Directory of Open Access Journals (Sweden)
Ziaei Poor Hamed
2016-01-01
Full Text Available This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer, hyperbolic (thermal wave and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.
Empirical comparison of Pennes' bio-heat equation
Cundin, Luisiana X.; Roach, William P.; Millenbaugh, Nancy
2009-02-01
We solve a transient one-dimensional inhomogeneous Bio-Heat equation on a semi-infinite isotropic domain. The external source was modeled after Beer's law of deposition; the penetration depth was left arbitrary. The theoretical model is tested against experimental whole-body irradiation data. Pennes' thermal model correctly modeled the initial surface temperature rise, but experiment diverged from theoretical predictions after 30 minutes of exposure. Mortality statistics from a limited irreversibility study provided another means of comparison. All three major quartiles describing irreversibility are to be found well within the divergent space, where theory and experimental data diverge. Also, the mortality statistics seem to converge onto the divergence point.
Kalman Filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry.
Zhang, Yuxin; Chen, Shuo; Deng, Kexin; Chen, Bingyao; Wei, Xing; Yang, Jiafei; Wang, Shi; Ying, Kui
2017-01-01
To develop a self-adaptive and fast thermometry method by combining the original hybrid magnetic resonance thermometry method and the bio heat transfer equation (BHTE) model. The proposed Kalman filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry, abbreviated as KalBHT hybrid method, introduced the BHTE model to synthesize a window on the regularization term of the hybrid algorithm, which leads to a self-adaptive regularization both spatially and temporally with change of temperature. Further, to decrease the sensitivity to accuracy of the BHTE model, Kalman filter is utilized to update the window at each iteration time. To investigate the effect of the proposed model, computer heating simulation, phantom microwave heating experiment and dynamic in-vivo model validation of liver and thoracic tumor were conducted in this study. The heating simulation indicates that the KalBHT hybrid algorithm achieves more accurate results without adjusting λ to a proper value in comparison to the hybrid algorithm. The results of the phantom heating experiment illustrate that the proposed model is able to follow temperature changes in the presence of motion and the temperature estimated also shows less noise in the background and surrounding the hot spot. The dynamic in-vivo model validation with heating simulation demonstrates that the proposed model has a higher convergence rate, more robustness to susceptibility problem surrounding the hot spot and more accuracy of temperature estimation. In the healthy liver experiment with heating simulation, the RMSE of the hot spot of the proposed model is reduced to about 50% compared to the RMSE of the original hybrid model and the convergence time becomes only about one fifth of the hybrid model. The proposed model is able to improve the accuracy of the original hybrid algorithm and accelerate the convergence rate of MR temperature estimation.
Gkigkitzis, Ioannis; Austerlitz, Carlos; Haranas, Ioannis; Campos, Diana
2015-01-01
The aim of this report is to propose a new methodology to treat prostate cancer with macro-rod-shaped gold seeds irradiated with ultrasound and develop a new computational method for temperature and thermal dose control of hyperthermia therapy induced by the proposed procedure. A computer code representation, based on the bio-heat diffusion equation, was developed to calculate the heat deposition and temperature elevation patterns in a gold rod and in the tissue surrounding it as a result of different therapy durations and ultrasound power simulations. The numerical results computed provide quantitative information on the interaction between high-energy ultrasound, gold seeds and biological tissues and can replicate the pattern observed in experimental studies. The effect of differences in shapes and sizes of gold rod targets irradiated with ultrasound is calculated and the heat enhancement and the bio-heat transfer in tissue are analyzed.
Transfer equations for modeling interrill erosion
Nouhou bako, Amina; Darboux, Frédéric; James, François; Lucas, Carine
2016-01-01
Numerous models are available for matter transfer along an hillslope. They are usually process-specific, requiring to use several models to simulate transfers along an hillslope. To overcome this issue, we develop a new model valid for chemical (nutrients, pollutants, dissolved carbon) and particle transfers by water. It is able to simulate both interrill and rill erosion. This new equation encompasses the previous models of Gao et al. (2004), Hairsine and Rose (1992, 1991) and Lajeunesse et ...
Fem Formulation of Coupled Partial Differential Equations for Heat Transfer
Ameer Ahamad, N.; Soudagar, Manzoor Elahi M.; Kamangar, Sarfaraz; Anjum Badruddin, Irfan
2017-08-01
Heat Transfer in any field plays an important role for transfer of energy from one region to another region. The heat transfer in porous medium can be simulated with the help of two partial differential equations. These equations need an alternate and relatively easy method due to complexity of the phenomenon involved. This article is dedicated to discuss the finite element formulation of heat transfer in porous medium in Cartesian coordinates. A triangular element is considered to discretize the governing partial differential equations and matrix equations are developed for 3 nodes of element. Iterative approach is used for the two sets of matrix equations involved representing two partial differential equations.
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Some fundamental considerations of the equation of radiative transfer
International Nuclear Information System (INIS)
Kuriyan, J.G.; Sudarshan, E.C.G.
1978-10-01
The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references
Application of the Radiative Transfer Equation (RTE) to Scattering by ...
African Journals Online (AJOL)
Application of the Radiative Transfer Equation (RTE) to Scattering by a Dust Aerosol Layer. ... Incident radiation in its journey through the atmosphere before reaching the earth surface encounters particles of different sizes and composition such as dust aerosols resulting in interactions that lead to absorption and scattering.
A new class of bio-heat resisted polymer blend.
Pack, Seongchan; Kashiwagi, Takashi; Koga, Tadanori; Rafailovich, Miriam
2009-03-01
Increasing in oil prices and environmental concerns is a driving force to seek out alternative materials. A completely biodegradable starch is a candidate for the alternative materials. Since the starch is brittle, it must be mixed with other polymers. In order to make a thermoplastic starch (TPS), we need a bio-compatiblizer to increase a degree of compatibilization. The biocompatibilzer can be a small molecules or nanoparticles with the small molecules, which leads to improved material properties. In order to demonstrate a possible biocompatibilzer, we first developed a corn-based starch impregnated with non-halogenated flame retardant formulations. The starch was blended with Ecoflex, a biodegradable polymer. Using SAXS and USAXS we characterized structures of the compounds with different amount of Ecoflex by weight. Furthermore, the addition of 5% nanoparticles in the compounds increased the Young's Modulus and impact toughness significantly. The compounds also did flame test. It is indicated that the compound with the addition of the nanopaticles would pass with a UL-94V0 rating. Therefore, the procedure for producing these TPS compounds can be applied to any biodegradable polymers, manufacturing a new bio-heat resisted compound.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem
2018-01-01
In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Fire Intensity Data for Validation of the Radiative Transfer Equation
Energy Technology Data Exchange (ETDEWEB)
Blanchat, Thomas K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jernigan, Dann A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
A set of experiments and test data are outlined in this report that provides radiation intensity data for the validation of models for the radiative transfer equation. The experiments were performed with lightly-sooting liquid hydrocarbon fuels that yielded fully turbulent fires 2 m diameter). In addition, supplemental measurements of air flow and temperature, fuel temperature and burn rate, and flame surface emissive power, wall heat, and flame height and width provide a complete set of boundary condition data needed for validation of models used in fire simulations.
Symmetry-preserving difference schemes for some heat transfer equations
Bakirova, M. I.; Dorodnitsyn, V. A.; Kozlov, R. V.
1997-12-01
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modelling helps to retain qualitative properties of the differential equations in their difference counterparts.
Yifat, Jonathan; Gannot, Israel
2015-03-01
Early detection of malignant tumors plays a crucial role in the survivability chances of the patient. Therefore, new and innovative tumor detection methods are constantly searched for. Tumor-specific magnetic-core nano-particles can be used with an alternating magnetic field to detect and treat tumors by hyperthermia. For the analysis of the method effectiveness, the bio-heat transfer between the nanoparticles and the tissue must be carefully studied. Heat diffusion in biological tissue is usually analyzed using the Pennes Bio-Heat Equation, where blood perfusion plays an important role. Malignant tumors are known to initiate an angiogenesis process, where endothelial cell migration from neighboring vasculature eventually leads to the formation of a thick blood capillary network around them. This process allows the tumor to receive its extensive nutrition demands and evolve into a more progressive and potentially fatal tumor. In order to assess the effect of angiogenesis on the bio-heat transfer problem, we have developed a discrete stochastic 3D model & simulation of tumor-induced angiogenesis. The model elaborates other angiogenesis models by providing high resolution 3D stochastic simulation, capturing of fine angiogenesis morphological features, effects of dynamic sprout thickness functions, and stochastic parent vessel generator. We show that the angiogenesis realizations produced are well suited for numerical bio-heat transfer analysis. Statistical study on the angiogenesis characteristics was derived using Monte Carlo simulations. According to the statistical analysis, we provide analytical expression for the blood perfusion coefficient in the Pennes equation, as a function of several parameters. This updated form of the Pennes equation could be used for numerical and analytical analyses of the proposed detection and treatment method. Copyright © 2014 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Forristall, R.
2003-10-01
This report describes the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver. The model determines the performance of a parabolic trough solar collector's linear receiver, also called a heat collector element. All heat transfer and thermodynamic equations, optical properties, and parameters used in the model are discussed. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.
Methods for the solution of the two-dimensional radiation-transfer equation
International Nuclear Information System (INIS)
Weaver, R.; Mihalas, D.; Olson, G.
1982-01-01
We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed
Spatial discretizations for self-adjoint forms of the radiative transfer equations
International Nuclear Information System (INIS)
Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.
2006-01-01
There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes
Zhang, Chuang; Guo, Zhaoli; Chen, Songze
2017-12-01
An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
Gorpas, Dimitris; Andersson-Engels, Stefan
2012-12-01
The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower.
Research on high-order approximation of radiative transfer equation for image reconstruction
Ma, Wenjuan; Gao, Feng; Wu, Linhui; Yi, Xi; Zhu, Pingping; Zhao, Huijuan
2011-03-01
In this article, we derive the two-dimensional spherical harmonics equations to three-order (P3) of Radiative Transfer Equation for anisotropic scattering. We also solved this equations using Galerkin finite element method and compared the solutions with the first-order diffusion equation and Monte Carlo simulation. the benchmark problems are tested, and we found that the developed three-order model with high absorb coefficient is able to significantly improve the diffusion solution in circle geometry, and the radiance distribution close to light source is more accurate. It is significant for accurate modeling of light propagation in small tissue geometries in small animal imaging. Then, the inverse model for the simultaneous reconstruction of the absorption images is proposed based on P3 equations, and the feasibility and effectiveness of this method are proved by the simulation.
Turbulence equations in incompressible two-phase flow without mass transfer
International Nuclear Information System (INIS)
Lance, Michel; Marie, J.-L.; Charnay, Georges; Bataille, Jean
1979-01-01
In order to adapt the modelling methods of one-phase turbulence, the equations describing the evolution of the Reynolds stress tensor, of the dissipation and of the fluctuating pressure in each phase of an incompressible two-phase flow without mass transfer were established [fr
Small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere
International Nuclear Information System (INIS)
Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas
2013-01-01
The conventional pseudo-spherical technique relies on the separation of the total radiance into the direct solar beam and the diffuse radiance; the direct solar radiance is treated in a spherical geometry, while the diffuse radiance is computed in a plane-parallel geometry. In the small-angle modification of the radiative transfer equation, the total radiance is separated into an anisotropic part and a regular part. In this paper, we pOresent two formulations of the small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere. In the first formulation, we solve the radiative transfer equation for the diffuse radiance in a pseudo-spherical atmosphere with an additional anisotropic source term computed in a plane-parallel atmosphere, while in the second formulation we solve the radiative transfer equation for the regular solution in a plane-parallel atmosphere with an additional pseudo-spherical correction term. The numerical analysis revealed that the accuracy of the small-angle models is acceptable. -- Highlights: ► The small-angle modification of DOM for a pseudo-spherical atmosphere is formulated. ► The small-angle modification is tested for atmospheric remote sensing. ► The accuracy of small-angle modification is higher than delta-M approximation.
Simplified equations for transient heat transfer problems at low Fourier numbers
DEFF Research Database (Denmark)
Christensen, Martin Gram; Adler-Nissen, Jens
2015-01-01
This paper proposes an analytical solution to transient heat transfer, which also applies for the initial heating/cooling period (Fo equation is presented...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...... and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...
A Multiagent Transfer Function Neuroapproach to Solve Fuzzy Riccati Differential Equations
Directory of Open Access Journals (Sweden)
Mohammad Shazri Shahrir
2014-01-01
Full Text Available A numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach for neural networks (NN. This proposed new approach provides different degrees of polynomial subspaces for each of the transfer function. This multitude of transfer functions creates unique “agents” in the structure of the NN. Hence it is named as multiagent neuroapproach (multiagent NN. Previous works have shown that results using Runge-Kutta 4th order (RK4 are reliable. The results can be achieved by solving the 1st order nonlinear differential equation (ODE that is found commonly in Riccati differential equation. Multiagent NN shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al. (2013, RK-4, and the existing neuromethod (NM. Numerical examples are discussed to illustrate the proposed method.
Directory of Open Access Journals (Sweden)
Younsi Ramdane
2015-01-01
Full Text Available In the present paper, three-dimensional equations for coupled heat and mass conservation equations for wood are solved to study the transient heat and mass transfer during high thermal treatment of wood. The model is based on Luikov’s approach, including pressure. The model equations are solved numerically by the commercial package FEMLfor the temperature and moisture content histories under different treatment conditions. The simulation of the proposed conjugate problem allows the assessment of the effect of the heat and mass transfer within wood. A parametric study was also carried out to determine the effects of several parameters such as initial moisture content and the sample thickness on the temperature, pressure and moisture content distributions within the samples during heat treatment.
About Navier-Stokes Equation in the Theory of Convective Heat Transfer
Davidzon, M. Y.
2017-10-01
A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).
Li, Chunqing; Tie, Xiaobo; Liang, Kai; Ji, Chanjuan
2016-01-01
After conducting the intensive research on the distribution of fluid's velocity and biochemical reactions in the membrane bioreactor (MBR), this paper introduces the use of the mass-transfer differential equation to simulate the distribution of the chemical oxygen demand (COD) concentration in MBR membrane pool. The solutions are as follows: first, use computational fluid dynamics to establish a flow control equation model of the fluid in MBR membrane pool; second, calculate this model by adopting direct numerical simulation to get the velocity field of the fluid in membrane pool; third, combine the data of velocity field to establish mass-transfer differential equation model for the concentration field in MBR membrane pool, and use Seidel iteration method to solve the equation model; last but not least, substitute the real factory data into the velocity and concentration field model to calculate simulation results, and use visualization software Tecplot to display the results. Finally by analyzing the nephogram of COD concentration distribution, it can be found that the simulation result conforms the distribution rule of the COD's concentration in real membrane pool, and the mass-transfer phenomenon can be affected by the velocity field of the fluid in membrane pool. The simulation results of this paper have certain reference value for the design optimization of the real MBR system.
A computational procedure for finding multiple solutions of convective heat transfer equations
International Nuclear Information System (INIS)
Mishra, S; DebRoy, T
2005-01-01
In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations
Li, Changping
2014-11-10
In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.
Dimensionality-reduction approach to the thermal radiative transfer equation inverse problem
Masiello, G.; Serio, C.
2004-06-01
An original algorithm is illustrated for the inversion of geophysical parameters from spectral observations in the thermal band. The algorithm exploits the Hotelling transform and projects the linearized version of the radiative transfer equation in a space of reduced dimensionality. The inversion is performed in this latter space, which speeds up the computations and makes the method attractive for real-time retrieval from high spectral resolution infrared observations.
Kylling, A.
1991-01-01
The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.
International Nuclear Information System (INIS)
Ben Jaffel, L.; Vidal-Madjar, A.
1989-01-01
The discrete ordinate method for the resolution of the radiative transfer equation is developed. We show that the construction of a quasi-analytical solution to the corresponding matrix diagonalization problem reduces the time calculation and allows the use of more dense discrete frequency and angle grids. Comparison with previous work is made, showing that the present method reduces by more than a factor of ten the computational time, and is more appropriate in all cases
Study on the key technologies of the Transfer Equipment Cask for Tokamak Equator Port Plug
Energy Technology Data Exchange (ETDEWEB)
Wang, Buyun, E-mail: ayun@iim.ac.cn [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Gao, Lifu [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Cao, Huibin; Sun, Jian [Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Sun, Yuxiang; Song, Quanjun; Ma, Chengxue; Chang, Li; Shuang, Feng [Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027 (China); Robot Sensors and Human-Machine Interaction Laboratory, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 230031 (China)
2014-12-15
Highlights: • Design on Intelligent Air Transfer System (IATS) for Transfer Equipment Cask (TECA). • A rhombic-like parallel robot for docking with minimum misalignment. • Design on electro-hydraulic servo system of the TECA for Tokamak Equator Port Plug (TEPP) manipulation. • A control architecture with several algorithms and information acquired from sensors could be used by the TECA for Remote Handling (RH). - Abstract: The Transfer Equipment Cask (TECA) is a key solution for Remote Handling (RH) in Tokamak Equator Port Plug (TEPP) operations. From the perspectives of both engineering and technical designs of effective experiments on the TEPP, key technologies on these topics covering the TECA are required. According to conditions in ITER (International Thermonuclear Experimental Reactor) and features of the TEPP, this paper introduces the design of an Intelligent Air Transfer System (IATS) with an adaptive attitude and high precision positioning that transports a cask system of more than 30 tons from the Tokamak Building (TB) to the Hot Cell Building (HCB). Additionally, different actuators are discussed, and the hydraulic power drive is eventually selected and designed. A rhombic-like parallel robot is capable of being used for docking with minimum misalignment. Practical mechanisms of the cask system are presented for hostile environments. A control architecture with several algorithms and information acquired from sensors could be used by the TECA. These designs yield realistic and extended applications for the RH of ITER.
Towards a General Equation for the Survival of Microbes Transferred between Solar System Bodies
Fries, M.; Steele, A.
2014-01-01
It should be possible to construct a general equation describing the survival of microbes transferred between Solar System bodies. Such an equation will be useful for constraining the likelihood of transfer of viable organisms between bodies throughout the lifetime of the Solar System, and for refining Planetary Protection constraints placed on future missions. We will discuss the construction of such an equation, present a plan for definition of pertinent factors, and will describe what research will be necessary to quantify those factors. Description: We will examine the case of microbes transferred between Solar System bodies as residents in meteorite material ejected from one body (the "intial body") and deposited on another (the "target body"). Any microbes transferred in this fashion will experience four distinct phases between their initial state on the initial body, up to the point where they colonize the target body. Each of these phases features phenomena capable of reducing or exterminating the initial microbial population. They are: 1) Ejection: Material is ejected from the initial body, imparting shock followed by rapid desiccation and cooling. 2) Transport: Material travels through interplanetary space to the target body, exposing a hypothetical microbial population to extended desiccation, irradiation, and temperature extremes. 3) Infall: Material is deposited on the target body, diminishing the microbial population through shock, mass loss, and heating. 4) Adaptation: Any microbes which survive the previous three phases must then adapt to new chemophysical conditions of the target body. Differences in habitability between the initial and target bodies dominate this phase. A suitable general-form equation can be assembled from the above factors by defining the initial number of microbes in an ejected mass and applying multiplicitive factors based on the physical phenomena inherent to each phase. It should be possible to present the resulting equation
Non-Isothermal Constitutive Relations and Heat Transfer Equations of a Two-Phase Medium
Directory of Open Access Journals (Sweden)
Uciechowska-Grakowicz Anna
2017-09-01
Full Text Available In the case of a two-phase medium – such as the soil, which consists of an elastic skeleton and is filled with pore fluids – stress and strain within the medium are dependent on both phases. Similarly, in the case of heat transfer, heat is conducted through the two phases at different rates, with an additional heat transfer between the phases. In the classical approach to modelling a porous medium, it is assumed that the fluid filling the pore space is water, which is incompressible. In the case of gas, the volume of which is strongly dependent on temperature and pressure, one should take this behavior into account in the constitutive relations for the medium. This work defines the physical relations of a two-phase medium and provides heat transfer equations, constructed for a porous, elastic skeleton with fluid-filled pores, which may be: liquid, gas, or mixture of liquid and a gas in non-isothermal conditions. The paper will present constitutive relations derived from the laws of irreversible thermodynamics, assuming that pores are filled with either a liquid or a gas. These relations, in the opinion of the authors, may be used as the basis for the construction of a model of the medium filled partly with a liquid and partly with a gas. It includes the possibility of independent heat transfer through any given two-phase medium phase, with the transfer of heat between the phases.
Energy Technology Data Exchange (ETDEWEB)
Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
Directory of Open Access Journals (Sweden)
Sun Huan
2016-01-01
Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.
Generalized solutions of the radiative transfer equations in a singular case
International Nuclear Information System (INIS)
Golse, F.; Perthame, B.
1985-07-01
This paper is devoted to the study of the radiative transfer equations (TR). First, we prove a global existence theorem, which allows a blow-up of the opacity σsub(ν)(E) when E → 0. Thus, it extends Mercier's previous result. This proof relies mainly on a non linear version of Hille-Yosida theorem. Then, we prove the uniqueness of the semigroup solving (TR), and some regularity results (in the class of functions with bounded variation). Finally, we prove the convergence of some splitting algorithms associated to (TR)
The Explicit Green's Approach with stability enhancement for solving the bioheat transfer equation
Loureiro, FS; Mansur, WJ; Wrobel, LC; Silva, JEA
2014-01-01
The aim of this paper is to propose a strategy for performing a stability enhancement into the Explicit Green’s Approach (ExGA) method applied to the bioheat transfer equation. The ExGA method is a time-stepping technique that uses numerical Green’s functions in the time domain; these functions are here computed by the FEM. Basically, a new two nonequal time substeps procedure is proposed to compute Green’s functions at the first time step. This is accomplished by adopting the standard explic...
International Nuclear Information System (INIS)
Tishkovets, Victor P.; Jockers, Klaus
2006-01-01
The theory of light scattering by systems of spherical particles is applied to study the light scattering by discrete random media. A microphysical approach of statistical electromagnetics is used to derive the vector radiative transfer equation for semi-infinite densely packed media composed of identical spherical particles. The equation obtained corresponds to the sum of the ladder diagrams in the diagrammatic representation of the Bethe-Salpeter equation. The new vector radiative transfer equation is compared with that for sparse media. The effective refractive index as it enters in our equation is calculated from the known generalization of the Lorentz-Lorenz equation. Some numerical results of calculations of the reflection matrix are presented and compared with those for sparse media. The differences between the theoretical description of light scattering by closely packed and sparse media are discussed in detail
Modeling ARRM Xenon Tank Pressurization Using 1D Thermodynamic and Heat Transfer Equations
Gilligan, Patrick; Tomsik, Thomas
2016-01-01
As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.
Modeling Xenon Tank Pressurization using One-Dimensional Thermodynamic and Heat Transfer Equations
Gilligan, Ryan P.; Tomsik, Thomas M.
2017-01-01
As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.
Directory of Open Access Journals (Sweden)
Sawicki Dominik
2015-09-01
Full Text Available One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES, which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems, as well as transient heat transfer problems. The purpose of this paper is to test the efficacy of the PIES method with time discretization in solving problem of laser heating of a material, with different pulse shape approximation functions.
Optical properties reconstruction using the adjoint method based on the radiative transfer equation
Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir
2018-01-01
An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.
Pulkkinen, Aki; Tarvainen, Tanja
2013-03-01
The radiative transfer equation (RTE) is widely accepted to accurately describe light transport in a medium with scattering particles, and it has been successfully applied as a light-transport model, for example, in diffuse optical tomography. Due to the computationally expensive nature of the RTE, most of these applications have been in the frequency domain. In this paper, an efficient solution method for the time-domain RTE is proposed. The method is based on solving the frequency-domain RTE at multiple modulation frequencies and using the Fourier-series representation of the radiance to obtain approximation of the time-domain solution. The approach is tested with simulations. The results show that the method can be used to obtain the solution of the time-domain RTE with good accuracy and with significantly fewer computational resources than are needed in the direct time-domain solution.
Gao, Hao; Phan, Lan; Lin, Yuting
2012-09-01
A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/.
Matsugi, Akira
2015-08-01
Collisional energy transfer plays an important role in unimolecular reaction kinetics. This Letter presents classical trajectory calculations of the energy transfer processes in collisions between selected alkanes (ethane, propane, isobutane, and neopentane) and krypton at high temperature. The primary aim of this study was to elucidate the validity of the predicted energy transfer parameters by performing master equation analyses of their vibrational relaxation times and comparing the predicted values with the available experimental data. The results demonstrate the ability of classical trajectory calculations to accurately predict the parameters for vibrational energy transfer.
Directory of Open Access Journals (Sweden)
Soloviev Igor A.
2016-01-01
Full Text Available Stochastic differential equations are proposed on the basis of generalized Fokker-Planck-Kolmogorov equation. From the statements of boundary and initial value problems for probabilistic density, dispersion and differential entropy the conditions for stability of solutions and changes in scenarios of development of random phenomena of heat and nuclear particle transfer are obtained. [Projekat Ministartsva nauke Republike Srbije, br. 174005 i br. 174024
Oberlack, M.; McComb, W. D.; Quinn, A. P.
2001-02-01
It is shown that the set of integrodifferential and algebraic functional equations of the local energy transfer theory may be considerably reduced in dimension for the case of isotropic turbulence. This is achieved without restricting the solution space. The basis for this is a complete analytical solution to the functional equations Q(kt,t')=H(kt,t')Q(kt',t') and H(kt,s)H(ks,t')=H(kt,t'). The solution is proved to depend only on a single function φ(kt) solely determining Q and H. Hence the dimension of both the dependent and the independent variables is reduced by one. From the latter, the corresponding two integrodifferential equations are lowered to a single integrodifferential equation for φ(kt), extended by an integral side condition on the k dependence of φ(kt). In the limit ν-->0, a partial solution to the reduced set of equations is presented in the Appendix.
Comparison of linear forms of the radiative transfer equation with analytic Jacobians.
Huang, Bormin; Smith, William L; Huang, Hung-Lung; Woolf, Harold M
2002-07-20
Determining the Jacobians of the radiative transfer equation (RTE) is important to the qualities of the simultaneous retrieval of geophysical parameters from satellite radiance observations and the assimilation of radiance data into a numerical weather prediction system. Two linear forms of the RTE with analytic Jacobians are formulated. The first linear form has approximate analytic Jacobians, which involves some monochromatic approximation applied to a fast transmittance model. Unlike previous research, which lacks the transmittance Jacobian with respect to the atmospheric temperature profile, this form is complete in the sense that the transmittance Jacobians with respect to atmospheric temperature and absorbing constituent profiles are both present. The second linear form has exact analytic Jacobians derived consistently from the same fast transmittance model without using any monochromatic approximation. By numerical comparison between the two linear forms for the NOAA-12 High-Resolution Infrared Sounder, we show significant errors in the linear form with approximate analytic Jacobians. The relative absolute linearization error from the linear form with approximate analytic Jacobians is shown to be 2-4 orders of magnitude larger than that from the linear form with exact analytic Jacobians, even for the case of a 0.1% perturbation of the U.S. Standard Atmosphere. The errors unnecessarily complicate the ill-posed retrieval problem of atmospheric remote sensing and can be avoided if the correct linear form of the RTE with exact analytic Jacobians is adopted.
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.
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-03-01
In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.
International Nuclear Information System (INIS)
Gupply, C.B.
1964-08-01
The report describes how the Transfer Functions of a system of ordinary differential equations can be derived in terms of the latent roots and vectors of the matrix of coefficient for the dependent variables of the system. It is shown that when the latent roots and vectors are known the formulation of the modes of the system and of its transfer functions is straight forward. The treatment itself is simple and starts almost from first principles. The report describes how to get a general set of differential equations into the correct form, the meaning of latent roots and vectors, how the transfer functions arise, the significance of complex latent roots and vectors and, finally, the modal significance of a system at its stability limit. Two simple fully worked examples are included. (author)
Directory of Open Access Journals (Sweden)
D. A. Neudegg
1999-06-01
Full Text Available Observations of a flux transfer event (FTE have been made simultaneously by the Equator-S spacecraft near the dayside magnetopause whilst corresponding transient plasma flows were seen in the near-conjugate polar ionosphere by the CUTLASS Finland HF radar. Prior to the occurrence of the FTE, the magnetometer on the WIND spacecraft ~226 RE upstream of the Earth in the solar wind detected a southward turning of the interplanetary magnetic field (IMF which is estimated to have reached the subsolar magnetopause ~77 min later. Shortly afterwards the Equator-S magnetometer observed a typical bipolar FTE signature in the magnetic field component normal to the magnetopause, just inside the magnetosphere. Almost simultaneously the CUTLASS Finland radar observed a strong transient flow in the F region plasma between 78° and 83° magnetic latitude, near the ionospheric region predicted to map along geomagnetic field lines to the spacecraft. The flow signature (and the data set as a whole is found to be fully consistent with the view that the FTE was formed by a burst of magnetopause reconnection.Key words. Interplanetary physics (ionosphere-magnetosphere interaction · Magnetospheric physics (magnetopause · cusp · and boundary layers; solar wind-magnetosphere interactions
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.
Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger
2016-09-28
Electron transfer reactions are commonly described by the phenomenological Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Although the general structure of the equation is well accepted, for modern electrochemical systems like batteries and fuel cells there is still intensive discussion about the specific dependencies of the coefficients. A general guideline for the derivation of Butler-Volmer type equations is missing in the literature. We derive very general relations of Butler-Volmer structure which are based on a rigorous non-equilibrium thermodynamic model and allow for adaption to a wide variety of electrochemical systems. We discuss the application of the new thermodynamic approach to different scenarios like the classical electron transfer reactions at metal electrodes and the intercalation process in lithium-iron-phosphate electrodes. Furthermore we show that under appropriate conditions also adsorption processes can lead to Butler-Volmer equations. We illustrate the application of our theory by a strongly simplified example of electroplating.
Prediction equations for diffusing capacity (transfer factor) of lung for North Indians.
Chhabra, Sunil Kumar; Kumar, Rajeev; Gupta, Uday A
2016-01-01
Prediction equations for diffusing capacity of lung for carbon monoxide (DLCO), alveolar volume (VA), and DLCO/VA using the current standardization guidelines are not available for Indian population. The present study was carried out to develop equations for these parameters for North Indian adults and examine the ethnic diversity in predictions. DLCO was measured by single-breath technique and VA by single-breath helium dilution using standardized methodology in 357 (258 males, 99 females) normal nonsmoker adult North Indians and DLCO/VA was computed. The subjects were randomized into training and test datasets for development of prediction equations by multiple linear regressions and for validation, respectively. For males, the following equations were developed: DLCO, -7.813 + 0.318 × ht -0.624 × age + 0.00552 × age(2); VA, -8.152 + 0.087 × ht -0.019 × wt; DLCO/VA, 7.315 - 0.037 × age. For females, the equations were: DLCO, -44.15 + 0.449 × ht -0.099 × age; VA, -6.893 + 0.068 × ht. A statistically acceptable prediction equation was not obtained for DLCO/VA in females. It was therefore computed from predicted DLCO and predicted VA. All equations were internally valid. Predictions of DLCO by Indian equations were lower than most Caucasian predictions in both males and females and greater than the Chinese predictions for males. This study has developed validated prediction equations for DLCO, VA, and DLCO/VA in North Indians. Substantial ethnic diversity exists in predictions for DLCO and VA with Caucasian equations generally yielding higher values than the Indian or Chinese equations. However, DLCO/VA predicted by the Indian equations is slightly higher than that by other equations.
Energy Technology Data Exchange (ETDEWEB)
Aursand, Eskil, E-mail: eskil.aursand@sintef.no; Gjennestad, Magnus Aa.; Yngve Lervåg, Karl; Lund, Halvor
2016-03-15
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base fluid. The magnetization model is based on statistical mechanics, taking into account non-uniform particle size distributions. An implementation of the proposed model is validated against experiments from the literature, and found to give good predictions for the thermomagnetic pumping performance. However, the results reveal a very large sensitivity to uncertainties in heat transfer coefficient predictions. - Highlights: • A multi-phase flow model for thermomagnetically pumped ferrofluid is proposed. • An implementation is validated against experiments from the literature. • Predicted thermomagnetic pumping effect agrees with experiments. • However, a very large sensitivity to heat transfer coefficient is revealed.
Directory of Open Access Journals (Sweden)
Cieśliński Janusz T.
2016-09-01
Full Text Available This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx. The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.
Directory of Open Access Journals (Sweden)
Han Zhang
2017-09-01
Full Text Available China’s new round tenure reform has devolved collective forests to individuals on an egalitarian basis. To balance the equity–efficiency dilemma, forestland transfers are highly advocated by policymakers. However, the forestland rental market is still inactive after the reform. To examine the role of off-farm employment in forestland transfers, a simultaneous Tobit system of equations was employed to account for the endogeneity, interdependency, and censoring issues. Accordingly, the Nelson–Olson two-stage procedure, embedded with a multivariate Tobit estimator, was applied to a nationally representative dataset. The estimation results showed that off-farm employment plays a significantly negative role in forestland rent-in, at the 5% risk level. However, off-farm activities had no significant effect on forestland rent-out. Considering China’s specific situation, a reasonable explanation is that households hold forestland as a crucial means of social security against the risk of unemployment. In both rent-in and rent-out equations, high transaction costs are one of the main obstacles impeding forestland transfer. A remarkable finding was that forestland transactions occurred with a statistically significant factor equalization effect, which would be helpful to adjust the mismatched labor–land ratio and improve the land-use efficiency.
Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.
2017-09-01
Land Surface Temperature (LST) is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE). However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11) and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI) and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE) is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.
Directory of Open Access Journals (Sweden)
B. Godongwana
2010-01-01
Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.
Li, Changping
2015-07-22
In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.
Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.
Kumar, Dinesh; Kumar, P; Rai, K N
2017-11-01
This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Srisaipet, A.; Aryusuk, K.; Lilitchan, S.; Krisnangkura, K.
2007-01-01
Martin's equation, Δ sln g G=Δ sln g G o +zδ sln g G, is extended to cover vaporization free energy (Δ l g G). The extended equation is further expanded in terms of enthalpy and entropy and then used to correlate vaporization enthalpy (Δ l g H) and enthalpy of transfer from solution to gas (Δ sln g H). Data available in the literatures are used to validate and support the speculations derived from the proposed equation
Gusak, A. M.; Lyashenko, Yu. A.
1990-08-01
We employ numerical methods to study the equations of diffusion mass transfer in a two- phase zone, these equations derived from the general principles of nonequilibrium thermodynamics. We examine the case of a quasiequilibrium diffusion process in which the concentration, in grossly approximate terms, is a function exclusively of the single space variable and of time. The solutions of these equations proved to be unstable with respect to disruptions of the diffusions paths at the conoids.
A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations
Directory of Open Access Journals (Sweden)
Wenhua Zhang
2013-01-01
Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.
Hemmen, Andrea; Panagiotopoulos, Athanassios Z; Gross, Joachim
2015-06-11
In this study, we propose using an analytical equation of state for guiding molecular simulations in the grand canonical ensemble. Molecular simulations in the grand canonical ensemble deliver phase equilibrium properties with low statistical uncertainty. The entire phase envelope can be obtained when histograms of several simulations along the phase envelope are combined. In this study, we explore the use of an analytical equation of state for defining chemical potentials, temperatures, and intervals of molecule numbers for simulations in the grand canonical ensemble, such that the phase envelope is traced. We limit particle numbers to intervals and ensure even sampling of molecule numbers in each interval by applying a bias potential determined from transition-matrix sampling. The methodology is described for pure components and binary mixtures. We apply the simulation method to develop parameters of the transferable anisotropic Mie (TAMie) force field for ethers. We find that the partial charges optimized individually for diethyl ether and for dipropyl ether differ substantially from the partial charges optimized simultaneously to both substances. The concept of transferable partial charges is thus a significant assumption. For developing the (TAMie) force field, we constrained the partial charge to a range, where individually optimized partial charges were found.
Christensen, Martin Gram; Adler-Nissen, Jens; Løje, Hanne
2014-01-01
The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of food engineering such as equipment manufacture the use of predictive calculations, modelling activities and simulations for improved design is employed to a high degree. In food manufacture the use process calculations are seldom applied. Even though, the calculation of the...
Radiative Transfer Equation for Anisotropic Spherical Medium with Specular Reflective Index
International Nuclear Information System (INIS)
Elghazaly, A.
2009-01-01
Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with diffuse and angular dependent (specular) reflecting boundaries is solved using the Pomraning-Eddington approximation method. The angular dependent specular reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0, and 10 mfp and for different scattering albedo. Two different weight functions are used to verify the boundary conditions. Our results are compared with the available data and give an excellent agreement for thick and highly scattering media
DEFF Research Database (Denmark)
Christensen, Martin Gram
are conducted in food manufacture. The study provides a method where traditional processes can be calculated with a high precision by using an expanded 1st term approximation to the series expansion. This is an advantageous in terms of application in the industry where the solution can be incorporated...... in food manufacture. It is also hoped that the solutions provided and the insight to the [Fo-exp] will become a part of the engineering training for food science students. And most important, that the study will find application in the food industry.......The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of food engineering such as equipment manufacture the use of predictive...
International Nuclear Information System (INIS)
Jablonski, S.; Pantaleo, A.; Bauen, A.; Pearson, P.; Panoutsou, C.; Slade, R.
2008-01-01
How large is the potential demand for bio-heat in the UK? Whilst most research has focused on the supply of biomass for energy production, an understanding of the potential demand is crucial to the uptake of heat from bioenergy. We have designed a systematic framework utilising market segmentation techniques to assess the potential demand for biomass heat in the UK. First, the heat market is divided into relevant segments, characterised in terms of their final energy consumption, technological and fuel supply options. Second, the key technical, economic and organisational factors that affect the uptake of bioenergy in each heat segment are identified, classified and then analysed to reveal which could be strong barriers, which could be surmounted easily, and for which bioenergy heat represents an improvement compared to alternatives. The defined framework is applied to the UK residential sector. We identify provisionally the most promising market segments for bioenergy heat, and their current levels of energy demand. We find that, depending on the assumptions, the present potential demand for bio-heat in the UK residential sector ranges between 3% (conservative estimate) and 31% (optimistic estimate) of the total energy consumed in the heat market. (author)
Qiao, Yaobin; Qi, Hong; Chen, Qin; Ruan, Liming; Tan, Heping
2016-03-01
An efficient and robust method based on the complex-variable-differentiation method (CVDM) is proposed to reconstruct the distribution of optical parameters in two-dimensional participating media. An upwind-difference discrete-ordinate formulation of the time-domain radiative transfer equation is well established and used as forward model. The regularization term using generalized Gaussian Markov random field model is added in the objective function to overcome the ill-posed nature of the radiative inverse problem. The multi-start conjugate gradient method was utilized to accelerate the convergence speed of the inverse procedure. To obtain an accurate result and avoid the cumbersome formula of adjoint differentiation model, the CVDM was employed to calculate the gradient of objective function with respect to the optical parameters. All the simulation results show that the CVDM is efficient and robust for the reconstruction of optical parameters.
International Nuclear Information System (INIS)
Xiong Jinbiao; Koshizuka, Seiichi; Sakai, Mikio
2011-01-01
Highlights: → We selected and evaluated five two-equation eddy-viscosity turbulence models for modeling the separated and reattaching flow. → The behavior of the models in the simple flow is not consistent with that in the separated and reattaching flow. → The Abe-Kondoh-Nagano model is the best one among the selected model. → Application of the stress limiter and the Kato-Launder modification in the Abe-Kondoh-Nagano model helps to improve prediction of the peak mass transfer coefficient in the orifice flow. → The value of turbulent Schmidt number is investigated. - Abstract: The prediction of mass transfer rate is one of the key elements for estimation of the flow accelerated corrosion (FAC) rate. Three low Reynolds number (LRN) k-ε models (Lam-Bremhorst (LB), Abe-Kondoh-Nagano (AKN) and Hwang-Lin (HL)), one LRN k-ω (Wilcox, WX) model and the k-ω SST model are tested for the computation of the high Schmidt number mass transfer, especially in the flow through an orifice. The models are tested in the computation of three types of flow: (1) the fully developed pipe flow, (2) the flow over a backward facing step, (3) the flow through an orifice. The HL model shows a good performance in predicting mass transfer in the fully developed pipe flow but fails to give reliable prediction in the flow through an orifice. The WX model and the k-ω SST model underpredict the mass transfer rate in the flow types 1 and 3. The LB model underestimates the mass transfer in the flow type 1, but shows abnormal behavior at the reattaching point in type 3. Synthetically evaluating all the models in all the computed case, the AKN model is the best one; however, the prediction is still not satisfactory. In the evaluation in the flow over a backward facing step shows k-ω SST model shows superior performance. This is interpreted as an implication that the combination of the k-ε model and the stress limiter can improve the model behavior in the recirculation bubble. Both the
International Nuclear Information System (INIS)
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
Directory of Open Access Journals (Sweden)
Vasyl Chekurin
2017-01-01
Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.
Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.
2018-04-01
An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.
Reinhold, Sarah; Gegenfurtner, Andreas; Lewalter, Doris
2018-01-01
Social support and motivation to transfer are important components in conceptual models on transfer of training. Previous research indicates that both support and motivation influence transfer. To date, however, it is not yet clear if social support influences transfer of training directly, or if this influence is mediated by motivation to…
Mark A. Dietenberger; Charles R. Boardman
2014-01-01
Several years ago the Laplace transform solutions of Luikovâs differential equations were presented for one-dimensional heat and moisture transfer in porous hydroscopic orthotropic materials for the boundary condition of a gradual heat pulse applied to both surfaces of a flat slab. This paper presents calibration methods and data for the K-tester 637 (Lasercomp),...
Montejo, Ludguier D.; Klose, Alexander D.; Hielscher, Andreas H.
2010-01-01
We present the first algorithm for solving the equation of radiative transfer (ERT) in the frequency domain (FD) on three-dimensional block-structured Cartesian grids (BSG). This algorithm allows for accurate modeling of light propagation in media of arbitrary shape with air-tissue refractive index mismatch at the boundary at increased speed compared to currently available structured grid algorithms. To accurately model arbitrarily shaped geometries the algorithm generates BSGs that are finely discretized only near physical boundaries and therefore less dense than fine grids. We discretize the FD-ERT using a combination of the upwind-step method and the discrete ordinates (SN) approximation. The source iteration technique is used to obtain the solution. We implement a first order interpolation scheme when traversing between coarse and fine grid regions. Effects of geometry and optical parameters on algorithm performance are evaluated using numerical phantoms (circular, cylindrical, and arbitrary shape) and varying the absorption and scattering coefficients, modulation frequency, and refractive index. The solution on a 3-level BSG is obtained up to 4.2 times faster than the solution on a single fine grid, with minimal increase in numerical error (less than 5%). PMID:21258514
Hornišová, K; Billik, P
2014-01-01
Traditional technique of horn equation solved by transfer matrices as a model of vibration of ultrasonic systems consisting of sectional transducer, horn and load is discussed. Expression of vibration modes as a ratio of solutions of two Schrödinger equations gives better insight to the structure of a transfer matrix and properties of amplitudes of displacement and strain, and enables more systematic search for analytic solutions. Incorrectness of impedance matrix method and of equivalent circuit method on one hand and correctness and advantages of transfer matrix method in avoiding numerical artifacts and revealing the real features of the model on the other hand are demonstrated on examples. Discontinuous dependence of the nth resonant value on parameters of ultrasonic system, recently described in Sturm-Liouville theory, and consequently, a jump from half-wave to full-wave mode, is observed in a transducer model. Copyright © 2013 Elsevier B.V. All rights reserved.
Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I
2018-04-16
Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.
International Nuclear Information System (INIS)
Damiano, B.; March-Leuba, J.A.; Euler, J.A.
1990-01-01
This paper describes a technique for calculating boiling water reactor (BWR) behavior during steady-state limit-cycle oscillations. An approximate solution is obtained from the application of Galerkin's method to a BWR dynamic model consisting of the point-kinetics equations and the LAPUR-calculated power-to-reactivity feedback-transfer function. The approximate-solution technique is described, and comparisons of approximate solutions with numerical results and measured data are given. 7 refs., 5 figs
Tang, Yundong; Flesch, Rodolfo C. C.; Jin, Tao
2018-01-01
Magnetic nanoparticle (MNP) hyperthermia ablates malignant cells by heating the region of interest when MNPs are subjected to an external alternating magnetic field. The energy density to be dissipated into heat, and consequently the temperature profile during treatment, depends on the distribution of MNPs within the tumoral region. This paper uses numerical models to evaluate the temporal and spatial temperature distributions inside a tumor when intratumoral injection of MNPs is considered. To this end, the theories of mass transfer and diffusion in interstitial tissue are combined with Rosensweig’s theory and Pennes bio-heat transfer equation, and the finite element method is used for analyzing the temperature field under different scenarios. Simulation results demonstrate that the treatment temperature field strongly depends on factors, such as the injection method, particle size, injection concentration and injection dose. However, the maximal temperature reached during hyperthermia and the effective treatment area are difficult to control. In order to obtain better treatment effects, this paper investigates a solution that uses a kind of material with low Curie temperature and the results show that the effective treatment area of hyperthermia can be significantly improved using this type of MNP.
National Research Council Canada - National Science Library
Kosuge, Shingo
2000-01-01
The problem of heat transfer and temperature distribution in a binary mixture of rarefied gases between two parallel plates with different temperatures is investigated on the basis of kinetic theory...
International Nuclear Information System (INIS)
Jin Yaqiu; Liang Zichang
2005-01-01
To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed
Energy Technology Data Exchange (ETDEWEB)
Mikhailov, Andrei [California Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125 (United States)], E-mail: andrei@theory.caltech.edu; Schaefer-Nameki, Sakura [Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH (United Kingdom)], E-mail: ss299@theory.caltech.edu
2008-10-11
Integrability of the string worldsheet theory in AdS{sub 5}xS{sup 5} is related to the existence of a flat connection depending on the spectral parameter. The transfer matrix is the open-ended Wilson line of this flat connection. We study the product of transfer matrices in the near-flat space expansion of the AdS{sub 5}xS{sup 5} string theory in the pure spinor formalism. The natural operations on Wilson lines with insertions are described in terms of r- and s-matrices satisfying a generalized classical Yang-Baxter equation. The formalism is especially transparent for infinite or closed Wilson lines with simple gauge invariant insertions.
Zhokh, Alexey A.; Strizhak, Peter E.
2018-04-01
The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.
Thermal non-equilibrium heat transfer in a porous cavity in the presence of bio-chemical heat source
Directory of Open Access Journals (Sweden)
Nazari Mohsen
2015-01-01
Full Text Available This paper is concerned with thermal non-equilibrium natural convection in a square cavity filled with a porous medium in the presence of a biomass which is transported in the cavity. The biomass can consume a secondary moving substrate. The physics of the presented problem is related to the analysis of heat and mass transfer in a composting process that controlled by internal heat generation. The intensity of the bio-heat source generated in the cavity is equal to the rate of consumption of the substrate by the biomass. It is assumed that the porous medium is homogeneous and isotropic. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. A simplified Monod model is introduced along with the governing equations to describe the consumption of the substrate by the biomass. In other word, the transient biochemical heat source which is dependent on a solute concentration is considered in the energy equations. Investigation of the biomass activity and bio-chemical heat generation in the case of thermal non-equilibrium assumption has not been considered in the literature and they are open research topics. The effects of thermal non-equilibrium model on heat transfer, flow pattern and biomass transfer are investigated. The effective parameters which have a direct impact on the generated bio-chemical heat source are also presented. The influences of the non-dimensional parameters such as fluid-to-solid conductivity ratio on the temperature distribution are presented.
Angulo, Gonzalo; Jedrak, Jakub; Ochab-Marcinek, Anna; Pasitsuparoad, Pakorn; Radzewicz, Czesław; Wnuk, Paweł; Rosspeintner, Arnulf
2017-06-28
The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium for which a large number of theoretical descriptions have been used in the past. An accurate description of these reactions requires knowing the potential energy surface and the friction felt by the reactants. Most of these theories start from the Langevin equation to derive the dynamics, but there are few examples comparing it with experiments. Here we explore the applicability of a Generalized Langevin Equation (GLE) with an arbitrary potential and a non-Markovian friction. To this end, we have performed broadband fluorescence measurements with sub-picosecond time resolution of a covalently linked organic electron donor-acceptor system in solvents of changing viscosity and dielectric permittivity. In order to establish the free energy surface (FES) of the reaction, we resort to stationary electronic spectroscopy. On the other hand, the dynamics of a non-reacting substance, Coumarin 153, provide the calibrating tool for the non-Markovian friction over the FES, which is assumed to be solute independent. A simpler and computationally faster approach uses the Generalized Smoluchowski Equation (GSE), which can be derived from the GLE for pure harmonic potentials. Both approaches reproduce the measurements in most of the solvents reasonably well. At long times, some differences arise from the errors inherited from the analysis of the stationary solvatochromism and at short times from the excess excitation energy. However, whenever the dynamics become slow, the GSE shows larger deviations than the GLE, the results of which always agree qualitatively with the measured dynamics, regardless of the solvent viscosity or dielectric properties. The method applied here can be used to predict the dynamics of any other reacting system, given the FES parameters and solvent dynamics are provided. Thus no fitting parameters enter the GLE simulations, within the applicability
Menezes de Oliveira, Marilia; Wen, Peng; Ahfock, Tony
2016-09-01
This paper focuses on electroconvulsive therapy (ECT) and head models to investigate temperature profiles arising when anisotropic thermal and electrical conductivities are considered in the skull layer. The aim was to numerically investigate the threshold for which this therapy operates safely to the brain, from the thermal point of view. A six-layer spherical head model consisting of scalp, fat, skull, cerebro-spinal fluid, grey matter and white matter was developed. Later on, a realistic human head model was also implemented. These models were built up using the packages from COMSOL Inc. and Simpleware Ltd. In these models, three of the most common electrode montages used in ECT were applied. Anisotropic conductivities were derived using volume constraint and included in both spherical and realistic head models. The bio-heat transferring problem governed by Laplace equation was solved numerically. The results show that both the tensor eigenvalues of electrical conductivity and the electrode montage affect the maximum temperature, but thermal anisotropy does not have a significant influence. Temperature increases occur mainly in the scalp and fat, and no harm is caused to the brain by the current applied during ECT. The work assures the thermal safety of ECT and also provides a numerical method to investigate other non-invasive therapies. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
M. Gantri
2014-01-01
Full Text Available The present paper gives a new computational framework within which radiative transfer in a varying refractive index biological tissue can be studied. In our previous works, Legendre transform was used as an innovative view to handle the angular derivative terms in the case of uniform refractive index spherical medium. In biomedical optics, our analysis can be considered as a forward problem solution in a diffuse optical tomography imaging scheme. We consider a rectangular biological tissue-like domain with spatially varying refractive index submitted to a near infrared continuous light source. Interaction of radiation with the biological material into the medium is handled by a radiative transfer model. In the studied situation, the model displays two angular redistribution terms that are treated with Legendre integral transform. The model is used to study a possible detection of abnormalities in a general biological tissue. The effect of the embedded nonhomogeneous objects on the transmitted signal is studied. Particularly, detection of targets of localized heterogeneous inclusions within the tissue is discussed. Results show that models accounting for variation of refractive index can yield useful predictions about the target and the location of abnormal inclusions within the tissue.
da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques
2003-12-01
Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.
Xamán, J.; Zavala-Guillén, I.; Hernández-López, I.; Uriarte-Flores, J.; Hernández-Pérez, I.; Macías-Melo, E. V.; Aguilar-Castro, K. M.
2018-03-01
In this paper, we evaluated the convergence rate (CPU time) of a new mathematical formulation for the numerical solution of the radiative transfer equation (RTE) with several High-Order (HO) and High-Resolution (HR) schemes. In computational fluid dynamics, this procedure is known as the Normalized Weighting-Factor (NWF) method and it is adopted here. The NWF method is used to incorporate the high-order resolution schemes in the discretized RTE. The NWF method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) technique for the calculations of a two-dimensional cavity with emitting-absorbing-scattering gray media using the discrete ordinates method. Six parameters, viz. the grid size, the order of quadrature, the absorption coefficient, the emissivity of the boundary surface, the under-relaxation factor, and the scattering albedo are considered to evaluate ten schemes. The results showed that using the DC method, in general, the scheme that had the lowest CPU time is the SOU. In contrast, with the results of theDC procedure the CPU time for DIAMOND and QUICK schemes using the NWF method is shown to be, between the 3.8 and 23.1% faster and 12.6 and 56.1% faster, respectively. However, the other schemes are more time consuming when theNWFis used instead of the DC method. Additionally, a second test case was presented and the results showed that depending on the problem under consideration, the NWF procedure may be computationally faster or slower that the DC method. As an example, the CPU time for QUICK and SMART schemes are 61.8 and 203.7%, respectively, slower when the NWF formulation is used for the second test case. Finally, future researches to explore the computational cost of the NWF method in more complex problems are required.
Energy Technology Data Exchange (ETDEWEB)
Azevedo, Fabio Souto de, E-mail: fabio.azevedo@ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Inst. de Matematica; Sauter, Esequia, E-mail: esequia.sauter@canoas.ifrs.edu.b [Instituto Federal do Rio Grande do Sul (IFRS), Canoas, RS (Brazil); Thompson, Mark; Vilhena, Marco Tulio B., E-mail: mark.thompson@mat.ufrgs.b, E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2011-07-01
In this work we apply the Green Function Decomposition Method the radiative transport equation in a slab. The method consists in converting the radiative transport equation into a integral equation and projecting the integral operators involved into a finite dimensional space. This methodology does not involve an a priori discretization on the angular variable {mu}, requiring only that the kernel is numerically integrated on {mu}. Numerical results are provided for isotropic, linearly anisotropic, and Rayleigh scattering near the unitary albedo. (author)
Directory of Open Access Journals (Sweden)
Deimel Christian
2014-03-01
Full Text Available The most common method for simulating cavitating flows is using the governing flow equations in a form with a variable density and treats both phases as incompressible in combination with a transport equation for the vapour volume fraction. This approach is commonly referred to as volume of fluid method (VoF. To determine the transition of the liquid phase to vapour and vice versa, a relation for the mass transfer is needed. Several models exist, based on slightly differing physical assumptions, for example derivation from the dynamics of single bubbles or large bubble clusters. In our simulation, we use the model of Sauer and Schnerr which is based on the Rayleigh equation. One common problem of all mass transfer models is the use of model constants which often need to be tuned with regard to the examined problem. Furthermore, these models often overpredict the turbulent dynamic viscosity in the two-phase region which counteracts the development of transient shedding behaviour and is compensated by the modification proposed by Reboud. In the presented study, we vary the parameters of the Sauer-Schnerr model with Reboud modification that we implemented into an OpenFOAM solver to match numerical to experimental data.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019
Directory of Open Access Journals (Sweden)
A. D. Kliukvin
2014-01-01
Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and
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.
Mizuno, Yuta; Arasaki, Yasuki; Takatsuka, Kazuo
2016-01-01
A complicated yet interesting induced photon emission can take place by a nonadiabatic intramolecular electron transfer system like LiF under an intense CW laser [Y. Arasaki, S. Scheit, and K. Takatsuka, J. Chem. Phys. 138, 161103 (2013)]. Behind this phenomena, the crossing point between two potential energy curves of covalent and ionic natures in diabatic representation is forced to oscillate, since only the ionic potential curve is shifted significantly up and down repeatedly (called the Dynamical Stark effect). The wavepacket pumped initially to the excited covalent potential curve frequently encounters such a dynamically moving crossing point and thereby undergoes very complicated dynamics including wavepacket bifurcation and deformation. Intramolecular electron transfer thus driven by the coupling between nonadiabatic state-mixing and laser fields induces irregular photon emission. Here in this report we discuss the complicated spectral features of this kind of photon emission induced by infrared laser. In the low frequency domain, the photon emission is much more involved than those of ultraviolet/visible driving fields, since many field-dressed states are created on the ionic potential, which have their own classical turning points and crossing points with the covalent counterpart. To analyze the physics behind the phenomena, we develop a perturbation theoretic approach to the Riccati equation that is transformed from coupled first-order linear differential equations with periodic coefficients, which are supposed to produce the so-called Floquet states. We give mathematical expressions for the Floquet energies, frequencies, and intensities of the photon emission spectra, and the cutoff energy of their harmonic generation. Agreement between these approximate quantities and those estimated with full quantum calculations is found to be excellent. Furthermore, the present analysis provides with notions to facilitate deeper understanding for the physical and
Directory of Open Access Journals (Sweden)
Wazir Muhammad
Full Text Available The importance of Atomic Form Factors (f is well-known to the scientific community. Tabulated values for f are mostly used in calculating cross-sections and Monte Carlo sampling for the coherent scattering of photons. The uses of these values are subjected to different approximations and interpolation techniques because the available data points for f in the literature for specified momentum-transfer-grids are very limited. In order to make it easier to accurately use the tabulated data, a mathematical expression for f functions would be a great achievement. Therefore, the current study was designed to suggest an empirical expression for the f functions. In the results, an empirical equation for Hubbell's tabulated data for f is created in the momentum transfer range, q=0-50 Å(-1 for the elements in the range 1 ≤ Z ≤ 30. The number of applied parameters was seven. The fitting to f showed that the maximum deviation was within 3%, 4% and 5% for the element having, Z=1-11, Z=12-22 and Z=23-30, respectively, while the average deviations were within 0.3-2.25% for all elements (i.e., Z=1-30. The values generated by the analytical equation were used in the Monte Carlo code instead of Hubbell's tabulated values. The statistical noise in the Probability Distribution Functions of coherently scattered photons was efficiently removed. Furthermore, it also reduced the dependence on different interpolation techniques and approximations, and on the use of large tabulated data for f with the specified elements.
Muhammad, Wazir; Lee, Sang Hoon
2013-01-01
The importance of Atomic Form Factors (f) is well-known to the scientific community. Tabulated values for f are mostly used in calculating cross-sections and Monte Carlo sampling for the coherent scattering of photons. The uses of these values are subjected to different approximations and interpolation techniques because the available data points for f in the literature for specified momentum-transfer-grids are very limited. In order to make it easier to accurately use the tabulated data, a mathematical expression for f functions would be a great achievement. Therefore, the current study was designed to suggest an empirical expression for the f functions. In the results, an empirical equation for Hubbell's tabulated data for f is created in the momentum transfer range, q = 0–50 Å−1 for the elements in the range 1≤ Z ≤30. The number of applied parameters was seven. The fitting to f showed that the maximum deviation was within 3%, 4% and 5% for the element having, Z = 1–11, Z = 12–22 and Z = 23–30, respectively, while the average deviations were within 0.3–2.25% for all elements (i.e., Z = 1–30). The values generated by the analytical equation were used in the Monte Carlo code instead of Hubbell’s tabulated values. The statistical noise in the Probability Distribution Functions of coherently scattered photons was efficiently removed. Furthermore, it also reduced the dependence on different interpolation techniques and approximations, and on the use of large tabulated data for f with the specified elements. PMID:23936339
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
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
Equations of macrotransport in reactor fuel assemblies
International Nuclear Information System (INIS)
Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.
1986-01-01
The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given
Vrentas, James S
2013-01-01
The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedime...
Kakac, Sadik; Pramuanjaroenkij, Anchasa
2014-01-01
Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....
Resonance regions of extended Mathieu equation
Semyonov, V. P.; Timofeev, A. V.
2016-02-01
One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system is based on parametric resonance. Initial stage of this process can de described by equation similar to Mathieu equation. Such equation is studied by analytical and numerical approach. The numerical solution of the extended Mathieu equation is obtained for a wide range of parameter values. Boundaries of resonance regions, growth rates of amplitudes and times of onset are obtained. The energy transfer between the degrees of freedom of dusty plasma system can occur over a wide range of frequencies.
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
Discontinuous Galerkin for the Radiative Transport Equation
Guermond, Jean-Luc
2013-10-11
This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.
Kumar, Dinesh; Singh, Surjan; Rai, K. N.
2016-06-01
In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129-162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Constitutive equations for two-phase flows
International Nuclear Information System (INIS)
Boure, J.A.
1974-12-01
The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Influence of Heat Sources and Relaxation Time on Temperature Distribution in Tissues
Sharma S.; Sharma K.
2014-01-01
In the present study, the temperature fluctuations in tissues based on Penne’s bio-heat transfer equation is investigated by applying the Laplace and Hankel transforms. To get the solution in a physical form, a numerical inversion technique has been applied. The temporal and spatial distribution of temperature is investigated with the effect of relaxation time and is presented graphically.
Integration of Chandrasekhar's integral equation
International Nuclear Information System (INIS)
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Adaptive integral equation methods in transport theory
International Nuclear Information System (INIS)
Kelley, C.T.
1992-01-01
In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
General particle transport equation. Final report
International Nuclear Information System (INIS)
Lafi, A.Y.; Reyes, J.N. Jr.
1994-12-01
The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Particle methods for Boltzmann equation
International Nuclear Information System (INIS)
Hermeline, F.
1985-05-01
This work is aimed at showing how to discretize an equation such as Boltzmann equation in its most general form, by particle methods. Then method is applied to some equations of plasma physics which appear as peculiar cases of Boltzmann equation, such as Vlasov equation, Bhatnager-Gross-Krook equation, Fokker-Planck equation and neutron transport equation [fr
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Fay, Temple H.
2002-01-01
We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…
A Comparison of IRT Equating and Beta 4 Equating
Kim, Dong-In; Brennan, Robert; Kolen, Michael
2005-01-01
Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…
HEAT-MASS TRANSFER IN MOVING MELT
Directory of Open Access Journals (Sweden)
R. I. Yesman
2005-01-01
Full Text Available The paper gives mathematical formation and solution of the heat-mass transfer problem when liquid metals are flowing in the channels of complicated geometry. The problem is solved with the help of numerical methods. A method of control volume is used for finite-difference approximation of transfer equations. The research results can be applied for execution of a numerical experiment while investigating heat-mass transfer in liquid-metal heat-transfer and reological media.
Stability of stationary inverse transport equation in diffusion scaling
Chen, Ke; Li, Qin; Wang, Li
2018-02-01
We consider the inverse problem of reconstructing the optical parameters for the stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales, characterized by the magnitude of a dimensionless parameter—the Knudsen number ( \
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems. 2009 Elsevier Ltd. All rights reserved.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
The 'golden' algebraic equations
International Nuclear Information System (INIS)
Stakhov, A.; Rozin, B.
2006-01-01
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Larsen, Mads Grenaa; Nørgaard, Mads Frid; Hansen, Manjarita
2013-01-01
This project seeks to highlight some of the criticisms given towards the OECD Transfer Pricing Guidelines and the challenges Danish companies experience by pricing their goods and the problems this causes for trade. The project is based on a series of interviews that represent the different agents who are operating in Transfer Pricing business. These interviews, combined with the Transfer Pricing Guidelines, gives us the basis to analyse the challenges we want to clarify based on the hypothes...
DEFF Research Database (Denmark)
Rohde, Carsten; Rossing, Christian Plesner
trade internally as the units have to decide what prices should be paid for such inter-unit transfers. One important challenge is to uncover the consequences that different transfer prices have on the willingness in the organizational units to coordinate activities and trade internally. At the same time...... the determination of transfer price will affect the size of the profit or loss in the organizational units and thus have an impact on the evaluation of managers‟ performance. In some instances the determination of transfer prices may lead to a disagreement between coordination of the organizational units...
Asymptotic behavior for cross coupled parabolic equations
Directory of Open Access Journals (Sweden)
Yingzhen XUE
2017-04-01
Full Text Available In order to better describe the heat transfer process of three kinds of mixed substances, namely the reaction of the reactants in the three chemical reactions, a class of three variable cross coupling with non parabolic equations of the whole existence of local source and non local boundary flow and the finite time blow up problem with breaking method for the solution of the first commonly used feature value structure are studied. The structure of the equations of the upper and lower solutions by using the method of ordinary differential equation reference is broken, with comparison theorem, the proof shows that obtained by local source power function and exponential function of parabolic equations is broken, with the sufficient conditions for global existence of clegerate purubolic equations solutions cross coupled by local source power function and non local sources exponential function are proved, as soon as the solution of blowing up in finite time degradation of non local sources of cross coupling, providing better support for the theory of heat transfer and chemical reaction problem.
fractional differential equations
Indian Academy of Sciences (India)
We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Indian Academy of Sciences (India)
role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...
Partial differential equations
Indian Academy of Sciences (India)
been a regular stream of high quality work done in these areas. Talking of elliptic partial differen- tial equations, important contributions have been made in the ...... [6] Evans L C 1992 Periodic homogenisation of certain fully nonlinear partial differential equations; Proc. Roy. Soc. Edinburgh Sect. A 120 No. 3–4, 245–265.
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
DEFF Research Database (Denmark)
Rohde, Carsten; Rossing, Christian Plesner
trade internally as the units have to decide what prices should be paid for such inter-unit transfers. One important challenge is to uncover the consequences that different transfer prices have on the willingness in the organizational units to coordinate activities and trade internally. At the same time...
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano
2017-03-22
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
DEFF Research Database (Denmark)
Nielsen, Søren Bo
2014-01-01
Against a background of rather mixed evidence about transfer pricing practices in multinational enterprises (MNEs) and varying attitudes on the part of tax authorities, this paper explores how multiple aims in transfer pricing can be pursued across four different transfer pricing regimes. A MNE has...... a production subsidiary in one country, from where it sells the produced good locally as well as to a sales subsidiary in a second country. The latter subsidiary is engaged in duopolistic competition with a local competitor. The MNE has two aims in setting the transfer price: strategic delegation and tax...... minimization. We examine the extent to which the four transfer pricing regimes we set up allow the MNE to pursue these aims. While neither strategic delegation nor tax minimization will be eliminated, trade-offs are inevitable, albeit to varying degree....
DEFF Research Database (Denmark)
Nielsen, Søren Bo
2014-01-01
a production subsidiary in one country, from where it sells the produced good locally as well as to a sales subsidiary in a second country. The latter subsidiary is engaged in duopolistic competition with a local competitor. The MNE has two aims in setting the transfer price: strategic delegation and tax......Against a background of rather mixed evidence about transfer pricing practices in multinational enterprises (MNEs) and varying attitudes on the part of tax authorities, this paper explores how multiple aims in transfer pricing can be pursued across four different transfer pricing regimes. A MNE has...... minimization. We examine the extent to which the four transfer pricing regimes we set up allow the MNE to pursue these aims. While neither strategic delegation nor tax minimization will be eliminated, trade-offs are inevitable, albeit to varying degree....
Heat transfer from rough surfaces
International Nuclear Information System (INIS)
Dalle Donne, M.
1977-01-01
Artificial roughness is often used in nuclear reactors to improve the thermal performance of the fuel elements. Although these are made up of clusters of rods, the experiments to measure the heat transfer and friction coefficients of roughness are performed with single rods contained in smooth tubes. This work illustrated a new transformation method to obtain data applicable to reactor fuel elements from these annulus experiments. New experimental friction data are presented for ten rods, each with a different artificial roughness made up of two-dimensional rectangular ribs. For each rod four tests have been performed, each in a different outer smooth tube. For two of these rods, each for two different outer tubes, heat transfer data are also given. The friction and heat transfer data, transformed with the present method, are correlated by simple equations. In the paper, these equations are applied to a case typical for a Gas Cooled Fast Reactor fuel element. (orig.) [de
Neutronics methods for thermal radiative transfer
International Nuclear Information System (INIS)
Larsen, E.W.
1988-01-01
The equations of thermal radiative transfer are time discretized in a semi-implicit manner, yielding a linear transport problem for each time step. The governing equation in this problem has the form of a neutron transport equation with fission but no scattering. Numerical methods are described, whose origins lie in neutron transport, and that have been successfully adapted to this new problem. Acceleration methods that have been developed specifically for the radiative transfer problem, but may have generalizations applicable in neutronics problems, are also discussed
Ordinary differential equations
Ince, Edward Lindsay
1956-01-01
The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a diffe
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
–. (4)) by applying the exp-function method. The computer symbolic systems such as. Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Solutions of (N + 1)-dimensional generalized Boussinesq equation.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Department of Homeland Security — ixed rail transit external system transfers for systems within the Continental United States, Alaska, Hawaii, the District of Columbia, and Puerto Rico. The modes of...
Ordinary differential equations.
Lebl, Jiří
2013-01-01
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.
Indian Academy of Sciences (India)
continuous medium is μgrav ≡ μ + 3p/c2. Particular versions of this equation had been obtained earlier, at centers of symmetry by Tolman and Synge (see Raychaud- .... (8) by l ˙l and integrate to find. 3( ˙l)2 − κμl2 − Λl2 = const. (10). This is just the Friedmann equation which governs the time evolution of FLRW universe ...
Microscale and nanoscale heat transfer fundamentals and engineering applications
Sobhan, CB
2008-01-01
Preface Introduction to Microscale Heat Transfer Microscale Heat Transfer: A Recent Avenue in Energy Transport State of the Art: Some Introductory Remarks Overview of Microscale Transport Phenomena Discussions on Size-Effect Behavior Fundamental Approach for Microscale Heat Transfer Introduction to Engineering Applications of Microscale Heat Transfer Microscale Heat Conduction Review of Conduction Heat Transfer Conduction at the Microscale Space and Timescales Fundamental Approach Thermal Conductivity Boltzmann Equation and Phonon Transport Conduction in Thin Films
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
The Bernoulli-Poiseuille Equation.
Badeer, Henry S.; Synolakis, Costas E.
1989-01-01
Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)
Soliton multidimensional equations and integrable evolutions preserving Laplace's equation
International Nuclear Information System (INIS)
Fokas, A.S.
2008-01-01
The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Directory of Open Access Journals (Sweden)
G. Samchuk
2017-06-01
Full Text Available The article deals with the definition of traffic parameters that ensure the minimum value of the transfer waiting time for passengers. On the basis of experimental studies results, a regression equation to determine the probability of realisation of the planned transfer between a pair of vehicles was proposed. Using the identified regression equation, the transfer waiting time can be assessed for any headway exceeding 7,5 min.
Smith, Nanette R.
1995-01-01
The objective of this summer's work was to attempt to enhance Technology Application Group (TAG) ability to measure the outcomes of its efforts to transfer NASA technology. By reviewing existing literature, by explaining the economic principles involved in evaluating the economic impact of technology transfer, and by investigating the LaRC processes our William & Mary team has been able to lead this important discussion. In reviewing the existing literature, we identified many of the metrics that are currently being used in the area of technology transfer. Learning about the LaRC technology transfer processes and the metrics currently used to track the transfer process enabled us to compare other R&D facilities to LaRC. We discuss and diagram impacts of technology transfer in the short run and the long run. Significantly, it serves as the basis for analysis and provides guidance in thinking about what the measurement objectives ought to be. By focusing on the SBIR Program, valuable information regarding the strengths and weaknesses of this LaRC program are to be gained. A survey was developed to ask probing questions regarding SBIR contractors' experience with the program. Specifically we are interested in finding out whether the SBIR Program is accomplishing its mission, if the SBIR companies are providing the needed innovations specified by NASA and to what extent those innovations have led to commercial success. We also developed a survey to ask COTR's, who are NASA employees acting as technical advisors to the SBIR contractors, the same type of questions, evaluating the successes and problems with the SBIR Program as they see it. This survey was developed to be implemented interactively on computer. It is our hope that the statistical and econometric studies that can be done on the data collected from all of these sources will provide insight regarding the direction to take in developing systematic evaluations of programs like the SBIR Program so that they can
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Low-Flow Film Boiling Heat Transfer on Vertical Surfaces
DEFF Research Database (Denmark)
Munthe Andersen, J. G.; Dix, G. E.; Leonard, J. E.
1976-01-01
The phenomenon of film boiling heat transfer for high wall temperatures has been investigated. Based on the assumption of laminar flow for the film, the continuity, momentum, and energy equations for the vapor film are solved and a Bromley-type analytical expression for the heat transfer...... length, an average film boiling heat transfer coefficient is obtained....
A Model For Non-Fickian Moisture Transfer In Wood
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2004-01-01
A model for non-Fickian moisture transfer in wood is presented. The model considers the transfer of water vapour separate from the transfer of bound water. These two components are linked by an equation describing the sorption on the cell wall level. Hereby, a formulation capable of describing kn...
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
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...
Conservation laws for equations related to soil water equations
C. M. Khalique; F. M. Mahomed
2005-01-01
We obtain all nontrivial conservation laws for a class of ( 2+1 ) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Conservation laws for equations related to soil water equations
Directory of Open Access Journals (Sweden)
Khalique C. M.
2005-01-01
Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Abstract. In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian ...
International Nuclear Information System (INIS)
Boury, C.
1986-01-01
This paper emphasizes in the specific areas of design, engineering and component production. This paper presents what Framatome has to offer in these areas and its export oriented philosophy. Then, a typical example of this technology transfer philosophy is the collaboration with the South Korean firm, Korea Heavy Industries Corporation (KHIC) for the supply of KNU 9 and KNU 10 power stations
Nucleate boiling heat transfer
Energy Technology Data Exchange (ETDEWEB)
Saiz Jabardo, J.M. [Universidade da Coruna (Spain). Escola Politecnica Superior], e-mail: mjabardo@cdf.udc.es
2009-07-01
Nucleate boiling heat transfer has been intensely studied during the last 70 years. However boiling remains a science to be understood and equated. In other words, using the definition given by Boulding, it is an 'insecure science'. It would be pretentious of the part of the author to explore all the nuances that the title of the paper suggests in a single conference paper. Instead the paper will focus on one interesting aspect such as the effect of the surface microstructure on nucleate boiling heat transfer. A summary of a chronological literature survey is done followed by an analysis of the results of an experimental investigation of boiling on tubes of different materials and surface roughness. The effect of the surface roughness is performed through data from the boiling of refrigerants R-134a and R-123, medium and low pressure refrigerants, respectively. In order to investigate the extent to which the surface roughness affects boiling heat transfer, very rough surfaces (4.6 {mu}m and 10.5 {mu}m ) have been tested. Though most of the data confirm previous literature trends, the very rough surfaces present a peculiar behaviour with respect to that of the smoother surfaces (Ra<3.0 {mu}m). (author)
African Journals Online (AJOL)
Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Indian Academy of Sciences (India)
Design of Four-Link Mechanisms. Ashitava Ghosal. Ashitava Ghosal is a. Professor in the Depart- ment of Mechanical. Engineering and Centre for Product Design, IISc,. Bangalore. His research interests are in the areas of analysis and design of mechanisms and ... Freudenstein's thesis and the equation named af- ter him.
Indian Academy of Sciences (India)
Amalkumar Raychaudhuri's remarkable paper [1] for the first time gave a general derivation of the fundamental equation of gravitational attraction for pressure- free matter, showing the repulsive nature of a positive cosmological constant, and underlying the basic singularity theorem (see below). He used special coordinates.
Solving Equations Applet Project
Thatcher, Kimberly
2011-01-01
The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
Department of Civil Engineering. University of Nigeria Nsukka. ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
International Nuclear Information System (INIS)
Tian Chou.
1991-05-01
It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2007-01-01
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
International Nuclear Information System (INIS)
Anon.
1977-01-01
Illustrated by the example of the FRG's nuclear energy exports, it is shown that the nuclear technology transfer leads to new dimensions of intergovernmental relations, which hold within themselves on account of multiple state-to-state, scientific, industrial and - last but not least - personal contacts the chance of far-reaching friendships between countries and people. If the chance is taken, this can also be seen as an important contribution towards maintaining the peace. (orig.) [de
Dicko, Ali Hamadi; Liu, Tiantian; Gilles, Benjamin; Kavan, Ladislav; Faure, François; Palombi, Olivier; Cani, Marie-Paule
2013-01-01
International audience; Characters with precise internal anatomy are important in film and visual effects, as well as in medical applications. We propose the first semi-automatic method for creating anatomical structures, such as bones, muscles, viscera and fat tissues. This is done by transferring a reference anatomical model from an input template to an arbitrary target character, only defined by its boundary representation (skin). The fat distribution of the target character needs to be sp...
Pan, Daniel; Wilson, Karl A; Tan-Wilson, Anna
2017-01-01
The technique described here, transfer zymography, was developed to overcome two limitations of conventional zymography. When proteolytic enzymes are resolved by nonreducing SDS-PAGE into a polyacrylamide gel with copolymerized protein substrate, the presence of the protein substrate can result in anomalous, often slower, migration of the protease and an estimated mass higher than its actual mass. A further drawback is that the presence of a high background of substrate protein interferes with proteomic analysis of the protease band by excision, tryptic digestion, and LC-MS/MS analysis. In transfer zymography, the proteolytic enzymes are resolved by conventional nonreducing SDS-PAGE, without protein substrate in the gel. The proteins in the resolving gel are then electrophoretically transferred to a receiving gel that contains the protein substrate, by a process similar to western blotting. The receiving gel is then processed in a manner similar to conventional zymography. SDS is removed by Triton X-100 and incubated in conditions suitable for the proteolytic activity. After protein staining, followed by destaining, bands representing regions with active protease are visualized as clear bands in a darkly stained background. For proteomic analysis, electrophoresis is carried out simultaneously on a second resolving gel, and the bands corresponding to the clear regions in the receiving gel after zymogram development are excised for proteomic analysis.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
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.
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Lidar equation for ocean surface and subsurface.
Josset, Damien; Zhai, Peng-Wang; Hu, Yongxiang; Pelon, Jacques; Lucker, Patricia L
2010-09-27
The lidar equation for ocean at optical wavelengths including subsurface signals is revisited using the recent work of the radiative transfer and ocean color community for passive measurements. The previous form of the specular and subsurface echo term are corrected from their heritage, which originated from passive remote sensing of whitecaps, and is improved for more accurate use in future lidar research. A corrected expression for specular and subsurface lidar return is presented. The previous formalism does not correctly address angular dependency of specular lidar return and overestimates the subsurface term by a factor ranging from 89% to 194% for a nadir pointing lidar. Suggestions for future improvements to the lidar equation are also presented.
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Nonelliptic Partial Differential Equations
Tartakoff, David S
2011-01-01
This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this tec
Kuznetsov equation with variable coefficients
Indian Academy of Sciences (India)
like solutions of the PDE in (2+1) dimension with variable coefficients. ... Shivamoggi [12] gives only four polynomial conservation laws of the ZK equation ..... [3] P J Olver, Application of Lie group to differential equation (Springer, New York,.
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Functional equations for Feynman integrals
International Nuclear Information System (INIS)
Tarasov, O.V.
2011-01-01
New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains
Classical solutions of quasielliptic equations
International Nuclear Information System (INIS)
Belonosov, V S
1999-01-01
Fundamental solutions of quasielliptic equations are constructed; this allows the author to develop a relevant theory of volume potentials, establish estimates for the Holder norms of solutions of equations with constant coefficients, and extend them after that to equations with variable coefficients. As a result, sharp Schauder-type interior estimates are obtained, of which the well-known classical results for elliptic and parabolic equations are special cases
Obtention of an empirical equation for annular channels
International Nuclear Information System (INIS)
Diaz H, C.; Salinas R, G.A.
1996-01-01
Using a trial circuit, the experimental heat transfer coefficient is determined, in forced convection at one phase only within an annular channel in which water flows ascendantly and for this reason an empirical equation is determined. This work tries to contribute to the understanding of the forced convection phenomena in non tubular geometries like the annular channels. (Author)
The role of energy conservation in the BFKL equation
International Nuclear Information System (INIS)
Forshaw, J.R.; Harriman, P.N.; Sutton, P.J.
1993-01-01
We study a modification to the BFKL equation at zero momentum transfer due to the imposition of energy conservation. The significance of our modification, which enters in the form of an ultraviolet cutoff, is illustrated directly and is discussed within the context of the gluon diffusion in k T . (Author)
Heat and Mass Transfer in an L Shaped Porous Medium
Salman Ahmed, N. J.; Azeem; Yunus Khan, T. M.
2017-08-01
This article is an extension to the heat transfer in L-shaped porous medium by including the mass diffusion. The heat and mass transfer in the porous domain is represented by three coupled partial differential equations representing the fluid movement, energy transport and mass transport. The equations are converted into algebraic form of equations by the application of finite element method that can be conveniently solved by matrix method. An iterative approach is adopted to solve the coupled equations by setting suitable convergence criterion. The results are discussed in terms of heat transfer characteristics influenced by physical parameters such as buoyancy ratio, Lewis number, Rayleigh number etc. It is found that these physical parameters have significant effect on heat and mass transfer behavior of L-shaped porous medium.
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
Completely integrable operator evolutionary equations
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
On the Saha Ionization Equation
Indian Academy of Sciences (India)
Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...
Fem Formulation of Heat Transfer in Cylindrical Porous Medium
Azeem; Khaleed, H. M. T.; Soudagar, Manzoor Elahi M.
2017-08-01
Heat transfer in porous medium can be derived from the fundamental laws of flow in porous region ass given by Henry Darcy. The fluid flow and energy transport inside the porous medium can be described with the help of momentum and energy equations. The heat transfer in cylindrical porous medium differs from its counterpart in radial and axial coordinates. The present work is focused to discuss the finite element formulation of heat transfer in cylindrical porous medium. The basic partial differential equations are derived using Darcy law which is the converted into a set of algebraic equations with the help of finite element method. The resulting equations are solved by matrix method for two solution variables involved in the coupled equations.
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Directory of Open Access Journals (Sweden)
Taouil Hajer
2012-08-01
Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.
Directory of Open Access Journals (Sweden)
Guo Zheng-Hong
2016-01-01
Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.
Directory of Open Access Journals (Sweden)
I. A. Pugachev
2013-01-01
Full Text Available A process of heat transfer in continuous casting mould is considered. The substantiated equations predict shell growth, temperature distributions, solidification rates and can be used for continuous casters control systems.
p-Euler equations and p-Navier-Stokes equations
Li, Lei; Liu, Jian-Guo
2018-04-01
We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.
Generalized quantal equation of motion
International Nuclear Information System (INIS)
Morsy, M.W.; Embaby, M.
1986-07-01
In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Energy Technology Data Exchange (ETDEWEB)
Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-17
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Differential equations with involutions
Cabada, Alberto
2015-01-01
This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.
Mathematical Model for Fluid Flow and Heat Transfer Processes in Plate Exchanger
Directory of Open Access Journals (Sweden)
Cvete B. Dimitrieska
2015-11-01
Full Text Available Within the analytical solution of the system of equations which solve fluid flow and heat transfer processes, the elliptical and parabolic differential equations based on initial and boundary conditions is usually unfamiliar in a closed form. Numerical solution of equation system is necessarily obtained by discretization of equations. When system of equations relate to estimation of two dimensional stationary problems, the applicable method for estimation in basic two – dimensional form is recommended.
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Deissler, Robert G.
1996-01-01
Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.
Theory of periodic conjugate heat transfer
Zudin, Yuri B
2016-01-01
This book presents the theory of periodic conjugate heat transfer in detail. It offers a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body.
Conjugate Compressible Fluid Flow and Heat Transfer in Ducts
Cross, M. F.
2011-01-01
A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.
Bullock, Kimberly R.
1995-01-01
The development and application of new technologies in the United States has always been important to the economic well being of the country. The National Aeronautics and Space Administration (NASA) has been an important source of these new technologies for almost four decades. Recently, increasing global competition has emphasized the importance of fully utilizing federally funded technologies. Today NASA must meet its mission goals while at the same time, conduct research and development that contributes to securing US economic growth. NASA technologies must be quickly and effectively transferred into commercial products. In order to accomplish this task, NASA has formulated a new way of doing business with the private sector. Emphasis is placed on forming mutually beneficial partnerships between NASA and US industry. New standards have been set in response to the process that increase effectiveness, efficiency, and timely customer response. This summer I have identified potential markets for two NASA inventions: including the Radially Focused Eddy Current Sensor for Characterization of Flaws in Metallic Tubing and the Radiographic Moire. I have also worked to establish a cooperative program with TAG, private industry, and a university known as the TAG/Industry/Academia Program.
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Directory of Open Access Journals (Sweden)
N. Amanifard
2007-06-01
Full Text Available In this work, the effects of electrical double layer (EDL near the solid/ liquid interface, on three dimensional heat transfer characteristic and pressure drop of water flow through a rectangular microchannel numerically are investigated. An additional body force originating from the existence of EDL is considered to modify the conventional Navier-stokes and energy equations. These modified equations are solved numerically for steady laminar flow on the basis of control volume approaches. Fluid velocity distribution and temperature with presence and absence of EDL effects are presented for various geometric cases and different boundary conditions. The results illustrate that, the liquid flow in rectangular microchannels is influenced significantly by the EDL, particularly in the high electric potentials, and hence deviates from flow characteristics described by classical fluid mechanics.
Energy transfer in structured and unstructured environments
DEFF Research Database (Denmark)
Iles-Smith, Jake; Dijkstra, Arend G.; Lambert, Neill
2016-01-01
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly...... used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations....... We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions. (C) 2016 AIP...
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Equations Holding in Hilbert Lattices
Mayet, René
2006-07-01
We produce and study several sequences of equations, in the language of orthomodular lattices, which hold in the ortholattice of closed subspaces of any classical Hilbert space, but not in all orthomodular lattices. Most of these equations hold in any orthomodular lattice admitting a strong set of states whose values are in a real Hilbert space. For some of these equations, we give conditions under which they hold in the ortholattice of closed subspaces of a generalised Hilbert space. These conditions are relative to the dimension of the Hilbert space and to the characteristic of its division ring of scalars. In some cases, we show that these equations cannot be deduced from the already known equations, and we study their mutual independence. To conclude, we suggest a new method for obtaining such equations, using the tensorial product.
Analytical Evalution of Heat Transfer Conductivity with Variable Properties
DEFF Research Database (Denmark)
Rahimi, Masoume; Hosseini, Mohammad Javad; Barari, Amin
2011-01-01
The homotopy analysis method (HAM) as a new technique which is powerful and easy-to-use, is applied to solve heat transfer problems. In this paper, we use HAM for heat transfer conductivity equation with variable properties which may contain highly nonlinear terms. The obtained results are also...
Mass transfer from smooth alabaster surfaces in turbulent flows
Opdyke, Bradley N.; Gust, Giselher; Ledwell, James R.
1987-11-01
The mass transfer velocity for alabaster plates in smooth-wall turbulent flow is found to vary with the friction velocity according to an analytic solution of the advective diffusion equation. Deployment of alabaster plates on the sea floor can perhaps be used to estimate the viscous stress, and transfer velocities for other species.
Transient heat transfer in longitudinal fins of various profiles with ...
Indian Academy of Sciences (India)
Transient heat transfer through a longitudinal ﬁn of various proﬁles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are ...
Transient heat transfer in longitudinal fins of various profiles with ...
Indian Academy of Sciences (India)
Abstract. Transient heat transfer through a longitudinal fin of various profiles is studied. The ther- mal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions ...
Theory of light transfer in food and biological materials
In this chapter, we first define the basic radiometric quantities that are needed for describing light propagation in food and biological materials. Radiative transfer theory is then derived, according to the principle of the conservation of energy. Because the radiative transfer theory equation is ...
Mode-to-mode energy transfers in convective patterns
Indian Academy of Sciences (India)
Abstract. We investigate the energy transfer between various Fourier modes in a low- dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical ...
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Hyperbolic Methods for Einstein's Equations
Directory of Open Access Journals (Sweden)
Reula Oscar
1998-01-01
Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
The generalized Airy diffusion equation
Directory of Open Access Journals (Sweden)
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S
A literature survey on numerical heat transfer
Shih, T. M.
1982-12-01
Technical papers in the area of numerical heat transfer published from 1977 through 1981 are reviewed. The journals surveyed include: (1) ASME Journal of Heat Transfer, (2) International Journal of Heat and Mass Transfer, (3) AIAA Journal, (4) Numerical Heat Transfer, (5) Computers and Fluids, (6) International Journal for Numerical Methods in Engineering, (7) SIAM Journal of Numerical Analysis, and (8) Journal of Computational Physics. This survey excludes experimental work in heat transfer and numerical schemes that are not applied to equations governing heat transfer phenomena. The research work is categorized into the following areas: (A) conduction, (B) boundary-layer flows, (C) momentum and heat transfer in cavities, (D) turbulent flows, (E) convection around cylinders and spheres or within annuli, (F) numerical convective instability, (G) radiation, (H) combustion, (I) plumes, jets, and wakes, (J) heat transfer in porous media, (K) boiling, condensation, and two-phase flows, (L) developing and fully developed channel flows, (M) combined heat and mass transfer, (N) applications, (O) comparison and properties of numerical schemes, and (P) body-fitted coordinates and nonuniform grids.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Half-linear differential equations
Dosly, Ondrej
2005-01-01
The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and var
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
International symposium on radiative heat transfer: Book of abstracts
International Nuclear Information System (INIS)
1995-01-01
The international symposium on radiative heat transfer was held on 14-18 August 1995 Turkey. The specialists discussed radiation transfer in materials processing and manufacturing, solution of radiative heat transfer equation, transient radiation problem and radiation-turbulence interactions, raditive properties of gases, atmospheric and stellar radiative transfer , radiative transfer and its applications, optical and radiative properties of soot particles, inverse radiation problems, partticles, fibres,thermophoresis and waves and modelling of comprehensive systems at the meeting. Almost 79 papers were presented in the meeting
Equations of motion for cross term modified gravitational field equations
Energy Technology Data Exchange (ETDEWEB)
Mueller, V. (Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Zentralinstitut fuer Astrophysik)
1982-01-01
As proposed by Treder, possible consequences of a unitary field theory may be described phenomenologically by additional cross terms in Einstein's equations. The violation of the weak principle of equivalence and potential observable effects are discussed in deriving hydrodynamic EIH equations. Conclusions on gravitational instabilities follow in the quasistatic approximation.
Difference equations theory, applications and advanced topics
Mickens, Ronald E
2015-01-01
THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...
Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond
Indian Academy of Sciences (India)
Ultrafast Dynamics of Chemical Reactions in Condensed Phase: Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond. Dipak K. Palit Radaition & Photochemistry Division Bhabha Atomic Research Centre Mumbai 400 085, India.
Simultaneous Heat and Mass Transfer Model for Convective Drying of Building Material
Upadhyay, Ashwani; Chandramohan, V. P.
2018-04-01
A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss-Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.
Theoretical aspects of electron transfer reactions of complex molecules
DEFF Research Database (Denmark)
Kuznetsov, A. M.; Ulstrup, Jens
2001-01-01
Features of electron transfer involving complex molecules are discussed. This notion presently refers to molecular reactants where charge transfer is accompanied by large molecular reorganization, and commonly used displaced harmonic oscillator models do not apply. It is shown that comprehensive...... theory of charge transfer in polar media offers convenient tools for the treatment of experimental data for such systems, with due account of large-amplitude strongly anharmonic intramolecular reorganization. Equations for the activation barrier and free energy relationships are provided, incorporating...
Method of calculating heat transfer in furnaces of small power
Directory of Open Access Journals (Sweden)
Khavanov Pavel
2016-01-01
Full Text Available This publication presents the experiences and results of generalization criterion equation of importance in the analysis of the processes of heat transfer and thermal calculations of low-power heat generators cooled combustion chambers. With generalizing depending estimated contribution of radiation and convective heat transfer component in the complex for the combustion chambers of small capacity boilers. Determined qualitative and quantitative dependence of the integrated radiative-convective heat transfer from the main factors working combustion chambers of small volume.
Comparative analysis of solution methods of the punctual kinetic equations
International Nuclear Information System (INIS)
Hernandez S, A.
2003-01-01
The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)
Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability
Janett, Gioele; Paganini, Alberto
2018-04-01
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented.
Equations for transient flow-boiling in a duct
International Nuclear Information System (INIS)
Mathers, W.G.; Ferch, R.L.; Hancox, W.T.; McDonald, B.H.
1981-01-01
In this paper we derive a separated phase model for weakly coupled flows which extends a model presented elsewhere (BANERJEE, FERCH, MATHERS and McDONALD, 1978). A hyperbolic system of seven partial differential equations results with ensemble-averaged phase velocities, enthalpies and pressures, and void fraction as dependent variables (UVUTUP model). The required constitutive equations for mass, momentum and energy transfer between phases and between the phases and the boundaries are discussed. The relationship of the UVUTUP model to other existing models is also presented
Solutions to Arithmetic Convolution Equations
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Averaging of multivalued differential equations
Directory of Open Access Journals (Sweden)
G. Grammel
2003-04-01
Full Text Available Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O(ÃÂµ1/3 as ÃÂµÃ¢Â†Â’0.
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
On the Saha Ionization Equation
Indian Academy of Sciences (India)
An example of the soci- etal impact of the famous equation can be discerned in a .... gaseous state and they behaved like a dilute classical gas, as in. Maxwell's kinetic theory. That is to say, the atoms do .... the Sackur–Tetrode equation for the entropy of an ideal gas at high temperatures, that Saha was quite aware of [13].
Higher order equations of motion
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1989-01-01
The possibility that the motion of elementary particles be described by higher order differential equations induced by supersymmetry in higher dimensional space-time is discussed. The specific example of six dimensions writing the corresponding Lagrangian and equations of motion, is presented. (author) [pt
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
International technology transfer
International Nuclear Information System (INIS)
Kwon, Won Gi
1991-11-01
This book introduces technology progress and economic growth, theoretical consideration of technology transfer, policy and mechanism on technology transfer of a developed country and a developing country, reality of international technology transfer technology transfer and industrial structure in Asia and the pacific region, technology transfer in Russia, China and Eastern Europe, cooperation of science and technology for development of Northeast Asia and strategy of technology transfer of Korea.
Technology transfer by multinationals
Kostyantyn Zuzik
2003-01-01
The paper analyses the issue of technology transfer by multinational corporations. The following questions are explored: (a) world market of technologies, the role of MNCs (b) Choice of the technology transfer mode, Dunning's OLI-theory as a factor of the choice of the mode of transfer (c) measurement and profitability of technology transfer (d) transfer of technology through partnerships, JVs, alliances and through M&As (e) aspects of technology transfer by services multinationals. Paper uti...
The relativistic electron wave equation
International Nuclear Information System (INIS)
Dirac, P.A.M.
1977-08-01
The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)
Fem Formulation for Heat and Mass Transfer in Porous Medium
Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan
2017-08-01
Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.
Discovering Evolution Equations with Applications, 1 Deterministic Equations
McKibben, Mark A
2010-01-01
Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical deve
Bethe ansatz equations for open spin chains from giant gravitons
International Nuclear Information System (INIS)
Nepomechie, Rafael I.
2009-01-01
We investigate the open spin chain describing the scalar sector of the Y = 0 giant graviton brane at weak coupling. We provide a direct proof of integrability in the SU(2) and SU(3) sectors by constructing the transfer matrices. We determine the eigenvalues of these transfer matrices in terms of roots of the corresponding Bethe ansatz equations (BAEs). Based on these results, we propose BAEs for the full SO(6) sector. We find that, in the weak-coupling limit, the recently-proposed all-loop BAEs essentially agree with those proposed in the present work.
Equation of State for Phospholipid Self-Assembly
DEFF Research Database (Denmark)
Marsh, Derek
2016-01-01
of transfer converge at ∼-18°C. An equation of state for the free energy of self-assembly formulated from this thermodynamic data depends on the heat capacity of transfer as the sole parameter needed to specify a particular lipid. For lipids lacking calorimetric data, measurement of the critical micelle...... concentration at a single temperature suffices to define an effective heat capacity according to the model. Agreement with the experimental temperature dependence of the critical micelle concentration is then good. The predictive powers should extend also to amphiphile partitioning and the kinetics of lipid...
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
be split into measurement noise and system noise. The system noise is used to compensate for those biological processes not explicitly described by the model. Many authors model conjugation by a simple mass action model first proposed by Levin et al. (1979). Also Michaelis-Menten dependence...... by an experiment conducted with E. faecium. In addition, we suggest that a 3rd order time-delay must be included in the model to account for the delay before a newly conjugated plasmid is expressed. A ML estimate of the parameters based on experimental data is found using the software CTSM. The conjugation rate......Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Ozdemir, Burhanettin
2017-01-01
The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…
A multilevel method for conductive-radiative heat transfer
Energy Technology Data Exchange (ETDEWEB)
Banoczi, J.M.; Kelley, C.T. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
We present a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. The equations can be formulated as a compact fixed point problem with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We use fast transport solvers developed by the second author, to construct an efficient evaluation of the fixed point map and then apply the Atkinson-Brakhage, method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system.
Stochastic Levy Divergence and Maxwell's Equations
Directory of Open Access Journals (Sweden)
B. O. Volkov
2015-01-01
Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
Stochastic differential equations, backward SDEs, partial differential equations
Pardoux, Etienne
2014-01-01
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...
Fractional delayed damped Mathieu equation
Mesbahi, Afshin; Haeri, Mohammad; Nazari, Morad; Butcher, Eric A.
2015-03-01
This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system.
Soliton equations and pseudospherical surfaces
International Nuclear Information System (INIS)
Sasaki, R.
1979-03-01
All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)
Galois theory of difference equations
Put, Marius
1997-01-01
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Tian, Gang
2002-11-26
We discuss some recent progress on the regularity theory of the elliptic Yang-Mills equation. We start with some basic properties of the elliptic Yang-Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang-Mills connections and compactness theorems on Yang-Mills connections with bounded L(2) norm of curvature. We also discuss in some detail self-dual solutions of the Yang-Mills equation and describe a compactification of their moduli space.
Tian, Gang
2002-01-01
We discuss some recent progress on the regularity theory of the elliptic Yang–Mills equation. We start with some basic properties of the elliptic Yang–Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang–Mills connections and compactness theorems on Yang–Mills connections with bounded L2 norm of curvature. We also discuss in some detail self-dual solutions of the Yang–Mills equation and describe a compactification of the...
Lectures on ordinary differential equations
Hurewicz, Witold
1958-01-01
Hailed by The American Mathematical Monthly as ""a rigorous and lively introduction,"" this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown funct
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Direct 'delay' reductions of the Toda equation
International Nuclear Information System (INIS)
Joshi, Nalini
2009-01-01
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)
DEFF Research Database (Denmark)
Bateman, I.J.; Brouwer, R.; Ferrini, S.
We develop and test guidance principles for benefits transfers. These argue that when transferring across relatively similar sites, simple mean value transfers are to be preferred but that when sites are relatively dissimilar then value function transfers will yield lower errors. The paper also p...
Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).
Murase, Kenya
2016-01-01
Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
Heat transfer, condensation and fog formation in crossflow plastic heat exchangers
Brouwers, Jos; van der Geld, C.W.M.
1996-01-01
In this paper heat transfer of air-water-vapour mixtures in plastic crossflow heat exchangers is studied theoretically and experimentally. First, a model for heat transfer without condensation is derived, resulting in a set of classical differential equations. Subsequently, heat transfer with wall
Barron, Randall F
2016-01-01
Cryogenic Heat Transfer, Second Edition continues to address specific heat transfer problems that occur in the cryogenic temperature range where there are distinct differences from conventional heat transfer problems. This updated version examines the use of computer-aided design in cryogenic engineering and emphasizes commonly used computer programs to address modern cryogenic heat transfer problems. It introduces additional topics in cryogenic heat transfer that include latent heat expressions; lumped-capacity transient heat transfer; thermal stresses; Laplace transform solutions; oscillating flow heat transfer, and computer-aided heat exchanger design. It also includes new examples and homework problems throughout the book, and provides ample references for further study.
Analytical Solution of Mathieu Equation
Yerchuck, Dmitri; Dovlatova, Alla; Yerchak, Yauhen; Borovik, Felix
2014-01-01
The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)
Saha equation in Rindler space
Indian Academy of Sciences (India)
The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.
An Investigation on Quadratic Equations.
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
The quasilinear parabolic kirchhoff equation
Directory of Open Access Journals (Sweden)
Dawidowski Łukasz
2017-04-01
Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
2015-11-27
Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quantum gravity; loop quantum cosmology. ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag ...
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Two-state approximation of the Fadeev-Hahn equations
International Nuclear Information System (INIS)
Brener, S.E.
1993-01-01
The equations have been chosen which allow both to solve the scattering problems and to calculate the parameters of bound states of three particles with Coulomb interaction when the system energy is below the decay to three separate particles. The method of constructing of equations which are most suitable for concrete problems is considered. Different numerical schemes to calculate the low energy scattering cross sections with two-particle clusterization in 'in' and 'out' collision's channels have been developed. The bounds of applied approaches were determined and the peculiarities connected with differently defined reaction amplitudes under these approaches have been considered. The interpretation of obtained results at different definitions of reaction amplitudes was demonstrated, and the elastic, inelastic cross sections and muon transfer rates in hydrogen isotope mesic atom collisions have been calculated using Fadeev-Hahn equations. (author)
Effective Bayesian Transfer Learning
2010-03-01
Classes: cougar, car, butterfly, rooster, bass, buddha •!Transferred knowledge: •!Keypoints (landmarks) that define the shape •!Location of...keypoints TL5 Raw Curves for Buddha Class Cartoons to real images Transfer No Transfer 27 TL5 Raw Curves for all classes Cartoons to real images...bass buddha butterfly car cougar rooster TL5 Average Curve for Butterfly class Cartoons to real images Transfer No Transfer TL5 Average Curves for
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Computational partial differential equations using Matlab
Li, Jichun
2008-01-01
Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE
Theory of coherent resonance energy transfer
International Nuclear Information System (INIS)
Jang, Seogjoo; Cheng, Y.-C.; Reichman, David R.; Eaves, Joel D.
2008-01-01
A theory of coherent resonance energy transfer is developed combining the polaron transformation and a time-local quantum master equation formulation, which is valid for arbitrary spectral densities including common modes. The theory contains inhomogeneous terms accounting for nonequilibrium initial preparation effects and elucidates how quantum coherence and nonequilibrium effects manifest themselves in the coherent energy transfer dynamics beyond the weak resonance coupling limit of the Foerster and Dexter (FD) theory. Numerical tests show that quantum coherence can cause significant changes in steady state donor/acceptor populations from those predicted by the FD theory and illustrate delicate cooperation of nonequilibrium and quantum coherence effects on the transient population dynamics.
Heat transfer with freezing and thawing
Lunardini, VJ
1991-01-01
This volume provides a comprehensive overview on the vast amount of literature on solidification heat transfer. Chapter one develops important basic equations and discusses the validity of considering only conductive heat transfer, while ignoring convection, in the large class of materials which make up the porous media. Chapters 2 to 4 deal with problems that can be expressed in plane (Cartesian) coordinates. These problems are further divided into boundary conditions of temperature, prescribed heat flux, and surface convection. Chapter 5 examines some plane geometries involving three-dime
Equationally Compact Acts : Coproducts / Peeter Normak
Normak, Peeter
1998-01-01
In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact
The soil moisture velocity equation
Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.
2017-06-01
Numerical solution of the one-dimensional Richards' equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyperresolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards' equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards' equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.type="synopsis">type="main">Plain Language SummarySince its original publication in 1922, the so-called Richards' equation has been the only rigorous way to couple groundwater to the land surface through the unsaturated zone that lies between the water table and land surface. The soil
CFD simulations of heat transfer in internally helically ribbed tubes
Directory of Open Access Journals (Sweden)
Majewski Karol
2016-06-01
Full Text Available Heating surfaces in power boilers are exposed to very high heat flux. For evaporator protection against overheating, internally helically ribbed tubes are used. The intensification of the heat transfer and the maintenance of the thin water layer in the intercostal space, using ribbed tubes, enables better protection of the power boiler evaporator than smooth pipes. Extended inner surface changes flow and thermal conditions by influencing the linear pressure drop and heat transfer coefficient. This paper presents equations that are used to determine the heat transfer coefficient. The results of total heat transfer, obtained from CFD simulations, for two types of internally ribbed and plain tubes are also presented.
Exact results for the Boltzmann equation and Smoluchowski's coagulation equation
International Nuclear Information System (INIS)
Hendriks, E.M.
1983-01-01
Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)
Nonclassical energy transfer in photosynthetic FMO complex
Directory of Open Access Journals (Sweden)
Abramavicius Vytautas
2013-03-01
Full Text Available Excitation energy transfer in a photosynthetic FMO complex has been simulated using the stochastic Schrödinger equation. Fluctuating chromophore transition energies are simulated from the quantum correlation function which allows to properly include the finite temperature. The resulting excitation dynamics shows fast thermalization of chromophore occupations into proper thermal equilibrium. The relaxation process is characterized by entropy dynamics, which shows nonclassical behavior.
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.
Approximations of Stochastic Partial Differential Equations
Di Nunno, Giulia; Zhang, Tusheng
2014-01-01
In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.
Linear integral equations and soliton systems
International Nuclear Information System (INIS)
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
How to obtain the covariant form of Maxwell's equations from the continuity equation
International Nuclear Information System (INIS)
Heras, Jose A
2009-01-01
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations
Extraction of dynamical equations from chaotic data
International Nuclear Information System (INIS)
Rowlands, G.; Sprott, J.C.
1991-02-01
A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
Hypergeometric solutions to Schr\\"odinger equations for the quantum Painlev\\'e equations
Nagoya, Hajime
2011-01-01
We consider Schr\\"odinger equations for the quantum Painlev\\'e equations. We present hypergeometric solutions of the Schr\\"odinger equations for the quantum Painlev\\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\\"odinger equations for the quantum Painlev\\'e equations and those of the KZ equation or the confluent KZ equations.
Equation of state and general relativity in supernovae
International Nuclear Information System (INIS)
Baron, E.A.
1985-01-01
The results of an extensive numerical study of the outcome of massive star collapse and subsequent shock formation and propagation are presented. The stiffness of the equation of state at high density is shown to play a crucial role, a softer equation of state being helpful to shock production and propagation. The effect of neutrinos is investigated in a simple manner by varying the neutrino transport from a simple trapping density to a simple leakage scheme. With a softer equation of state, the maximum central densities reached are high enough that general relativity may become important. The effects of general relativity are investigated in detail. It is shown that while general relativity is generally harmful to the shock, once the equation of state becomes soft enough, general relativistic effects may conspire to transfer large amounts of energy from the gravitational field to the shock, resulting in powerful explosions. This is first investigated using simplified initial conditions, the initial models being constructed in an ad hoc fashion to facilitate numerical investigation. Finally, results are presented for detailed pre-supernovae initial models of 12 and 15 M/sub sun/. These models do explode, with explosion energies varying from approx.1 - 3 x 10 51 ergs depending on the degree of softness of the high density equation of state
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Integration of quantum hydrodynamical equation
Ulyanova, Vera G.; Sanin, Andrey L.
2007-04-01
Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
Integration rules for scattering equations
Energy Technology Data Exchange (ETDEWEB)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center,Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2015-09-21
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Numerical integration of variational equations.
Skokos, Ch; Gerlach, E
2010-09-01
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.
Integration rules for scattering equations
International Nuclear Information System (INIS)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Quantum Gross-Pitaevskii Equation
Directory of Open Access Journals (Sweden)
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
2017-07-01
Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
Heat transfer of laminar mixed convection of liquid
Shang, De-Yi
2016-01-01
This book presents a new algorithm to calculate fluid flow and heat transfer of laminar mixed convection. It provides step-by-step tutorial help to learn quickly how to set up the theoretical and numerical models of laminar mixed convection, to consider the variable physical properties of fluids, to obtain the system of numerical solutions, to create a series of formalization equations for the convection heat transfer by using a curve-fitting approach combined with theoretical analysis and derivation. It presents the governing ordinary differential equations of laminar mixed convection, equivalently transformed by an innovative similarity transformation with the description of the related transformation process. A system of numerical calculations of the governing ordinary differential equations is presented for the water laminar mixed convection. A polynomial model is induced for convenient and reliable treatment of variable physical properties of liquids. The developed formalization equations of mixed convec...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
(G /G)-expansion method for finding exact travelling wave solutions of Higgs field equa- tion. Section 3.2 is devoted to find travelling wave solutions of Hamiltonian amplitude equation. In §4, some conclusions are given. 2. Lie symmetry analysis. Lie's method [8–10] is an effective method and is the simplest among group ...
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
rived equation based on the concept of specific resistance, was used to i was used to i drying bed as a slud ... the sludge, it was observed that the specific resistance decreases with incr ng results: D ng results: Dosage increase of 10g, ..... Assessment of the Suitability of Anaerobic Digestion. Effluent for Direct Application as ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs ﬁeld equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...
Stability theory of differential equations
Bellman, Richard Ernest
1953-01-01
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
International Nuclear Information System (INIS)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.
Applied analysis and differential equations
Cârj, Ovidiu
2007-01-01
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Einstein Equations from Varying Complexity
Czech, Bartłomiej
2018-01-01
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of tensor network renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
SUNDÉN, B
2012-01-01
Presenting the basic mechanisms for transfer of heat, Introduction to Heat Transfer gives a deeper and more comprehensive view than existing titles on the subject. Derivation and presentation of analytical and empirical methods are provided for calculation of heat transfer rates and temperature fields as well as pressure drop. The book covers thermal conduction, forced and natural laminar and turbulent convective heat transfer, thermal radiation including participating media, condensation, evaporation and heat exchangers.
Directory of Open Access Journals (Sweden)
Gao Guo-Ping
2016-01-01
Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.
International Nuclear Information System (INIS)
Nepomechie, Rafael I
2013-01-01
An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues of the transfer matrix of this model. We also propose a generating function for the inhomogeneous T-Q equations of arbitrary spin. (fast track communication)
Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations
Directory of Open Access Journals (Sweden)
Umer Saeed
2014-01-01
Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.
Line radiative transfer and statistical equilibrium*
Directory of Open Access Journals (Sweden)
Kamp Inga
2015-01-01
Full Text Available Atomic and molecular line emission from protoplanetary disks contains key information of their detailed physical and chemical structures. To unravel those structures, we need to understand line radiative transfer in dusty media and the statistical equilibrium, especially of molecules. I describe here the basic principles of statistical equilibrium and illustrate them through the two-level atom. In a second part, the fundamentals of line radiative transfer are introduced along with the various broadening mechanisms. I explain general solution methods with their drawbacks and also specific difficulties encountered in solving the line radiative transfer equation in disks (e.g. velocity gradients. I am closing with a few special cases of line emission from disks: Radiative pumping, masers and resonance scattering.
Indian Academy of Sciences (India)
is to study the interaction properties between the periodic waves. Here, we take the (2+1)-dimensional KdV equation .... In fact, such limit for the present family of doubly periodic waves is especially rich, since one can proceed with the long .... ematical Society, Providence, 1997). [11] K Chandrasekharan, Elliptic functions ...
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Sonar equations for planetary exploration.
Ainslie, Michael A; Leighton, Timothy G
2016-08-01
The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.
Sonar equations for planetary exploration
Ainslie, M.A.; Leighton, T.G.
2016-01-01
The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels,
Saha equation in Rindler space
Indian Academy of Sciences (India)
Sanchari De
MS received 21 October 2016; revised 3 January 2017; accepted 25 January 2017; published online 31 May 2017. Abstract. The Saha equations for the photoionization process of hydrogen atoms .... [3] C W Misner, Kip S Thorne and J A Wheeler, Gravitation (W.H.. Freeman and Company, New York, 1972). [4] W Rindler ...
Equations for formally real meadows
Bergstra, J.A.; Bethke, I.; Ponse, A.
2015-01-01
We consider the signatures Σm = (0,1,−,+,⋅,−1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom
On the Saha Ionization Equation
Indian Academy of Sciences (India)
On the Saha Ionization Equation. Sushanta Dattagupta. General Article Volume 23 Issue 1 January 2018 pp 41-55. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/023/01/0041-0055. Keywords. Ionization, astrophysics, spectroscopy, chemical reaction, transition state. Abstract.
Pendulum Motion and Differential Equations
Reid, Thomas F.; King, Stephen C.
2009-01-01
A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Transport equation and shock waves
International Nuclear Information System (INIS)
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
Indian Academy of Sciences (India)
Abstract. By applying the bifurcation theory of dynamical system to the generalized. KP–BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...
Renaissance Learning Equating Study. Report
Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben
2007-01-01
An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Solutions of equations in languages
Hesselink, Wim H.
A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar
Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond
Indian Academy of Sciences (India)
Ultrafast Dynamics of Chemical Reactions in Condensed Phase: Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond · PowerPoint Presentation · Slide 3 · Slide 4 · Slide 5 · Slide 6 · Slide 7 · Slide 8 · Slide 9 · Slide 10 · Slide 11 · Slide 12 · Slide 13 · Slide 14 · Slide 15 · Slide 16 · Slide 17 · Slide 18 · Slide 19.
International Nuclear Information System (INIS)
Bernstein, I.
1978-01-01
A nuclear fuel transfer machine for transferring fuel assemblies through the fuel transfer tube of a nuclear power generating plant containment structure is described. A conventional reversible drive cable is attached to the fuel transfer carriage to drive it horizontally through the tube. A shuttle carrying a sheave at each end is arranged in parallel with the carriage to also travel into the tube. The cable cooperating with the sheaves permit driving a relatively short fuel transfer carriage a large distance without manually installing sheaves or drive apparatus in the tunnel. 8 claims, 3 figures
Cannon, R D
2013-01-01
Electron Transfer Reactions deals with the mechanisms of electron transfer reactions between metal ions in solution, as well as the electron exchange between atoms or molecules in either the gaseous or solid state. The book is divided into three parts. Part 1 covers the electron transfer between atoms and molecules in the gas state. Part 2 tackles the reaction paths of oxidation states and binuclear intermediates, as well as the mechanisms of electron transfer. Part 3 discusses the theories and models of the electron transfer process; theories and experiments involving bridged electron transfe
Simple Ion Transfer at Liquid|Liquid Interfaces
Directory of Open Access Journals (Sweden)
L. J. Sanchez Vallejo
2012-01-01
Full Text Available The main aspects related to the charge transfer reactions occurring at the interface between two immiscible electrolyte solutions (ITIES are described. The particular topics to be discussed involve simple ion transfer. Focus is given on theoretical approaches, numerical simulations, and experimental methodologies. Concerning the theoretical procedures, different computational simulations related to simple ion transfer are reviewed. The main conclusions drawn from the most accepted models are described and analyzed in regard to their relevance for explaining different aspects of ion transfer. We describe numerical simulations implementing different approaches for solving the differential equations associated with the mass transport and charge transfer. These numerical simulations are correlated with selected experimental results; their usefulness in designing new experiments is summarized. Finally, many practical applications can be envisaged regarding the determination of physicochemical properties, electroanalysis, drug lipophilicity, and phase-transfer catalysis.
A Versatile Technique for Solving Quintic Equations
Kulkarni, Raghavendra G.
2006-01-01
In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces. Keywords. Operator space; fixed point; Hyers–Ulam stability; Cauchy additive functional equation; quadratic functional equation. 2000 Mathematics Subject Classification. 47L25, 47H10, 39B82, 46L07, 39B52. 1.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation ...
An analytical solution of fractional burgers equation
Directory of Open Access Journals (Sweden)
Pang Jing
2017-01-01
Full Text Available Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.
The Complexity of One-Step Equations
Ngu, Bing
2014-01-01
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Algebraic entropy for differential-delay equations
Viallet, Claude M.
2014-01-01
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
A Large Deviation, Hamilton-Jacobi Equation Approach to a Statistical Theory for Turbulence
2012-09-03
and its associated compressible Euler equations, Comptes Rendus Mathematique , (09 2011): 973. doi: 10.1016/j.crma.2011.08.013 2012/09/03 14:17:15 6...Hamilton-Jacobi PDE is shown to be well-posed. (joint work with T Nguyen, Journal de Mathematique Pures et Appliquees). Future works focusing on large time behavior for such equations is currently under its way. Technology Transfer
Finite difference approximation of control via the potential in a 1-D Schrodinger equation
Directory of Open Access Journals (Sweden)
K. Kime
2000-04-01
Full Text Available We consider the problem of steering given initial data to given terminal data via a time-dependent potential, the control, in a 1-D Schrodinger equation. We determine a condition for existence of a transferring potential within our approximation. Using Maple, we give equations for the control and also examples in which the potential is restricted to be centralized and to be a step potential.
Numerical solutions of ordinary and partial differential equations in the frequency domain
International Nuclear Information System (INIS)
Hazi, G.; Por, G.
1997-01-01
Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)
Study on grey model in the heat transfer coefficient of supercritical water
International Nuclear Information System (INIS)
Xiaozhuang, Liu; Tao, Zhou
2009-01-01
Heat transfer coefficient is an important feature factor to describe supercritical water reactor(SCWR). With experimental data as basic, using Grey model to analyze the relationship between heat transfer coefficient and other influential factors, studying the inside law of heat transfer coefficient variation of supercritical water, so as to differ the traditional method that get the equations from fitting experimental data. Comparing it to other traditional equations, the results indicates that the data which are calculated by GM model are close to experimental data, GM model can describe the variation of supercritical water's heat transfer coefficient with other influential factors well
International Nuclear Information System (INIS)
Hasatani, Masanobu; Itaya, Yoshinori
1985-01-01
In order to develop energy-saving techniques and new energy techniques, and also most advanced techniques by making industrial equipment with high performance, heat transfer performance frequently becomes an important problem. In addition, the improvement of conventional heat transfer techniques and the device of new heat transfer techniques are often required. It is most proper that chemical engineers engage in the research and development for enhancing heat transfer. The research and development for enhancing heat transfer are important to heighten heat exchange efficiency or to cool equipment for preventing overheat in high temperature heat transfer system. In this paper, the techniques of enhancing radiative heat transfer and the improvement of radiative heat transfer characteristics are reported. Radiative heat transfer is proportional to fourth power of absolute temperature, and it does not require any heat transfer medium, but efficient heat-radiation converters are necessary. As the techniques of enhancing radiative heat transfer, the increase of emission and absorption areas, the installation of emissive structures and the improvement of radiative characteristics are discussed. (Kako, I.)
Transfer function combinations
Zhou, Liang
2012-10-01
Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions. © 2012 Elsevier Ltd.
Interplays between Harper and Mathieu equations.
Papp, E; Micu, C
2001-11-01
This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.
Ingestion Pathway Transfer Factors for Plutonium and Americium
Energy Technology Data Exchange (ETDEWEB)
Blanchard, A.
1999-07-28
Overall transfer factors for major ingestion pathways are derived for plutonium and americium. These transfer factors relate the radionuclide concentration in a given foodstuff to deposition on the soil. Equations describing basic relationships consistent with Regulatory Guide 1.109 are followed. Updated values and coefficients from IAEA Technical Reports Series No. 364 are used when a available. Preference is given to using factors specific to the Savannah River Site.
Discrete diffusion Monte Carlo for frequency-dependent radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffrey D [Los Alamos National Laboratory; Kelly, Thompson G [Los Alamos National Laboratory; Urbatish, Todd J [Los Alamos National Laboratory
2010-11-17
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique.
Ingestion Pathway Transfer Factors for Plutonium and Americium
International Nuclear Information System (INIS)
Blanchard, A.
1999-01-01
Overall transfer factors for major ingestion pathways are derived for plutonium and americium. These transfer factors relate the radionuclide concentration in a given foodstuff to deposition on the soil. Equations describing basic relationships consistent with Regulatory Guide 1.109 are followed. Updated values and coefficients from IAEA Technical Reports Series No. 364 are used when a available. Preference is given to using factors specific to the Savannah River Site
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Simple correlation equations for optimum design of annular fins with uniform thickness
International Nuclear Information System (INIS)
Arslanturk, Cihat
2005-01-01
Simple correlation equations for optimum design of annular fins with uniform cross section are obtained in the present work. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins of uniform thickness
Bhatti, Muhammad Awais; Battour, Mohamed Mohamed; Sundram, Veera Pandiyan Kaliani; Othman, Akmal Aini
2013-01-01
Purpose: The purpose of this study is to highlight the importance of selected environmental, situational and individual factors in the training transfer process. Design/methodology/approach: This study proposes and tests a framework via structural equation modelling by including supervisor and peer support, instrumentality and learner readiness on…
Maxwell's equations of electrodynamics an explanation
Ball, David W
2012-01-01
Maxwell's Equations of Electrodynamics: An Explanation is a concise discussion of Maxwell's four equations of electrodynamics - the fundamental theory of electricity, magnetism, and light. It guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms. The book not only provides a fundamental description of our universe but also explains how these equations predict the fact that light is better described as "electromagnetic radiation."
Variational principles in terms of entransy for heat transfer
International Nuclear Information System (INIS)
Xu, Mingtian
2012-01-01
A variational principle for heat conduction is formulated which results in the steady state heat conduction equation established from the Fourier law. Furthermore based on the thermodynamics in terms of entransy a more general functional is defined for incompressible fluids. We show that extremizing this functional gives rise to the state described by the Navier-Stokes-Fourier equations with vanishing substantive derivatives of the temperature and velocity field. In this sense one may conclude that this variational principle is consistent with the Navier-Stokes-Fourier equations. Therefore the variational principle developed in the present work demonstrates a great advantage over the minimum entropy production principle. -- Highlights: ► A variational principle for heat transfer of incompressible fluid is established in terms of entransy. ► For pure heat conduction the variational principle leads to the classical steady state heat conduction equation. ► For heat convection the variational principle is consistent with the Navier-Stokes-Fourier equations.
DEFF Research Database (Denmark)
Janssen, Hans; Blocken, Bert; Carmeliet, Jan
2007-01-01
While the transfer equations for moisture and heat in building components are currently undergoing standardisation, atmospheric boundary conditions, conservative modelling and numerical efficiency are not addressed. In a first part, this paper adds a comprehensive description of those boundary...
Heat transfer in flow past a continuously moving porous flat plate with heat flux
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Sarma, Y.V.B.
The analysis of the heat transfer in flow past a continuously moving semi-infinite plate in the presence of suction/ injection with heat flux has been presented. Similarity solutions have been derived and the resulting equations are integrated...
Heat transfer in a fixed bed and mass transfer in a counter-current moving bed
Dellaretti, F. O.
The behavior of gas-solid reactors known as compact-fixed and moving beds, is analyzed from a theoretical viewpoint. For a compact fixed-bed the solution of the energy balance equations is obtained for the cases of a uniform temperature inside the solid pellets (i.e., the Biot number is zero) and for the case in which there are temperature gradients within the pellets (Bi 0). For short contact times, beds with Bi 0 have gas- and solid- temperatures which are greater than the temperatures within beds with Bi = 0. For long times, the situation is reversed. For a compact-moving bed the solution of the mass balance equations is obtained for the cases of a feed-solid with an oscillating concentration. For both types of beds there is an equivalence between mass transfer and energy transfer so that the solutions can be interchanged with suitable definitions of dimensionless variables.
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions
Directory of Open Access Journals (Sweden)
T. V. Oblakova
2017-01-01
Full Text Available The paper considers a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical approach to search for analytical solution of such problems in the first phase involves variable substitution, leading to a problem with homogeneous boundary conditions. Reference materials [1] give, as a rule, the simplest types of variable substitutions where new and old unknown functions differ by a term, linear in the spatial variable. The form of this additive term depends on the type of the boundary conditions, but is in no way related to the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use a quadratic additive, since a linear substitution for this type of conditions may be unavailable. The courseware [2] - [4], usually, ends only with the first boundary-value problem generally formulated.The paper considers a substitution that takes into account, in principle, the form of a linear differential operator. Namely, as an additive term, it is proposed to use the parametrically time-dependent solution of the boundary value problem for an ordinary differential equation obtained from the original partial differential equation by the method of separation of the Fourier variables.The existence of the proposed substitution for boundary conditions of any type is proved by the example of a non-stationary heat-transfer equation with the heat exchange available with the surrounding medium. In this case, the additive term is a linear combination of hyperbolic functions. It is shown that, in addition to the "insensitivity" to the type of boundary conditions, the advantages of a new substitution in comparison with the traditional linear (or quadratic one include a much simpler structure of the solution obtained. Just the described approach allows us to obtain a solution with a clearly distinguished stationary component, in case a stationarity occurs, for
Equation of State Project Overview
Energy Technology Data Exchange (ETDEWEB)
Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Multiplication. If ux, f (x) and g(x) are differentiable in the opened interval D, then: D ux [f(x) · g(x)]=g(x)f (x) + f(x)g (x). + (gf + fg )(x)ux + u x. (f(x)g(x)). (2.5) ..... for solution of various nonlinear problems without usual restrictive assumptions. To solve equation. (4.2) by means of variational iteration method, we put (4.2) as ...
BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Directory of Open Access Journals (Sweden)
V. Ye. Belozerov
2013-03-01
Full Text Available Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Reduced equations of motion for quantum systems driven by diffusive Markov processes.
Sarovar, Mohan; Grace, Matthew D
2012-09-28
The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.
Effective methods of solving of model equations of certain class of thermal systems
International Nuclear Information System (INIS)
Lach, J.
1985-01-01
A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)
Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation
Directory of Open Access Journals (Sweden)
M. A. Castro
2017-01-01
Full Text Available The stability properties of a numerical method for the dual-phase-lag (DPL equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
El-Amin, Mohamed
2017-07-06
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.
Deriving the bond pricing equation
Directory of Open Access Journals (Sweden)
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
Wave equations in higher dimensions
Dong, Shi-Hai
2011-01-01
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
The parametric resonance features for theory of energy transfer in dusty plasma
Semyonov, V. P.; Timofeev, A. V.
2015-11-01
One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system can be described by equations similar to Mathieu equation with account of stochastic forces. Such equation is studied by analytical approach. The solutions for higher order of accuracy are obtained. The method for numerical solution and resonance zone detection is proposed. The solution for the extended Mathieu equation is obtained for wide range of parameter values. The results of numerical solution are compared with analytical solutions of different order and known analytical results for Mathieu equation.
Townsend, Harold E.; Barbanti, Giancarlo
1994-01-01
A nuclear fuel bundle fuel transfer system includes a transfer pool containing water at a level above a reactor core. A fuel transfer machine therein includes a carriage disposed in the transfer pool and under the water for transporting fuel bundles. The carriage is selectively movable through the water in the transfer pool and individual fuel bundles are carried vertically in the carriage. In a preferred embodiment, a first movable bridge is disposed over an upper pool containing the reactor core, and a second movable bridge is disposed over a fuel storage pool, with the transfer pool being disposed therebetween. A fuel bundle may be moved by the first bridge from the reactor core and loaded into the carriage which transports the fuel bundle to the second bridge which picks up the fuel bundle and carries it to the fuel storage pool.
DEFF Research Database (Denmark)
Christensen, Thomas Højlund
2011-01-01
tion and transport is usually the most costly part of any waste management system; and when waste is transported over a considerable distance or for a long time, transferring the waste from the collection vehicles to more efficient transportation may be economically beneficial. This involves...... a transfer station where the transfer takes place. These stations may also be accessible by private people, offering flexibility to the waste system, including facilities for bulky waste, household hazardous waste and recyclables. Waste transfer may also take place on the collection route from small...... satellite collection vehicles to large compacting vehicles that cannot effectively travel small streets and alleys within the inner city or in residential communities with narrow roads. However, mobile transfer is not dealt with in this chapter, which focuses on stationary transfer stations. This chapter...
GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS
Directory of Open Access Journals (Sweden)
Túlio Jardim Raad
2006-06-01
Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.
State-space representation of the reactor dynamics equations
International Nuclear Information System (INIS)
Bernard, J.A.
1995-01-01
This paper describes a novel formulation of the reactor space-independent kinetics equations. The intent is to present these equations in a form that is both compatible with modern control theory and mathematically rigorous. It is desired to write the kinetics equations in the standard state variable representation, x = Ax, where x is the state vector and A is the system matrix and, at the same time, avoid mathematical compromises such as the linearization of an equation about a particular operating point. The advantage to this proposed formulation is that it may allow the lateral transfer of existing control concepts, some that have been developed for other fields, to the operation of nuclear reactors. For example, sliding mode control has been developed to allow robots to function in a robust manner in the presence of changes in the system model. This is necessary because a robot is expected to be capable of picking up an object of unknown mass and moving that object along a specified trajectory. The variability of the object's mass introduces an uncertainty into the system model that is used to deduce the appropriate control action. Thus, the robot controller must be made robust against such variations. Sliding mode control is one means of accomplishing this. A reactor controller might benefit from the same concept if its objective were to cause the reactor power to move along a demanded trajectory despite the presence of some uncertainty in the net amount of reactivity that is present
International Nuclear Information System (INIS)
Oberlin, J.C.; Frick, G.; Kempfer, C.; North, C.
1988-09-01
The state of work on the Vivitron gas transfer system and the system functions are summarized. The system has to: evacuate the Vivitron reservoir; transfer gas from storage tanks to the Vivitron; recirculate gas during operation; transfer gas from the Vivitron to storage tanks; and assure air input. The system is now being installed. Leak alarms are given by SF6 detectors, which set off a system of forced ventilation. Another system continuously monitors the amount of SF6 in the tanks [fr
From convolutionless generalized master to Pauli master equations
International Nuclear Information System (INIS)
Capek, V.
1995-01-01
The paper is a continuation of previous work within which it has been proved that time integrals of memory function (i.e. Markovian transfer rates from Pauli Master Equations, PME) in Time-Convolution Generalized Master Equations (TC-GME) for probabilities of finding a state of an asymmetric system interacting with a bath with a continuous spectrum are exactly zero, provided that no approximation is involved, irrespective of the usual finite-perturbation-order correspondence with the Golden Rule transition rates. In this paper, attention is paid to an alternative way of deriving the rigorous PME from the TCL-GME. Arguments are given in favor of the proposition that the long-time limit of coefficients in TCL-GME for the above probabilities, under the same assumption and presuming that this limit exists, is equal to zero. 11 refs
Bacon, D H
2013-01-01
Basic Heat Transfer aims to help readers use a computer to solve heat transfer problems and to promote greater understanding by changing data values and observing the effects, which are necessary in design and optimization calculations.The book is concerned with applications including insulation and heating in buildings and pipes, temperature distributions in solids for steady state and transient conditions, the determination of surface heat transfer coefficients for convection in various situations, radiation heat transfer in grey body problems, the use of finned surfaces, and simple heat exc
Nonparametric Transfer Function Models
Liu, Jun M.; Chen, Rong; Yao, Qiwei
2009-01-01
In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584
Forced convection heat transfer in He II
International Nuclear Information System (INIS)
Kashani, A.
1986-01-01
An investigation of forced convection heat transfer in He II is conducted. The study includes both experimental and theoretical treatments of the problem. The experiment consists of a hydraulic pump and a copper flow tube, 3 mm in ID and 2m long. The system allows measurements of one-dimensional heat and mass transfer in He II. The heat transfer experiments are performed by applying heat at the midpoint along the length of the flow tube. Two modes of heat input are employed, i.e., step function heat input and square pulse heat input. The heat transfer results are discussed in terms of temperature distribution in the tube. The experimental temperature profiles are compared with numerical solutions of an analytical model developed from the He II energy equation. The bath temperature is set at three different values of 1.65, 1.80, and 1.95 K. The He II flow velocity is varied up to 90 cm/s. Pressure is monitored at each end of the flow tube, and the He II pressure drop is obtained for different flow velocities. Results indicate that He II heat transfer by forced convention is considerably higher than that by internal convection. The theoretical model is in close agreement with the experiment. He II pressure drop and friction factor are very similar to those of an ordinary fluid
Theory of Periodic Conjugate Heat Transfer
Zudin, Yuri B
2012-01-01
This book presents the theory of periodic conjugate heat transfer in a detailed way. The effects of thermophysical properties and geometry of a solid body on the commonly used and experimentally determined heat transfer coefficient are analytically presented from a general point of view. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body. At the body surface, the true heat transfer coefficient is composed of two parts: the true mean value resulting from the solution of the steady state heat transfer problem and a periodically variable part, the periodic time and length to describe the oscillatory hydrodynamic effects. The second edition is extended by (i) the analysis of stability boundaries in helium flow at supercritical conditions in a heated channel with respect to the interaction between a solid body and a fluid; (ii) a periodic model and a method of heat transfer sim...
The Evolution of a More Rigorous Approach to Benefit Transfer: Benefit Function Transfer
Loomis, John B.
1992-03-01
The desire for economic values of recreation for unstudied recreation resources dates back to the water resource development benefit-cost analyses of the early 1960s. Rather than simply applying existing estimates of benefits per trip to the study site, a fairly rigorous approach was developed by a number of economists. This approach involves application of travel cost demand equations and contingent valuation benefit functions from existing sites to the new site. In this way the spatial market of the new site (i.e., its differing own price, substitute prices and population distribution) is accounted for in the new estimate of total recreation benefits. The assumptions of benefit transfer from recreation sites in one state to another state for the same recreation activity is empirically tested. The equality of demand coefficients for ocean sport salmon fishing in Oregon versus Washington and for freshwater steelhead fishing in Oregon versus Idaho is rejected. Thus transfer of either demand equations or average benefits per trip are likely to be in error. Using the Oregon steelhead equation, benefit transfers to rivers within the state are shown to be accurate to within 5-15%.
Handbook of differential equations stationary partial differential equations
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
NANOFLUID PROPERTIES FOR FORCED CONVECTION HEAT TRANSFER: AN OVERVIEW
Directory of Open Access Journals (Sweden)
W.H.Azmi
2013-06-01
Full Text Available Nanoﬂuids offer a significant advantage over conventional heat transfer ﬂuids and consequently, they have attracted much attention in recent years. The engineered suspension of nano-sized particles in a base liquid alters the properties of these nanofluids. Many researchers have measured and modeled the thermal conductivity and viscosity of nanofluids. The estimation of forced convective heat transfer coefficients is done through experiments with either metal or nonmetal solid particles dispersed in water. Regression equations are developed for the determination of the thermal conductivity and viscosity of nanofluids. The parameters influencing the decrease in convection heat transfer, observed by certain investigators, is explained.
A Model For Non-Fickian Moisture Transfer In Wood
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2004-01-01
A model for non-Fickian moisture transfer in wood is presented. The model considers the transfer of water vapour separate from the transfer of bound water. These two components are linked by an equation describing the sorption on the cell wall level. Hereby, a formulation capable of describing...... known non-Fickian effects, including the effects of step size, absolute moisture content, and sample length, is achieved. The sorption curves predicted by the model are compared with experimental results and good agreement is found....
Non-steady-state heat transfer of finned surface
International Nuclear Information System (INIS)
Okamoto, Y.; Kameoka, T.
1974-01-01
For many purposes, the finned surface is being used to increase heat transfer. Heat exchangers and fuel elements of gas cooled nuclear reactors require the use of the finned surface for high flux heat transfer. The problem is analytically treated by deriving a non-steady-state equation of radiative and convective heat transfer of annular and radial fins in case of sudden change of the fin-root temperature or heat flux. The numerical solution of temperature distribution along the fin is obtained for several typical transient cases. (U.S.)
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
Semilinear Schrödinger equations
Cazenave, Thierry
2003-01-01
The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique
General and exact pressure evolution equation
Toutant, Adrien
2017-11-01
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. This new pressure equation is valid for all real dense fluids for which the pressure tensor is isotropic. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial compressibility.
Using fundamental equations to describe basic phenomena
DEFF Research Database (Denmark)
Jakobsen, Arne; Rasmussen, Bjarne D.
1999-01-01
When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equation...... and subcooling are introduced. Since the degree of freedom was equal to one, using both the superheat and subcooling require that one of the fundamental equations must be omitted from the equation system.The main purpose of the paper is to clarify the relation between the fundamental balance equations...
International Workshop on Elliptic and Parabolic Equations
Schrohe, Elmar; Seiler, Jörg; Walker, Christoph
2015-01-01
This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.
International Nuclear Information System (INIS)
Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan
2014-01-01
In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations
Boundary value problemfor multidimensional fractional advection-dispersion equation
Directory of Open Access Journals (Sweden)
Khasambiev Mokhammad Vakhaevich
2015-05-01
Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
Cox, S.G.
2012-01-01
The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Reduction of lattice equations to the Painlevé equations: PIV and PV
Nakazono, Nobutaka
2018-02-01
In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.
Coupled transfers; Transferts couples
Energy Technology Data Exchange (ETDEWEB)
Nicolas, X.; Lauriat, G.; Jimenez-Rondan, J. [Universite de Marne-la-Vallee, Lab. d' Etudes des Transferts d' Energie et de Matiere (LETEM), 77 (France); Bouali, H.; Mezrhab, A. [Faculte des Sciences, Dept. de Physique, Lab. de Mecanique et Energetique, Oujda (Morocco); Abid, C. [Ecole Polytechnique Universitaire de Marseille, IUSTI UMR 6595, 13 Marseille (France); Stoian, M.; Rebay, M.; Lachi, M.; Padet, J. [Faculte des Sciences, Lab. de Thermomecanique, UTAP, 51 - Reims (France); Mladin, E.C. [Universitaire Polytechnique Bucarest, Faculte de Genie Mecanique, Bucarest (Romania); Mezrhab, A. [Faculte des Sciences, Lab. de Mecanique et Energetique, Dept. de Physique, Oujda (Morocco); Abid, C.; Papini, F. [Ecole Polytechnique, IUSTI, 13 - Marseille (France); Lorrette, C.; Goyheneche, J.M.; Boechat, C.; Pailler, R. [Laboratoire des Composites ThermoStructuraux, UMR 5801, 33 - Pessac (France); Ben Salah, M.; Askri, F.; Jemni, A.; Ben Nasrallah, S. [Ecole Nationale d' Ingenieurs de Monastir, Lab. d' Etudes des Systemes Thermiques et Energetiques (Tunisia); Grine, A.; Desmons, J.Y.; Harmand, S. [Laboratoire de Mecanique et d' Energetique, 59 - Valenciennes (France); Radenac, E.; Gressier, J.; Millan, P. [ONERA, 31 - Toulouse (France); Giovannini, A. [Institut de Mecanique des Fluides de Toulouse, 31 (France)
2005-07-01
This session about coupled transfers gathers 30 articles dealing with: numerical study of coupled heat transfers inside an alveolar wall; natural convection/radiant heat transfer coupling inside a plugged and ventilated chimney; finite-volume modeling of the convection-conduction coupling in non-stationary regime; numerical study of the natural convection/radiant heat transfer coupling inside a partitioned cavity; modeling of the thermal conductivity of textile reinforced composites: finite element homogenization on a full periodical pattern; application of the control volume method based on non-structured finite elements to the problems of axisymmetrical radiant heat transfers in any geometries; modeling of convective transfers in transient regime on a flat plate; a conservative method for the non-stationary coupling of aero-thermal engineering codes; measurement of coupled heat transfers (forced convection/radiant transfer) inside an horizontal duct; numerical simulation of the combustion of a water-oil emulsion droplet; numerical simulation study of heat and mass transfers inside a reactor for nano-powders synthesis; reduction of a combustion and heat transfer model of a direct injection diesel engine; modeling of heat transfers inside a knocking operated spark ignition engine; heat loss inside an internal combustion engine, thermodynamical and flamelet model, composition effects of CH{sub 4}H{sub 2} mixtures; experimental study and modeling of the evolution of a flame on a solid fuel; heat transfer for laminar subsonic jet of oxygen plasma impacting an obstacle; hydrogen transport through a A-Si:H layer submitted to an hydrogen plasma: temperature effects; thermal modeling of the CO{sub 2} laser welding of a magnesium alloy; radiant heat transfer inside a 3-D environment: application of the finite volume method in association with the CK model; optimization of the infrared baking of two types of powder paints; optimization of the emission power of an infrared
Thermosolutal MHD flow and radiative heat transfer with viscous ...
African Journals Online (AJOL)
This paper investigates double diffusive convection MHD flow past a vertical porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic ...
Radiative Transfer Reconsidered as a Quantum Kinetic Theory ...
Indian Academy of Sciences (India)
Abstract. We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a bal- ance relation in the phase space, which ...
Radiative Transfer Reconsidered as a Quantum Kinetic Theory ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a balance relation in the phase space, ...
Thermosolutal MHD flow and radiative heat transfer with viscous ...
African Journals Online (AJOL)
porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic solutions for the steady velocity, temperature and concentration. The parameters ...