1000, however, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in present work show that, by applying the contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with the new...
Shi, Yifei
2015-10-26
Graphene is a monolayer of carbon atoms structured in the form of a honeycomb lattice. Recent experimental studies have revealed that it can support surface plasmons at Terahertz frequencies thanks to its dispersive conductivity. Additionally, characteristics of these plasmons can be dynamically adjusted via electrostatic gating of the graphene sheet (K. S. Novoselov, et al., Science, 306, 666–669, 2004). These properties suggest that graphene can be a building block for novel electromagnetic and photonic devices for applications in the fields of photovoltaics, bio-chemical sensing, all-optical computing, and flexible electronics. Simulation of electromagnetic interactions on graphene-based devices is not an easy task. The thickness of the graphene sheet is orders of magnitude smaller than any other geometrical dimension of the device. Consequently, discretization of such a device leads to significantly large number of unknowns and/or ill-conditioned matrix systems.
Contact angle adjustment in equation-of-state-based pseudopotential model.
Hu, Anjie; Li, Longjian; Uddin, Rizwan; Liu, Dong
2016-05-01
The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.
A Radiation Chemistry Code Based on the Green's Function of the Diffusion Equation
Plante, Ianik; Wu, Honglu
2014-01-01
Stochastic radiation track structure codes are of great interest for space radiation studies and hadron therapy in medicine. These codes are used for a many purposes, notably for microdosimetry and DNA damage studies. In the last two decades, they were also used with the Independent Reaction Times (IRT) method in the simulation of chemical reactions, to calculate the yield of various radiolytic species produced during the radiolysis of water and in chemical dosimeters. Recently, we have developed a Green's function based code to simulate reversible chemical reactions with an intermediate state, which yielded results in excellent agreement with those obtained by using the IRT method. This code was also used to simulate and the interaction of particles with membrane receptors. We are in the process of including this program for use with the Monte-Carlo track structure code Relativistic Ion Tracks (RITRACKS). This recent addition should greatly expand the capabilities of RITRACKS, notably to simulate DNA damage by both the direct and indirect effect.
Patched based methods for adaptive mesh refinement solutions of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Saltzman, J.
1997-09-02
This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.
Fuel rod model based on Non-Fourier heat conduction equation
Energy Technology Data Exchange (ETDEWEB)
Espinosa-Paredes, G. [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico DF., CP 09340 (Mexico)], E-mail: gepe@xanum.uam.mx; Espinosa-Martinez, E-G. [Retorno Quebec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor. (Mexico)
2009-05-15
In this paper we explore the applicability of a fuel rod mathematical model based on Non-Fourier transient heat conduction as constitutive law for the Light Water Reactors transient analysis (LWRs). In the classical theory of diffusion, Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The motivation for this research was to eliminate the paradox of an infinite thermal wave speed. The time-dependent heat sources were considered in the fuel rod heat transfer model. The close of the Main Steam Isolated Valves (MSIV) transient in a Boiling Water Reactor (BWR) was analyzed by different relaxation times. The results show that for long-times the heat fluxes on the clad surface under Non-Fourier approach can be important, while for short-times and from the engineering point of view the changes are very small. Some results from transient calculations are examined.
Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.
2017-02-01
A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Directory of Open Access Journals (Sweden)
Cagatan Taskin
2010-04-01
Full Text Available In today’s markets, many products are perceived to be similar because of information and commuication technologies that are developing fastly. In spite of this, enterprises should make their products different and unique to compete in a sustainable manner. Besides, marketing strategies based solely on concepts such as price, quality, product differentiation and appropriate payment options, may not always provide sustainable competitive advantages under today’s severe competition conditions. Consumer based brand equity, which can be also defined as the meaning of a brand to the consumer, is one of the basic ways of developing sustainable and efficient marketing srategies. The aim of this research is to explore the relationships between consumer based brand equity of a durable consumer good brand, namely Bosch and its dimensions by means of structural equation modeling and to show how to use the model for developing efficient marketing strategies with strategy propositions. The research is conducted in Bursa, so the results of this study can not be generalized to Turkey or any other cities.
Mathias, Simon A.; Skaggs, Todd H.; Quinn, Simon A.; Egan, Sorcha N. C.; Finch, Lucy E.; Oldham, Corinne D.
2015-01-01
Given a time series of potential evapotranspiration and rainfall data, there are at least two approaches for estimating vertical percolation rates. One approach involves solving Richards' equation (RE) with a plant uptake model. An alternative approach involves applying a simple soil moisture accounting procedure (SMAP) based on a set of conceptual stores and conditional statements. It is often desirable to parameterize distributed vertical percolation models using regional soil texture maps. This can be achieved using pedotransfer functions when applying RE. However, robust soil texture based parameterizations for more simple SMAPs have not previously been available. This article presents a new SMAP designed to emulate the response of a one-dimensional homogenous RE model. Model parameters for 231 different soil textures are obtained by calibrating the SMAP model to 20 year time series from equivalent RE model simulations. The results are then validated by comparing to an additional 13 years of simulated RE model data. The resulting work provides a new simple two parameter (% sand and % silt) SMAP, which provides consistent vertical percolation data as compared to RE based models. Results from the 231 numerical simulations are also found to be qualitatively consistent with intuitive ideas concerning soil texture and soil moisture dynamics. Vertical percolation rates are found to be highest in sandy soils. Sandy soils are found to provide less water for evapotranspiration. Surface runoff is found to be more important in soils with high clay content.
Toporkov, Jakov V.
A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects of numerical simulations crucial to obtaining correct results in the demanding low grazing angle regime. It was found that when the MFIE propagator matrix is used with zeros on its diagonal (as has often been the practice) the results appear to show an unexpected sensitivity to the sampling interval. This sensitivity is especially pronounced in the case of horizontal polarization and at low grazing angles. We show---both numerically and analytically---that the problem lies not with the particular numerical technique used (MOMI) but rather with how the MFIE is discretized. It is demonstrated that the inclusion of so-called "curvature terms" (terms that arise from a correct discretization procedure and are proportional to the second surface derivative) in the diagonal of the propagator matrix eliminates the problem completely. A criterion for the choice of the sampling interval used in discretizing the MFIE based on both electromagnetic wavelength and the surface spectral cutoff is established. The influence of the surface spectral cutoff value on the results of scattering simulations is investigated and a recommendation for the choice of this spectral cutoff for numerical simulation purposes is developed. Also studied is the applicability of the tapered incident field at low grazing incidence angles. It is found that when a Gaussian-like taper with fixed beam waist is used there is a characteristic pattern (anomalous jump) in the calculated average backscattered cross section at
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Pierre-Henri Chavanis
2013-01-01
Full Text Available We consider a cosmological model based on a quadratic equation of state (where is the Planck density and is the cosmological density “unifying” vacuum energy, radiation, and dark energy. For , it reduces to leading to a phase of early accelerated expansion (early inflation with a constant density equal to the Planck density g/m3 (vacuum energy. For , we recover the equation of state of radiation . For , we get leading to a phase of late accelerated expansion (late inflation with a constant density equal to the cosmological density g/m3 (dark energy. The temperature is determined by a generalized Stefan-Boltzmann law. We show a nice “symmetry” between the early universe (vacuum energy + radiation and the late universe (radiation + dark energy. In our model, they are described by two polytropic equations of state with index and respectively. Furthermore, the Planck density in the early universe plays a role similar to that of the cosmological density in the late universe. They represent fundamental upper and lower density bounds differing by 122 orders of magnitude. We add the contribution of baryonic matter and dark matter considered as independent species and obtain a simple cosmological model describing the whole evolution of the universe. We study the evolution of the scale factor, density, and temperature. This model gives the same results as the standard CDM model for , where is the Planck time and completes it by incorporating the phase of early inflation in a natural manner. Furthermore, this model does not present any singularity at and exists eternally in the past (although it may be incorrect to extrapolate the solution to the infinite past. Our study suggests that vacuum energy, radiation, and dark energy may be the manifestation of a unique form of “generalized radiation.” By contrast, the baryonic and dark matter components of the universe are treated as different species. This is at variance with usual models
Implementation of duffing system based on Euler equations%Duffing系统的欧拉实现方法研究
Institute of Scientific and Technical Information of China (English)
芮国胜; 史特; 张洋
2012-01-01
在研究Duffing系统的基础上,为了利用Duffing系统进行弱信号检测,必须实现一种可靠的Duffing系统模型.对3种基于欧拉方程的模型实现方式进行了对比,通过分析欧拉方程的几何意义,并结合DSP Builder的特点,提出了一种易于工程实现的改进欧拉形式.通过对四种算法进行仿真实验得出,运用不同的状态模型建立Duffing系统会改变振子相变的临界策动力幅值,但不会对系统固有存在的状态产生影响.%In order to use the Duffing system to detect weak signal; a reliable Duffing system model must be achieved. Three realization modes of model based on Euler equations are compared. By analyzing the geometric meaning of the Euler equations and combining the characteristics of DSP Builder, an improved Euler form which is easy to realize in engineering is proposed on the basis of the related research on Duffing system. The simulation experiments for four algorithms indicate that the establishment of Buffing system with different state models can change the critical driving force amplitude of the oscillator phase transition, but can not affect the inherent status of the system.
Rumyantseva, O. D.; Shurup, A. S.
2017-01-01
The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.
Hanasoge, S M; Gizon, L
2010-01-01
Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.
Hu, Kainan; Geng, Shaojuan
2016-01-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e. the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
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Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Luo, Songting; Payne, Nicholas
2017-07-01
We present an effective asymptotic method for approximating the density of particles for kinetic equations with a Bhatnagar-Gross-Krook (BGK) relaxation operator in the large scale hyperbolic limit. The density of particles is transformed via a Hopf-Cole transformation, where the phase function is expanded as a power series with respect to the Knudsen number. The expansion terms can be determined by solving a sequence of equations. In particular, it has been proved in [3] that the leading order term is the viscosity solution of an effective Hamilton-Jacobi equation, and we show that the higher order terms can be formally determined by solving a sequence of transport equations. Both the effective Hamilton-Jacobi equation and the transport equations are independent of the Knudsen number, and are formulated in the physical space, where the effective Hamiltonian is obtained as the solution of a nonlinear equation that is given as an integral in the velocity variable, and the coefficients of the transport equations are given as integrals in the velocity variable. With appropriate Gauss quadrature rules for evaluating these integrals effectively, the effective Hamilton-Jacobi equation and the transport equations can be solved efficiently to obtain the expansion terms for approximating the density function. In this work, the zeroth, first and second order terms in the expansion are used to obtain second order accuracy with respect to the Knudsen number. The proposed method balances efficiency and accuracy, and has the potential to deal with kinetic equations with more general BGK models. Numerical experiments verify the effectiveness of the proposed method.
Qiao, Yao-Bin; Qi, Hong; Zhao, Fang-Zhou; Ruan, Li-Ming
2016-12-01
Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation (FD-RTE) to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method (FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient (MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure. Project supported by the National Natural Science Foundation of China (Grant No. 51476043), the Major National Scientific Instruments and Equipment Development Special Foundation of China (Grant No. 51327803), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51121004).
Galka, Andreas; Ozaki, Tohru; Muhle, Hiltrud; Stephani, Ulrich; Siniatchkin, Michael
2008-06-01
We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to the electric potentials at the surface of the head, the model can be put into relation with recordings of the electroencephalogram (EEG). Through this step it becomes possible to employ EEG recordings for the purpose of estimating the primary current density vector field, i.e. finding a solution of the inverse problem of EEG generation. As a technique for inferring the unobserved high-dimensional primary current density field from EEG data of much lower dimension, a linear state space modelling approach is suggested, based on a generalisation of Kalman filtering, in combination with maximum-likelihood parameter estimation. The resulting algorithm for estimating dynamical solutions of the EEG inverse problem is applied to the task of localising the source of an epileptic spike from a clinical EEG data set; for comparison, we apply to the same task also a non-dynamical standard algorithm.
Henriques, David; Rocha, Miguel; Saez-Rodriguez, Julio; Banga, Julio R
2015-09-15
Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters. In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two-component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cells. Supplementary data are available at Bioinformatics online. julio@iim.csic.es or saezrodriguez@ebi.ac.uk. © The Author 2015. Published by Oxford University Press.
Energy Technology Data Exchange (ETDEWEB)
Kushwah, S.S. [Department of Physics, Rishi Galav College, Morena, 476001 MP (India); Shrivastava, H.C. [Department of Physics, S.M.S. Government Model Science P.G. College, Gwalior, 474001 MP (India)]. E-mail: hcs2050@yahoo.com; Singh, K.S. [Department of Physics, R.B.S. College, Agra, UP (India)
2007-01-15
We have generalized the pressure-volume (P-V) relationships using simple polynomial and logarithmic expansions so as to make them consistent with the infinite pressure extrapolation according to the model of Stacey. The formulations are used to evaluate P-V relationships and pressure derivatives of bulk modulus upto third order (K', K'' and K''') for the earth core material taking input parameters based on the seismological data. The results based on the equations of state (EOS) generalized in the present study are found to yield good agreement with the Stacey EOS. The generalized logarithmic EOS due to Poirier and Tarantola deviates substantially from the seismic values for P, K and K'. The generalized Rydberg EOS gives almost identical results with the Birch-Murnaghan third-order EOS. Both of them yield deviations from the seismic data, which are in opposite direction as compared to those found from the generalized Poirier-Tarantola logarithmic EOS.
Institute of Scientific and Technical Information of China (English)
LIANG Hui; ZHAO Wei; DAI Dejun; ZHANG Jun
2014-01-01
Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography. It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.
Directory of Open Access Journals (Sweden)
Abdollah BORHANIFAR
2013-01-01
Full Text Available In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.
New application to Riccati equation
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Institute of Scientific and Technical Information of China (English)
Tarquinio; Mateus; Magalhães
2016-01-01
Background:Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors (BEFs). Yet, national and regional biomass estimates are general y calculated based on BEFs, especial y when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. Methods:The data were col ected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were fel ed outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates;those estimates were then compared in terms of the fol owing sources of error: plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. Results:The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3%larger than the BEF-based ones. For the whole tree biomass stock, the percentage of the total error attributed to first phase (random plot selection and variability) was 90 and 88%for regression-and BEF-based estimates, respectively, being the remaining attributed to biomass models (regression and BEF models, respectively). The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were−2.7 and 5.4%, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models (than for regression models), except for stem and stem wood components. Conclusions:The regression equation based biomass stocks were found to be slightly larger
Directory of Open Access Journals (Sweden)
Tarquinio Mateus Magalhães
2015-10-01
Full Text Available Background Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors (BEFs. Yet, national and regional biomass estimates are generally calculated based on BEFs, especially when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. Methods The data were collected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were felled outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates; those estimates were then compared in terms of the following sources of error: plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. Results The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3 % larger than the BEF-based ones. For the whole tree biomass stock, the percentage of the total error attributed to first phase (random plot selection and variability was 90 and 88 % for regression- and BEF-based estimates, respectively, being the remaining attributed to biomass models (regression and BEF models, respectively. The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were −2.7 and 5.4 %, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models (than for regression models, except for stem and stem wood components. Conclusions The regression equation based biomass stocks were found to
Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming
2016-10-17
Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.
DEFF Research Database (Denmark)
Iolov, Alexandre; Ditlevsen, Susanne; Longtin, Andrë
2014-01-01
Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose two methods to estimate input parameters using interspike interval data only. One is based...... on numerical solutions of the Fokker–Planck equation, and the other is based on an integral equation, which is fulfilled by the interspike interval probability density. This generalizes previous methods tailored to stationary data to the case of time-dependent input. The main contribution is a binning method...
Nishiyama, Seiya
2014-01-01
In this paper we present the induced representation of SO(2N) canonical transformation group and introduce SO(2N)/U(N) coset variables. We give a derivation of the time dependent Hartree-Bogoliubov (TDHB) equation on the Kaehler coset space G/H=SO(2N)/U(N) from the Euler-Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of TDRHB equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO(2N) matrix based on the nonlinear Moebius transformation together with the geodesic flow on the manifold.
Nishiyama, Seiya; da Providência, João
2015-02-01
In this paper we present the induced representation of SO(2N) canonical transformation group and introduce (SO(2N))/(U(N)) coset variables. We give a derivation of the time-dependent Hartree-Bogoliubov (TDHB) equation on the Kähler coset space (G)/(H) = (SO(2N))/(U(N)) from the Euler-Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of time-dependent Riccati-Hartree-Bogoliubov equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO(2N) matrix based on the nonlinear Möbius transformation together with the geodesic flow on the manifold.
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
Nguyen-Trong, Khanh; Nguyen-Thi-Ngoc, Anh; Nguyen-Ngoc, Doanh; Dinh-Thi-Hai, Van
2017-01-01
The amount of municipal solid waste (MSW) has been increasing steadily over the last decade by reason of population rising and waste generation rate. In most of the urban areas, disposal sites are usually located outside of the urban areas due to the scarcity of land. There is no fixed route map for transportation. The current waste collection and transportation are already overloaded arising from the lack of facilities and insufficient resources. In this paper, a model for optimizing municipal solid waste collection will be proposed. Firstly, the optimized plan is developed in a static context, and then it is integrated into a dynamic context using multi-agent based modelling and simulation. A case study related to Hagiang City, Vietnam, is presented to show the efficiency of the proposed model. From the optimized results, it has been found that the cost of the MSW collection is reduced by 11.3%. Copyright © 2016 Elsevier Ltd. All rights reserved.
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
Directory of Open Access Journals (Sweden)
Amir R. Ali
2017-01-01
Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.
Feki, Saber
2013-07-01
An explicit marching-on-in-time (MOT)-based time-domain volume integral equation (TDVIE) solver has recently been developed for characterizing transient electromagnetic wave interactions on arbitrarily shaped dielectric bodies (A. Al-Jarro et al., IEEE Trans. Antennas Propag., vol. 60, no. 11, 2012). The solver discretizes the spatio-temporal convolutions of the source fields with the background medium\\'s Green function using nodal discretization in space and linear interpolation in time. The Green tensor, which involves second order spatial and temporal derivatives, is computed using finite differences on the temporal and spatial grid. A predictor-corrector algorithm is used to maintain the stability of the MOT scheme. The simplicity of the discretization scheme permits the computation of the discretized spatio-temporal convolutions on the fly during time marching; no \\'interaction\\' matrices are pre-computed or stored resulting in a memory efficient scheme. As a result, most often the applicability of this solver to the characterization of wave interactions on electrically large structures is limited by the computation time but not the memory. © 2013 IEEE.
Kim, Miji; Ryu, Eunjung
2015-12-01
The purpose of this study was to construct and test a structural equation model of quality of work life for clinical nurses based on Peterson and Wilson's Culture-Work-Health model (CWHM). A structured questionnaire was completed by 523 clinical nurses to analyze the relationships between concepts of CWHM-organizational culture, social support, employee health, organizational health, and quality of work life. Among these conceptual variables of CWHM, employee health was measured by perceived health status, and organizational health was measured by presenteeism. SPSS21.0 and AMOS 21.0 programs were used to analyze the efficiency of the hypothesized model and calculate the direct and indirect effects of factors affecting quality of work life among clinical nurses. The goodness-of-fit statistics of the final modified hypothetical model are as follows: χ²=586.03, χ²/df=4.19, GFI=.89, AGFI=.85, CFI=.91, TLI=.90, NFI=.89, and RMSEA=.08. The results revealed that organizational culture, social support, organizational health, and employee health accounted for 69% of clinical nurses' quality of work life. The major findings of this study indicate that it is essential to create a positive organizational culture and provide adequate organizational support to maintain a balance between the health of clinical nurses and the organization. Further repeated and expanded studies are needed to explore the multidimensional aspects of clinical nurses' quality of work life in Korea, including various factors, such as work environment, work stress, and burnout.
LSER-based modeling vapor pressures of (solvent+salt) systems by application of Xiang-Tan equation
Institute of Scientific and Technical Information of China (English)
Aynur Senol
2015-01-01
The study deals with modeling the vapor pressures of (solvent+salt) systems depending on the linear solvation energy relation (LSER) principles. The LSER-based vapor pressure model clarifies the simultaneous impact of the vapor pressure of a pure solvent estimated by the Xiang-Tan equation, the solubility and solvatochromic parameters of the solvent and the physical properties of the ionic salt. It has been performed independently two structural forms of the generalized solvation model, i.e. the unified solvation model with the integrated properties (USMIP) containing nine physical descriptors and the reduced property-basis solvation model. The vapor pressure data of fourteen (solvent+salt) systems have been processed to analyze statistical y the reliabil-ity of existing models in terms of a log-ratio objective function. The proposed vapor pressure approaches reproduce the observed performance relatively accurately, yielding the overall design factors of 1.0643 and 1.0702 for the integrated property-basis and reduced property-basis solvation models.
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyun Keol [Departement des Sciences Appliquees, Universite du Quebec a Chicoutimi, Chicoutimi, Que., G7H 2B1 (Canada); Charette, Andre [Departement des Sciences Appliquees, Universite du Quebec a Chicoutimi, Chicoutimi, Que., G7H 2B1 (Canada)]. E-mail: andre_charette@uqac.ca
2007-03-15
The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved.
Latcharote, P.; Leelawat, N.; Suppasri, A.; Imamura, F.
2017-02-01
The 2011 Great East Japan tsunami caused a wide range of devastating tsunami with maximum tsunami height of 40 m and 19,000 casualties especially along the Tohoku coast of Japan. The purpose of this study is to develop estimating equations of fatality ratio from tsunami arrival time for future tsunami loss assessment and investigate the effect of two coastal topography types namely, Sanriku-ria coast and Sendai plain. In this study, fatality ratio was defined as number of fatality divided by total number of people in a small scale of towns along the shoreline and tsunami arrival time was calculated from TUNAMI modelling with nesting-grids of 1350 m, 450 m, 150 m, and 50 m. Then, linear and nonlinear regression analysis were performed to develop a relationship model between fatality ratio and tsunami arrival time. Based on the results, a strong correlation that fatality ratio decreases with longer arrival time was found in both Sanriku-ria coast and Sendai plain. For different coastal types, different distributions of fatality ratio with tsunami arrival time are observed, in which fatality ratio of Sendai plain is higher than that of Sanriku ria-coast at the same arrival time generally.
da Silva Schneider, Andre; Roberts, Luke; Ott, Christian
2017-01-01
The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of many astrophysical phenomena. We implement a modular open-source Fortran 90 code to construct the EOS of hot dense matter for astrophysical applications. For high density matter we use a non-relativistic liquid-drop description of nuclei that includes surface effects in a single nucleus approximation (SNA). The model is based on the work of Lattimer and Swesty and has been generalized to accommodate most Skyrme parametrizations available in the literature. Low density matter is described as an ensemble of nuclei in nuclear statistical equilibrium (NSE). The transition between the SNA and NSE regimes is performed via a continuous function that smoothly blends their Helmholtz free energy. To account for the existence of 2 solar mass neutron stars, we extend the formalism to allow for a stiffening of the EOS at densities above 3 times nuclear saturation density, where the properties of matter are presently poorly constrained. We study how different Skyrme parametrizations affect the EOS, neutron star mass-radius relationships, and the spherically symmetric collapse and post-bounce supernova evolution of massive stars.
Hill's方程的Magnus积分%A New and Better Method Based on Magnus Integrator for Hill' s Equations
Institute of Scientific and Technical Information of China (English)
王博; 邓子辰; 李文成; 徐晓建
2011-01-01
Aim. The introduction of the full paper reviews some relevant papers in the open literature, points out what we believe to be their shortcomings,and then proposes the numerical method mentioned in the title,which we believe is new and better than previous ones and which is explaind in sections 1 and 2. Their core consists of; "Based on Magnus integrator method,the Hills equations were reduced-order and numerically simulated for the rail errors of the satellite formation flying in Hamiltonian system. The second-order dynamic system was reformulated as a system of first-order and the frame of reference was transferred by introducing new state variables so that the canonical characteristic was inherited from the dynamic system. This method was designed for solving the above new first-order system equations, which provide simpler calculations and better accuracy than the traditional fourth-order Runge-Kutta method. "With the presented method,the rail errors problem of two radiuses is studied;the numerical results, presented in Figs 1, and their analysis show preliminarily that it can indieed give good computational accuracy and stability.%基于Magnus积分方法,针对Hamilton系统下卫星编队绕飞轨道误差问题,对二阶Hill's方程进行了降阶变换和数值模拟.通过引进新状态变量将二阶动力学系统表示为一阶动力学系统,从而保留了原二阶动力学系统的典则性质.采用Magnus积分方法求解一阶系统方程,与传统四阶Runge -Kutta方法相比,该方法计算简单,精度高.文中采用该方法分析了两种绕飞半径的轨道误差问题,分析结果表明该方法具有良好的精度和稳定性.
Imanidis, Georgios; Luetolf, Peter
2006-07-01
An extended model for iontophoretic enhancement of transdermal drug permeation under constant voltage is described based on the previously modified Nernst-Planck equation, which included the effect of convective solvent flow. This model resulted in an analytical expression for the enhancement factor as a function of applied voltage, convective flow velocity due to electroosmosis, ratio of lipid to aqueous pathway passive permeability, and weighted average net ionic valence of the permeant in the aqueous epidermis domain. The shift of pH in the epidermis compared to bulk caused by the electrical double layer at the lipid-aqueous domain interface was evaluated using the Poisson-Boltzmann equation. This was solved numerically for representative surface charge densities and yielded pH differences between bulk and epidermal aqueous domain between 0.05 and 0.4 pH units. The developed model was used to analyze the experimental enhancement of an amphoteric weak electrolyte measured in vitro using human cadaver epidermis and a voltage of 250 mV at different pH values. Parameter values characterizing the involved factors were determined that yielded the experimental enhancement factors and passive permeability coefficients at all pH values. The model provided a very good agreement between experimental and calculated enhancement and passive permeability. The deduced parameters showed (i) that the pH shift in the aqueous permeation pathway had a notable effect on the ionic valence and the partitioning of the drug in this domain for a high surface charge density and depending on the pK(a) and pI of the drug in relation to the bulk pH; (ii) the magnitude and the direction of convective transport due to electroosmosis typically reflected the density and sign, respectively, of surface charge of the tissue and its effect on enhancement was substantial for bulk pH values differing from the pI of epidermal tissue; (iii) the aqueous pathway predominantly determined passive
Directory of Open Access Journals (Sweden)
Ibrahim Karatay
2012-01-01
Full Text Available We consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville fractional derivative of order α, where . The main purpose of this work is to extend the idea on Crank-Nicholson method to the time-fractional heat equations. We prove that the proposed method is unconditionally stable, and the numerical solution converges to the exact one with the order . Numerical experiments are carried out to support the theoretical claims.
Salama, Amgad
2015-06-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
Directory of Open Access Journals (Sweden)
M.H.T. Alshbool
2017-01-01
Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Wang, Huimin
2017-01-01
In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.
Miller, Jonah M
2016-01-01
Discontinuous Galerkin Finite Element (DGFE) methods offer a mathematically beautiful, computationally efficient, and efficiently parallelizable way to solve hyperbolic PDEs. These properties make them highly desirable for numerical calculations in relativistic astrophysics and many other fields. The BSSN formulation of the Einstein equations has repeatedly demonstrated its robustness. The formulation is not only stable but allows for puncture-type evolutions of black hole systems. To-date no one has been able to solve the full (3+1)-dimensional BSSN equations using DGFE methods. This is partly because DGFE discretization often occurs at the level of the equations, not the derivative operator, and partly because DGFE methods are traditionally formulated for manifestly flux-conservative systems. By discretizing the derivative operator, we generalize a particular flavor of DGFE methods, Local DG methods, to solve arbitrary second-order hyperbolic equations. Because we discretize at the level of the derivative o...
Fortenbaugh, R. L.
1980-01-01
Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.
Dey, Bijoy K; Janicki, Marek R; Ayers, Paul W
2004-10-08
Classical dynamics can be described with Newton's equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian's fast marching method. Using this method, we can--starting from an arbitrary initial conformation--find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H(2)-->H(2)+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.
Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v = kSt R2/3 I1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughn...
Program Transformation by Solving Equations
Institute of Scientific and Technical Information of China (English)
朱鸿
1991-01-01
Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.
Directory of Open Access Journals (Sweden)
Eun Young Lee
2013-01-01
Full Text Available Aim. To compare two creatinine-based estimated glomerular filtration rate (eGFR equations, the chronic kidney disease epidemiology collaboration (CKD-EPI and the modification of diet in renal disease (MDRD, for predicting the risk of CKD progression in type 2 diabetic patients with nephropathy. Methods. A total of 707 type 2 diabetic patients with 24 hr urinary albumin excretion of more than 30 mg/day were retrospectively recruited and traced until doubling of baseline serum creatinine (SCr levels was noted. Results. During the follow-up period (median, 2.4 years, the CKD-EPI equation reclassified 10.9% of all MDRD-estimated subjects: 9.1% to an earlier stage of CKD and 1.8% to a later stage of CKD. Overall, the prevalence of CKD (eGFR < 60 mL/min/1.73 m2 was lowered from 54% to 51.6% by applying the CKD-EPI equation. On Cox-regression analysis, both equations exhibited significant associations with an increased risk for doubling of SCr. However, only the CKD-EPI equation maintained a significant hazard ratio for doubling of SCr in earlier-stage CKD (eGFR ≥ 45 mL/min/1.73 m2, when compared to stage 1 CKD (eGFR ≥ 90 mL/min/1.73 m2. Conclusion. In regard to CKD progression, these results suggest that the CKD-EPI equation might more accurately stratify earlier-stage CKD among type 2 diabetic patients with nephropathy than the MDRD study equation.
Karimzadeh, Iman; Khalili, Hossein
2016-06-06
Serum cystatin C (Cys C) has a number of advantages over serum creatinine in the evaluation of kidney function. Apart from Cys C level itself, several formulas have also been introduced in different clinical settings for the estimation of glomerular filtration rate (GFR) based upon serum Cys C level. The aim of the present study was to compare a serum Cys C-based equation with Cockcroft-Gault serum creatinine-based formula, both used in the calculation of GFR, in patients receiving amphotericin B. Fifty four adult patients with no history of acute or chronic kidney injury having been planned to receive conventional amphotericin B for an anticipated duration of at least 1 week for any indication were recruited. At three time points during amphotericin B treatment, including days 0, 7, and 14, serum cystatin C as well as creatinine levels were measured. GFR at the above time points was estimated by both creatinine (Cockcroft-Gault) and serum Cys C based equations. There was significant correlation between creatinine-based and Cys C-based GFR values at days 0 (R = 0.606, P = 0.001) and 7 (R = 0.714, P creatinine-and a cystatin C-based glomerular filtration rate equation in patients receiving amphotericin B.
Berim, Gersh O.; Ruckenstein, Eli
2003-11-01
A generalized kinetic Ising model is applied to the description of phase transformations in lattice systems. A procedure, based on the conjecture that the probability distribution function of the states of the system is similar to the equilibrium one, is used for closing the infinite chain of kinetic equations. The method is illustrated by treating as an example the one-dimensional Ising model. The predicted rate of phase transformation (RPT) demonstrates various time behaviors dependent upon the details of the interactions between spins and a heat bath. If the parameters W0 and W the reciprocals of which characterize, respectively, the time scales of growth (decay) and splitting (coagulation) of clusters have the same order of magnitude, then the RPT is constant during almost the entire transformation process. For the case W=0, which corresponds to the absence of splitting and coagulation of clusters, the phase transformation follows an exponential law in the final stage and is linear with respect to time during the initial one. It has a similar behavior for W0≫W≠0; however, the RPT in the final stage is much smaller in the last case than for W=0. In the absence of supersaturation, RPT decreases to zero as T→Tc, where Tc(=0 K) is the phase transition temperature for a one-dimensional model. The time-dependent size distribution of clusters is for all times exponential with respect to the cluster size. The average size of the cluster far from both equilibrium and initial state grows linearly in time. Both the above quantities behave in a manner similar to those obtained by Monte Carlo simulations for systems of higher dimension.
Langthjem, M. A.; Nakano, M.
2005-11-01
An axisymmetric numerical simulation approach to the hole-tone self-sustained oscillation problem is developed, based on the discrete vortex method for the incompressible flow field, and a representation of flow noise sources on an acoustically compact impingement plate by Curle's equation. The shear layer of the jet is represented by 'free' discrete vortex rings, and the jet nozzle and the end plate by bound vortex rings. A vortex ring is released from the nozzle at each time step in the simulation. The newly released vortex rings are disturbed by acoustic feedback. It is found that the basic feedback cycle works hydrodynamically. The effect of the acoustic feedback is to suppress the broadband noise and reinforce the characteristic frequency and its higher harmonics. An experimental investigation is also described. A hot wire probe was used to measure velocity fluctuations in the shear layer, and a microphone to measure acoustic pressure fluctuations. Comparisons between simulated and experimental results show quantitative agreement with respect to both frequency and amplitude of the shear layer velocity fluctuations. As to acoustic pressure fluctuations, there is quantitative agreement w.r.t. frequencies, and reasonable qualitative agreement w.r.t. peaks of the characteristic frequency and its higher harmonics. Both simulated and measured frequencies f follow the criterion L/uc+L/c0=n/f where L is the gap length between nozzle exit and end plate, uc is the shear layer convection velocity, c0 is the speed of sound, and n is a mode number (n={1}/{2},1,{3}/{2},…). The experimental results however display a complicated pattern of mode jumps, which the numerical method cannot capture.
Aldoghaither, Abeer
2015-12-01
In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.
Banda Guzmán, V. M.; Kirchbach, M.
2016-09-01
A boson of spin j≥ 1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second-order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly D^{(j,0)oplus (0,j)} representation specific second-order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum-independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank 2 j.
Miller, Jonah M.; Schnetter, Erik
2017-01-01
Discontinuous Galerkin finite element (DGFE) methods offer a mathematically beautiful, computationally efficient, and efficiently parallelizable way to solve partial differential equations (PDEs). These properties make them highly desirable for numerical calculations in relativistic astrophysics and many other fields. The BSSN formulation of the Einstein equations has repeatedly demonstrated its robustness. The formulation is not only stable but allows for puncture-type evolutions of black hole systems. To-date no one has been able to solve the full (3 + 1)-dimensional BSSN equations using DGFE methods. This is partly because DGFE discretization often occurs at the level of the equations, not the derivative operator, and partly because DGFE methods are traditionally formulated for manifestly flux-conservative systems. By discretizing the derivative operator, we generalize a particular flavor of DGFE methods, Local DG methods, to solve arbitrary second-order hyperbolic equations. Because we discretize at the level of the derivative operator, our method can be interpreted as either a DGFE method or as a finite differences stencil with non-constant coefficients.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Directory of Open Access Journals (Sweden)
Md Shamsul Arefin
2012-12-01
Full Text Available This work presents a technique for the chirality (n, m assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n, m with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.
Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.
2017-03-01
Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.
Arefin, Md Shamsul
2012-01-01
This work presents a technique for the chirality (n, m) assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n− m) with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m) of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.
Energy Technology Data Exchange (ETDEWEB)
Javidi, M. [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: mo_javidi@yahoo.com; Golbabai, A. [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: golbabai@iust.ac.ir
2009-01-30
In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge-Kutta method for time integration to solve the generalized Burger's-Huxley equation (GBHE). To reduce round-off error in spectral collocation (pseudospectral) method we use preconditioning. Firstly, theory of application of Chebyshev spectral collocation method with preconditioning (CSCMP) and domain decomposition on the generalized Burger's-Huxley equation presented. This method yields a system of ordinary differential algebric equations (DAEs). Secondly, we use fourth order Runge-Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.
Indian Academy of Sciences (India)
Z AMERIAN; M K SALEM; A SALAR ELAHI; M GHORANNEVISS
2017-03-01
Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad–Shafranov equation (an axisymmetric,magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular crosssection of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Wu, Zhen; Zhang, Xian; Zhou, Chunjiao; Pang, Jing-Lin; Zhang, Panyue
2017-02-22
Single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The characteristics and coagulation properties of these prepared aluminum salts were investigated. The Langmuir, Freundlich, and Sips adsorption isotherms were first used to describe the adsorption neutralization process in coagulation, and the Boltzmann equation was used to fit the reaction kinetics of floc growth in flocculation. It was novel to find that the experimental data fitted well with the Sips and Boltzmann equation, and the significance of parameters in the equations was discussed simultaneously. Through the Sips equation, the adsorption neutralization reaction was proved to be spontaneous and the adsorption neutralization capacity was HPAC > PAC > AlCl3. Sips equation also indicated that the zeta potential of water samples would reach a limit with the increase of coagulant dosage, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower equilibrium zeta potential value of HPAC might be the reason why the water sample was not easy to achieve restabilization at a high coagulant dosage. Through the Boltzmann equation modeling, the maximum average floc size formed by AlCl3, PAC, and HPAC were 196.0, 188.0, and 203.6 μm, respectively, and the halfway time of reactions were 31.23, 17.08, and 9.55 min, respectively. The HPAC showed the strongest floc formation ability and the fastest floc growth rate in the flocculation process, which might be caused by the stronger adsorption and bridging functions of Alb and Alc contained in HPAC.
Weberszpil, J; Cherman, A; Helayël-Neto, J A
2012-01-01
The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\\"odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding continuity equation is worked out and we also identify the contribution of the relativistic correction the quantum potential in the coarse-grained treatment. As a consequence, in the classical regime, we derive the sort of fractional Newtonian law with the quantum potential included and the fractional conterparts of the De Broglies's energy and momentum relations.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Energy Technology Data Exchange (ETDEWEB)
Chen, Xueli, E-mail: xlchen@xidian.edu.cn, E-mail: jimleung@mail.xidian.edu.cn; Zhang, Qitan; Yang, Defu; Liang, Jimin, E-mail: xlchen@xidian.edu.cn, E-mail: jimleung@mail.xidian.edu.cn [School of Life Science and Technology, Xidian University, Xi' an, Shaanxi 710071 (China)
2014-01-14
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP{sub 3} equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP{sub 3}) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Given a time series of potential evapotranspiration and rainfall data, there are at least two approaches for estimating vertical percolation rates. One approach involves solving Richards' equation (RE) with a plant uptake model. An alternative approach involves applying a simple soil moisture accoun...
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the
Enders, Craig K.
2008-01-01
Recent missing data studies have argued in favor of an "inclusive analytic strategy" that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to…
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the stabl
Ursavas, Omer Faruk; Reisoglu, Ilknur
2017-01-01
Purpose: The purpose of this paper is to explore the validity of extended technology acceptance model (TAM) in explaining pre-service teachers' Edmodo acceptance and the variation of variables related to TAM among pre-service teachers having different cognitive styles. Design/methodology/approach: Structural equation modeling approach was used to…
基于双层位势的Poisson方程无奇异方法%A Nonsingular Method Based on Double Layer Potential for Poisson Equation
Institute of Scientific and Technical Information of China (English)
林鑫; 高发玲
2014-01-01
针对求解Poisson方程的边值问题，利用虚边界上分布的矩密度，得出基于双层位势的虚边界元方程。该方法有效地避免了奇异和强奇异积分的计算。数值算例证明了算法的有效性和精确性。%Towards the boundary problem of Poisson equation,different from the virtual boundary element equation based on the single layer potential,another virtual boundary collocation method (VBCM)is conducted based on double layer potential for Poisson problem,with the moment density distributed on the virtual boundary. The VBCM can avoid the singular,hyper-singular integral ,the numerical example presents the efficiency and accuracy of the method.
Steyerl, A; Müller, G; Malik, S S; Desai, A M; Golub, R
2014-01-01
Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.
Directory of Open Access Journals (Sweden)
Fangyuan Chen
2013-05-01
Full Text Available This paper presents a model-based cell-health-conscious thermal energy management method. An Arrhenius equation-based mathematical model is firstly identified to quantify the effect of temperature on the cell lifetime of a Nickel Metal Hydride (NiMH battery pack. The cell aging datasets collected under multiple ambient temperatures are applied to extract the Arrhenius equation parameters. The model is then used as an assessment criterion and guidance for the thermal management design of battery packs. The feasibility and applicability of a pack structure with its cooling system, is then evaluated, and its design problems are studied by a computational fluid dynamics (CFD analysis. The performance and eligibility of the design method is validated by both CFD simulations and experiments.