... (Author). Descriptors : (*ELASTIC SHELLS, MATHEMATICAL ANALYSIS), (*INTEGRAL EQUATIONS, DIFFERENTIAL EQUATIONS), BODIES OF ...
DTIC Science & Technology
... EQUATIONS, TURBULENCE, AFTERBURNERS, EXHAUST GASES, INTEGRAL EQUATIONS, DIFFERENTIAL EQUATIONS, MATHEMATICAL ...
flows is transformable to a singular integro-differential equation which can ... ing singular integro-differential equation (refs. 1, 2 and 11): ...
NASA Website
... DIMENSIONS ASTII ... integro-differential equations in several dimensions of a type in- cluding linearized forms of Boltzmann's equation. ...
Mar 1, 2011 ... The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. ...
singular integro-differential equation. For the general case the solution of this equation is not practical and a numerical approach is taken. ...
By using the method of variation of constants sufficient conditions are given for error estimates of solutions of stochastic integro-differential equations are relative to corresponding smooth system. Several examples are given to demonstrate the usefulne...
National Technical Information Service (NTIS)
The transonic integro-differential equation is solved using a decay function which can be applied in front and aft of the airfoil rather than on the airfoil surface only. The computational domain is discretized into rectangular elements and the integrals ...
In this paper, numerical solution of Volterra integro-differential equation by means of the Sinc collocation method is considered. Convergence analysis is given, it is shown that the Sinc solution produces an error of order Oe- where k>0 is a constant. This approximation reduces the Volterra integro-differential ...
NASA Astrophysics Data System (ADS)
... Title : APPLICATION OF THE RUNGE-KUTTA METHOD TO THE SOLUTION OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS,. ...
Existence, uniqueness and asymptotic behavior of solutions to integro-differential equations involving monotone operators are discussed. 18 references.
Energy Citations Database
In this paper, we propose an effective numerical method for solving nonlinear Volterra partial integro-differential equations. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function as the ``memory'' of system. Radial basis functions and finite difference method ...
... flow at incidence past a thin flat plate is set up with a vortex sheet to represent the wake, leading to a singular integro-differential equation for the ...
The problem of microstrip antennas covered by a dielectric substrate is formulated in terms of coupled integro-differential equations with the current distribution on the conducting patch as an unknown quantity. The Galerkin method is used to solve for th...
A class of the Hammerstein nonlinear integro-differential equations arising in the theory of income distribution is considered. The existence of solutions to these equations in the Sobolev space is proved. An application model described by such an equation is considered, and an algorithm for its solution is ...
A computational method for numerical solution of a nonlinear Volterra integro-differential equation of fractional (arbitrary) order which is based on CAS wavelets and BPFs is introduced. The CAS wavelet operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic ...
In this paper we present a computational method for solving a class of nonlinear Fredholm integro-differential equations of fractional order which is based on CAS (Cosine And Sine) wavelets. The CAS wavelet operational matrix of fractional integration is derived and used to transform the equation to a system of algebraic ...
ALPAL is a Macsyma-based tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. The Matrix Editor is a graphical, interactive tool for specifying the handling of Jacobian matrices and linear ...
ALPAL is a tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. Its Matrix Editor is brought into play when an ALPAL user wants to use an implicit time-integration scheme. The Matrix Editor is a ...
A Couette flow system is considered in which both conductive and radiative heat transfer occur. The energy equation for this type of system is a complicated nonlinear integro-differential equation. An approximation is applied to the radiant energy flux vector that is valid for intense absorption only. A comparison is made ...
In this paper, we study the local and global existence of mild solutions for impulsive fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. Also, we review some applications of fractional differential equations.
The transport approximation of the Boltzmann equation is generalized to cover the case of anisotropic scattering with energy degradation. It is shown that in such cases the approximation is a complicated integro-differential equation for the angular flux, which is still simpler to solve numerically than the original ...
A stable in C metric method of approximated solutions of singular integral equations (SIE) and singular integro-differential equations (SI-DE) with the Cauchy nucleus, which are solvable in a closed form, has been suggested. Quadrature formulas for the si...
An Integral Approximation (IA) method is proposed for the solution of certain integro-differential equations of which the linearized Boltzmann equation is one example. The lowest order solution in this method consists of replacing the integral operator of...
The characteristic method is used to transform the energy-space-angular Boltzmann integro-differential equation into the integral form in the cylindrical geometry. The solution of the integral equation obtained is investigated in the continuous space. (At...
Equations include time dependent transport equations. Problem is for zero boundary data on a rectangular domain with given initial values. The weak solutions are shown to depend continuously upon and under certain conditions of positivity can be ordered l...
In recent years considerable interest has focused on certain physically important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and the Inverse Scattering Transfor...
Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central diff...
A class of irreversible motions is defined by a variational principle based on information theory, and is shown to lead to the Navier-Stokes equations for gases and liquids. This entirely avoids the Boltzmann integro-differential equation, etc., with its ...
Initial-value systems are obtained for the scattering and transmission functions and emergent intensities for inhomogeneous, anisotropically scattering spherical media. Integro-differential equations are derived from transfer equations for each of the fol...
Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the correspon...
The reduction of the O(cu epsilon) integro differential equations to ordinary differential equations using a set of orthogonal functions is described. Attention was focused on the hover flight condition. The set of Galerkin integrals that appear in the re...
Energy loss straggling distributions are solutions of an integro- differential equation of transport, the Green's function of which is given as an Edgeworth series. The energy loss can be interpreted on a basis of shot effect. The correlation with Markov process and Kolmogorov equation is given. ...
ALPAL is a tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. Its Matrix Editor is brought into play when an A...
A Sinc Collocation method for solving linear integro-differential equations of the Fredholm type is discussed. The integro-differential equations are reduced to a system of algebraic equations and Q-R method is used to establish numerical procedures. The convergence rate of the method is O{left( {e^{{ - k{sqrt N ...
The outer potential problem for attached flow at incidence past a thin flat plate is set up with a vortex sheet to represent the wake, leading to a singular integro-differential equation for the mean slope of this sheet. Solution yields a correction to th...
This paper is concerned with the energy-dependent diffusion problem in nuclear reactor dynamics without the usual multigroup approximations. The mathematical problem consists of a system of N + 1 coupled partial integro-differential equations in either a ...
A new method based on volume integro-differential equations is examined as applied to scattering by doubly periodic magnetodielectric structures. The uniqueness and boundedness of the solution to the problem is proved.
The numerical integration in time of nonclassical parabolic initial boundary value problems which involve nonlocal integral terms over the spatial domain is described. The integral terms may appear in the boundary conditions and/or on the governing partia...
A computer program for the numerical solution of a nonlinear integro-differential equation representing a mathematic model of a coagulating aersol was developed. The mathematical statement of this problem is given, and the numerical methods employed from ...
A theory of antigen-antibody induced particulate aggregation is developed by investigating the stability of model systems of particles. A sufficient condition for the formation of large aggregate is derived by imposing the requirement that at equilibrium ...
This model examines the stability properties of a general system of first-order integro-differential equations which describe the dynamics of interacting species populations. A sufficient condition for the global stability of an equilibrium state is deriv...
A general electromagnetic scattering formulation is presented for the situation in which a perfectly conducting body is embedded in a horizontally or radially stratified medium. The electric field integro-differential equation (EFIDE) and magnetic field i...
In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive ...
This paper provides with a generalization of the work by Cattani (Math. Probl. Eng. (2008) 1�24), who has introduced the connection coefficients of the Shannon wavelets. We apply the Shannon wavelets approximation based on Cattani�s connection coefficients together the collocation points for solving the linear Fredholm integro-differential equations. ...
In this paper, the HAM is applied to obtained the series solution of the high-order nonlinear Volterra and Fredholm integro-differential problems with power-law nonlinearity. Two cases are considered, in the first case the set of base functions is introduced to represent solution of given nonlinear problem and in the other case, the set of base functions is not introduced. ...
The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov�Zabolotskaya equation, the Kadomtsev�Petviashvili equation and others. Since the solutions of ...
An abstract class of bifurcation problems is investigated from the essential spectrum of the associated Frechet derivative. This class is a very general framework for the theory of one-dimensional, steady-profile traveling- shock-wave solutions to a wide family of kinetic integro-differential equations from nonequilibrium statistical ...
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The work is based on the sl(2,R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some the integrable nonlinear partial differential equations are given explicitly. In ...
It is shown that it is possible to recast the Boltzmann integro- differential equation for hard spheres into a pair of linear partial differential equations of first and eighth orders, respectively. The eighth order equation is shown to be the non-dimensional Laplacian four times ...
Direct and inverse scattering problems in stratified media can be solved by first using invariant techniques to derive integro-differential equations and boundary conditions for the reflection kernels. These equations can be solved numerically to find the reflection kernels in the direct problem or the material parameter functions in ...
Starting from the general transport equation and within the limits of the P/sup 1/ approximation, a set of coupled second order partial integro- differential equations was obtained. These equations consider the effect of m groups of retarded neutrons and contain both the first and the ...
The theory of neutron spectra uses the Boltzmann integro-differential equation. In the case of plane geometry one usually develops the solution into Legendre functions. The integral equation of the transport problem is found, collision kernel for elastic collision is examined, and then a general method for getting the ...
In this paper, a sinc-collocation method is developed for solving linear systems of integro-differential equations of Fredholm and Volterra type with homogeneous boundary conditions. Some properties of the sinc procedure required for subsequent development are given and they are utilized to reduce the solution computation of systems of second-order boundary value ...
We consider the numerical discretization of singularly perturbed Volterra integro-differential equations (VIDE) and Volterra integral equations (VIE) by tension spline collocation methods in certain tension spline spaces, where [var epsilon] is a small parameter satisfying 0<[var epsilon]<<1, and q1, q2, g and K are functions ...
A new approach to one-dimensional inverse problem was recently introduced by Barry Simon. We continue the study on an intermediate object A, which satisfies a nonlinear integro-differential equation. We prove local solvability of this A-equation and find a necessary condition for global solvability. Some exact solutions are presented.
This work concerns the extension of a weak form of the Rolle's theorem to locally convex spaces that satisfy an axiom of separation. The result provides a condition for asserting the uniqueness of a solution to nonlinear functional equations, including nonlinear integro-differential equations. We use the extended Rolle's theorem to ...
The derivation of the kinetic equation for wave-wave interaction in a spatially homogeneous, dispersive system is critically examined. The integro- differential equation for the energy-spectrum function which is obtained seems to be more general, retaining in particular its validity also in the presence of ...
The paper gives the theory of magnetic propulsion of liquid lithium streams and their stability in tokamaks. In the approximation of a thin flowing layer the MHD equations are reduced to one integro-differential equation which takes into account the propulsion effect, viscosity and the drag force due to magnetic pumping and other ...
The solution of an integro-differential equation with the Cauchy core is reduced to a uniform Riemann conjugacy problem with the matrix coefficient, being a preset function of the initial value and parameter g. 4 refs. (Atomindex citation 21:076788)
A time-dependent description of the dissociative-attachment process is formulated within the framework of the projection-operator formalism of scattering theory. A generally applicable computational scheme for the solution of the resulting integro-differential equation of motion is developed. The concepts and computational techniques are illustrated for a ...
The problem of a two-dimensional jet-flapped hydrofoil operating near a free surface at infinite and zero Froude numbers is treated using thin-airfoil theory. The pair of coupled integro-differential equations which governs the system is derived and is re...
Optimally exploring and consuming a nonrenewable natural resource in the presence of uncertainties are addressed. Deshmukh and Pliska proved that the objective function, and the expected utility value of consumption minus the exploration costs, discounted...
Design modifications of a five-probe focusing collimator coincidence radioisotope scanning system are described. Clinical applications of the system were tested in phantoms using radioisotopes with short biological half-lives, including exp 75 Se, exp 192...
A numerical method for a time-dependent nonlinear partial integro-differential equation (PIDE) is considered. This PIDE describes a spatial population model that includes a given carrying capacity and the memory effect of this environment. To deal with this issue an adaptive method of third order in time is considered to save storage data in smooth parts ...
A new integro-differential equation with the only first order derivative describing diffraction of arbitrary transversely nonuniform light beam in the homogeneous transparent medium is obtained. At fist, it is introduced for the case of linear media. The ones approximation of the forward propagation is used. It is shown that derived ...
In the lattice theory of dislocation, the dislocation equation including the discreteness effect is a nonlinear integro-differential equation. It can hardly be solved. In this paper, the variational principle for the dislocation equation is presented. By using the Ritz approximation method, the variational solution ...
The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, ...
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We use the assumption that the potential for the A-boson system can be written as a sum of pairwise acting forces to decompose the wave function into Faddeev components that fulfill a Faddeev type equation. Expanding these components in terms of potential harmonic (PH) polynomials and projecting on the potential basis for a specific pair of particles results in a two-variable ...
The solutions of a system of coupled integro-differential Bogolyubov equations for distribution functions have been used to determine conditions, both in temperature and in concentration, under which a spatially uniform distribution of excitons transforms spontaneously into a periodic state with a small amplitude. The analysis rests on the concept assuming ...
The problem of dynamic stability of viscoelastic extremely shallow and circular cylindrical shells with any hereditary properties, including time-dependence of Poisson�s ratio, are reduced to the investigation of stability of the zero solution of an ordinary integro-differential equation with variable coefficients. Using the Laplace integral transform, ...
We study the activity of a one-dimensional synaptically coupled neural network by means of a firing rate model developed by Coombes et al. [Physica D 178 (2003)]. Their approach incorporates the biologically motivated finite conduction velocity of action potentials into a neural field equation of Wilson and Cowan type [Kybernetik 13 (1973)]. The resulting ...
A thermal analysis was performed to investigate the thermal behavior of the deployed solar array of the Communications Technology Satellite. Continuum theory was used to derive equations for the temperature distributions on both the blanket and BI-STEM boom of the solar array, and the resulting set of coupled integro-differential ...
The aim of this manuscript is to elucidate some models focusing on the dynamics of cell populations in vitro and to bring them in line with methods established in the context of inverse problems. We concentrate on a population balance model that describes the cell number as a function of time and single cell mass, where the key variable fulfills a partial integro-differential ...
This model examines the stability properties of a general system of first-order integro-differential equations which describe the dynamics of interacting species populations. A sufficient condition for the global stability of an equilibrium state is derived. This condition is an improvement over the condition derived by Woerz-Busekros (1978) for similar ...
This paper proposes two approximate methods to solve Volterra�s population model for population growth of a species in a closed system. Volterra�s model is a nonlinear integro-differential equation on a semi-infinite interval, where the integral term represents the effect of toxin. The proposed methods have been established based on collocation ...
Employing the ballooning-mode formalism, the two-dimensional eigenmode equation for trapped-electron instabilities in tokamaks is reduced to a one-dimensional integro-differential equation along the magnetic field lines; which is then analyzed both analytically and numerically. Dominant toroidal coupling effects are due to ion magnetic ...
ALPAL is a tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. ALPAL is designed to handle the sort of complicated mathematical models used in very large scientific simulation codes. Other ...
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar nonlinear systems excited by L�vy white noises. The proposed numerical procedure relies on the introduction of an integral transform of the Wiener�Hopf type into the equation governing the characteristic function. Once this equation is ...
We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case ...
The subject of this work is the application of fully discrete Galerkin finite element methods to initial-boundary value problems for linear partial integro-differential equations of parabolic type. We investigate numerical schemes based on the Pade discretization with respect to time and associated with certain quadrature formulas to approximate the ...
Some classes of nonlinear equations of mathematical physics are described that admit order reduction through the use of a hydrodynamic-type transformation, where the unknown function is taken as a new independent variable and an appropriate partial derivative is taken as the new dependent variable. RF-pairs and associated B�cklund transformations are constructed for ...
Electron scattering by diatomic molecules involving the formation of a single resonance is treated within the configuration-interaction formalism. A technique is presented for solving the resulting nonlocal integro-differential equation for the nuclear motion in the resonant state. This technique is applied to the scattering of electrons by molecular ...
The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique ...
PubMed
A unified approach to the theory of correlations in a plasma is presented, based on the BBKGY hierarchy. The theory is applied to a one-component plasma with the Coulomb interaction modified to include effects of the background. Closed integro-differential equations in space and time are obtained for the two-particle correlation function in both the strong ...
A model has been developed to describe the behavior of naturally fractured reservoirs with black oil in which high transmissibility in the fractures and low oil production rates allow the gravitational segregation of the gas, oil and water phases. The presented formulation results in a system of three simultaneous integro-differential equations where the ...
ABS>The two-channel five-nucleon reaction is formulated using the resonating group method and including the two groupings dt, nHe/sup 4/. The central potential used is of Gaussian shape with exchange dependence. The wave functions for the nuclear ground states are Gaussian (double Gaussian for the deuteron and single Gaussian for t and He/sup 4/), the parameter being determined by ...
Single and multiple intra-beam scattering are usually considered separately. Such separation works well for electron-positron colliders but usually yields only coarse description in the case of hadron colliders. Boltzmann type integro-differential equation is used to describe evolution of longitudinal distribution due to IBS. The finite size of the ...
A particular solution to the eddy current integro-differential equations is found in the form of a perturbation expansion with separated time dependence. No reference to field values outside the conductor is required and a full three-dimensional treatment is maintained. Transient behavior of the eddy currents is obtained by this method through the ...
In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from ...
A theory of antigen-antibody induced particulate aggregation is developed by investigating the stability of model systems of particles. A sufficient condition for the formation of large aggregate is derived by imposing the requirement that at equilibrium a statistically significant number of redundant bonds would occur in a reduced monomer-dimer model system. A basic relationship is obtained which ...
In this brief, we discuss some variants of generalized Halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks, integro-differential systems, and Volterra functional differential equations. We provide some generalizations of the Halanay inequality, which is more accurate than the existing results. As ...
As a base for the theory of moving striations a partial integro- differential equation is derived from the equations of continuity, the Laplace- Poisson equation, and a further relation between the electric field and the temperature of the electrons. Apart from the processes necessary for ...
In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integro-differential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential ...
In this article the problem of an interface fracture between two isotropic linear elastic materials is studied within a continuum modeling framework, which incorporates important nanoscale effects. The proposed model of bi-material crack ascribes curvature-dependent surface tension to both the fracture surfaces and the solid-solid interface. Further, it uses as boundary conditions the jump ...
By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo w0 ~ 1, an integral equation for the emergent intensity has been derived. Application of the Wiener- Hopf technique to this integral ...
This paper considers multiple scattering of waves propagating in a non-lossy one-dimensional random medium with short- or long-range correlations. Using stochastic homogenization theory it is possible to show that pulse propagation is described by an effective deterministic fractional wave equation, which corresponds to an effective medium with a frequency-dependent ...
In this paper, we describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) ...
The kinetic collection equation (KCE) has been widely used to describe the evolution of the average droplet spectrum due to the collection process that leads to the development of precipitation in warm clouds. This deterministic, integro-differential equation only has analytic solution for very simple kernels. For more realistic ...
An analytical model that is based on purely differential equations of the nonlinear dynamics of two plasma modes driven resonantly by high-energy ions near the instability threshold is presented here. The well-known integro-differential model of Berk and Breizman (BB) extended to the case of two plasma modes is simplified here to a system of two coupled ...
The integro-differential equation d{sup 2}f/dx{sup 2} + Af = {integral}{sub 0}{sup {infinity}}K(x-t)f(t)dt + g(x) with kernel K(x)={lambda}{integral}{sub a}{sup {infinity}}e{sup -|x|p}G(p)dp, a{>=}0, is considered, in which A>0, {lambda} element of 9-{infinity},{infinity}), G(p){>=}0, 2{integral}{sub a}{sup {infinity}}1/p g(p)dp=1. These ...
In this paper an oblique derivative problem for parabolic singular integro-differential operators was studied. In this problem the direction of the derivative may be tangent to the boundary of the domain. By the large parameter method theorems of existenc...
In spite of many efforts devoted to this phenomenon, the electron-positron interaction in metals remains an unsolved problem. The development of the partial density amplitude approach to the electronic structure of simple metals offers the possibility to perform direct many-body calculations of the electron-positron interaction in these materials. A theory of this interaction based on the ...
We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integro-differential operators that is expressive enough for specifying regular boundary problems with ...
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Singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh-Taylor instability are discussed. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, results describing the precise form, number, and location of singularities in the unphysical domain as the wave height is increased are presented. It is shown how ...
Graphics Processing Units (GPUs) were originally designed to manipulate images, but due to their intrinsic parallel nature, they turned into a powerful tool for scientific applications. In this article, we evaluated GPU performance in an implementation of a traditional stochastic simulation � the correlated Brownian motion. This movement can be described by the Generalized Langevin ...
We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using ...
In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron diffusion is small. It consists of two integro-differential equations defined at the boundary of the plasma region: one ...
A Livermore Physics Applications Language (ALPAL) is a tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. ALPAL is designed to handle the sort of complicated mathematical models used in very ...
A new mathematical model for the dynamics of prion proliferation involving an ordinary differential equation coupled with a partial integro-differential equation is analyzed, continuing the work in [J. Pruss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. 6 (2006) ...
... the geometric and physical aspects that permit introduction of the ... To estimate the a - characteristics, possible algorithms are formulated, namely a ...
In view of recent interest in the problem of macroscopic quantum tunneling in systems involving the Josephson effect, we present an accurate numerical calculation of the tunneling rate of a system from a metastable well, at zero temperature, in the presence of dissipative coupling to the environment. Although we concentrate on a specific form of dissipation, as discussed by Caldeira and Leggett, ...
A system of two coupled integro-differential equations is derived and solved for the non-linear evolution of two waves excited by the resonant interaction with fast ions just above the linear instability threshold. The effects of a resonant particle source and classical relaxation processes represented by the Krook, diffusion, and dynamical friction ...
This work investigates the approximate solution for fourth-order multi-point boundary value problem represented by linear integro-differential equation involving nonlocal integral boundary conditions by using the reproducing kernel method (RKM). The investigated solution is represented in the form of a series with easily computable components in the ...
We report on the development of the self-consistent model of magnetization reversal dynamics in polycrystalline materials taking into account magnetodipole interaction, number of domain walls in grains, influence of microinhomogeneities, nucleation and collision of walls. The evolution of angular distribution of magnetic moments and the shape of output voltage produced by impulsive reversal of ...
Fractional calculus extends the notions of the classical calculus of space and time variations to allow non-integer dimensions. The corresponding partial differential equations (PDEs) become integro-differential PDEs, i.e., introduce memory effects in the description of transport. But what is the physics behind the application of these operators? In this ...
We consider an evolving dendrite in the small undercooling limit for a two-sided symmetric model with equal diffusivity in the solid and in the melt. We derive integro-differential equations for the interface evolution for both two- and three-dimensional cases. In each case, we consider how an initially localized disturbance evolves as it advects away from ...
The steady one-dimensional planar plasma sheath problem, originally considered by Tonks and Langmuir, is revisited. Assuming continuously generated free-falling ions and isothermal electrons and taking into account electron inertia, it is possible to describe the problem in terms of three coupled integro-differential equations that can be numerically ...
Flexible motion of a uniform Euler-Bernoulli beam attached to a rotating rigid hub is investigated. Fully coupled non-linear integro-differential equations, describing axial, transverse and rotational motions of the beam, are derived by using the extended Hamilton's principle. The centrifugal stiffening effect is included in the derivation. A ...
This paper addresses the issue of the convergence dynamics of stochastic Cohen-Grossberg neural networks (SCGNNs) with white noise, whose state variables are described by stochastic nonlinear integro-differential equations. With the help of Lyapunov functional, semi-martingale theory, and inequality techniques, some novel sufficient conditions on pth ...
A formulation of the continuum random-phase approximation (CRPA) nuclear response with a velocity-dependent residual interaction of the Skyrme type is presented. The inhomogeneous coupled-channel integro-differential equations obtained are modified so as to use the Lanczos method, by means of which they can be solved relatively easy. The CRPA method here ...
The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich ...
We studied the possibilities for numerical integration of Lorentz-Dirac equation that is the equation describing the motion of a charged point particle when radiation reaction is taken into account. In numerical modelling based on particle models usually the equations of motion without radiation force are used and the corrections for ...
Do phenomenological master equations with a memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological ...
An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the ...
Automatic Chebyshev spectral collocation methods for Fredholm and Volterra integral and integro-differential equations have been implemented as part of the chebfun software system. This system enables a symbolic syntax to be applied to numerical objects in order to pose and solve problems without explicit references to discretization. The same objects can be used in ...
The basic integral expressions for radiant energy transfer near a diffuse reflecting surface with uniform temperature are reviewed. The radiation diffusion approxi-mation is also reviewed. Conservation of energy transferred by radiation, diffusion, conduction, and convection is formulated as an integro- partial differential equation for a gray chemically reacting gas ...
In this paper we extend the subdiffusive Klein-Kramers model, in which the waiting times are modeled by the ?-stable laws, to the case of waiting times belonging to the class of tempered ?-stable distributions. We introduce a generalized version of the Klein-Kramers equation, in which the fractional Riemman-Liouville derivative is replaced with a more general ...
A functional integro-differential equation for the electron-positron Green's function is derived from a consideration of the effect of sources of the Dirac field. This equation contains an electron-positron interaction operator from which functional derivatives may be eliminated by an iteration procedure. The operator is evaluated so ...
The understanding and prediction of transport due to plasma microturbulence is a key open problem in modern plasma physics, and a grand challenge for fusion energy research. Ab initio simulations of such small-scale, low-frequency turbulence are to be based on the gyrokinetic equations, a set of nonlinear integro-differential equations ...
The one-speed, time-dependent, source-free Boltzmann integro- differential neutron transport equation is used to study the time dependence of monoenergetic neutrons in a spherical, homogeneous medium. By applying the Marshak boundary condition at the outer face instead of the usual vanishing of the scalar flux at some ...
We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the ...
A class of efficient algorithms is presented for reconstructing an image from noisy, blurred data. This methodology is based on Tikhonov regularization with a regularization functional of total variation type. Use of total variation in image processing was pioneered by Rudin and Osher. Minimization yields a nonlinear integro -differential ...
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical ...
Modeling of fluid flow through vertical cracks for the purpose of extracting heat from hot, dry rock masses is described. A basic equation for the two-dimensional problem of fluid flow through a crack is presented and an appropriate solution found for the crack profile and stress intensity factors. The basic equation is a nonlinear Cauchy-singular ...
We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency ...
We give more precise asymptotic behaviour of the spectrum of a singular integro-differential operator and find the regularized trace of its inverse operator. Bibliography: 12 titles.
In an asymptotic development of the equations governing the equilibria and linear stability of rapidly rotating polytropes we employed the slender aspect of these objects to reduce the three-dimensional partial differential equations to a somewhat simpler, ordinary integro-differential form. The earlier calculations dealt with isolated ...
Integro-differential equations are obtained which describe the variation of molecular weight distributions in a polymer substance caused by irradiation. The solutions of these equations give the gel point and the average molecular weights. In the case of cross-limking without cyclization, the results agree with those obtained ...
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ...
Motivated by the hierarchical multiscale image representation of Tadmor et al.,1 we propose a novel integrodifferential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive 'slices' of the image, which are balanced by a typical curvature term at the finer scale. Although the original ...
A deterministic analysis of the computational cost associated with geometric splitting/Russian roulette in Monte Carlo radiation transport calculations is presented. Appropriate integro-differential equations are developed for the first and second moments of the Monte Carlo tally as well as time per particle history, given that splitting with Russian ...
A new algorithm for implementing the adaptive Monte Carlo method is given. It is used to solve the Boltzmann equations that describe the time evolution of a nonequilibrium electron-positron pair plasma containing high-energy photons. These are coupled nonlinear integro-differential equations. The collision kernels for the photons as ...
As nuclear wave functions have to obey the Pauli principle, potentials issued from reaction theory or Hartree-Fock formalism using finite-range interactions contain a non-local part. Written in coordinate space representation, the Schr�dinger equation becomes integro-differential, which is difficult to solve, contrary to the case of local potentials, ...
A new transient analysis, that overcomes the limitations of the spatially discretized models, is developed in the present study for the response of axially moving materials interacting with external dynamic components. First, the complex response of a time-varying, cable transport system, such as a tramway or cable car, is predicted from the model of an axially moving string transporting a damped, ...
Increasing demands on the complexity of scientific models coupled with increasing demands for their scalability are placing programming models on equal footing with the numerical methods they implement in terms of significance. A recurring theme across several major scientific software development projects involves defining abstract data types (ADTs) that closely mimic ...
On the basis of differential transformations, a stable integro-differential method of solving the inverse heat conduction problem is suggested. The method has been tested on the example of determining the thermal diffusivity on quasi-stationary fusion and heating of a quartz glazed ceramics specimen.
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity free. Flames confined in channels with asymptotically straight impenetrable walls are considered. Besides a few free propagations along straight channels, attention is focused on flames propagating ...
This paper deals with optimal dividend payment problem in the general setup of a piecewise-deterministic compound Poisson risk model. The objective of an insurance business under consideration is to maximize the expected discounted dividend payout up to the time of ruin. Both restricted and unrestricted payment schemes are considered. In the case of restricted payment scheme, the value function is ...
A theory describing nonlinear electromagnetic rectification of BCS-paired electrons at a superconductor-vacuum interface by means of a monochromatic, plane electromagnetic wave incident at an oblique angle is presented. On the basis of a recently constructed nonlinear-response tensor, the forced nonlinear dc-current density is analyzed. A fundamental integro-differential ...
An isolated combustion spot-known as a flame ball (FB)-is considered while it is advected by a turbulent flow of a lean premixture of such a light fuel as hydrogen. A Batchelor approximation for the surrounding Lagrangian flow is made. This in principle gives one an access to the FB lifetime t(life) and to its response to the ambiant Lagrangian rate-of-strain tensor g(t), by means of a nonlinear ...
An isolated combustion spot�known as a flame ball (FB)�is considered while it is advected by a turbulent flow of a lean premixture of such a light fuel as hydrogen. A Batchelor approximation for the surrounding Lagrangian flow is made. This in principle gives one an access to the FB lifetime tlife and to its response to the ambiant Lagrangian rate-of-strain tensor g(t), by means of a nonlinear ...
A code for performing reactor calculations by the heterogeneous method is developed in FORTRAN for use on the IBM-704/709/7090 computers. The basic (integro-differential) equations of the method are derived initially ignoring any fuel resonances and subsequently introducing single lumped resonances in fuel. Cylindrically symmetric fuel assemblies ...
Fracturing of water-saturated rocks occurs frequently in cold climates and is caused by water freezing inside their pores. It is an important problem for both engineers and scientists as it can affect pavements and the foundations of buildings, and is a major erosional force in rocks. We consider the problem of the propagation of an ice-filled three-dimensional penny-shaped cavity in a ...
A two-dimensional electromagnetic analysis of the trapped-ion instability for the tokamak case with ..beta.. not equal to 0 has been made, based on previous work in the electrostatic limit. The quasineutrality condition and the component of Ampere's law along the equilibrium magnetic field are solved for the perturbed electrostatic potential and the component of the perturbed vector ...
This work deals with the characterization of the conductivity tensor of a carbon fiber reinforced polymer composite (CFRP) thin plate. We propose a contactless method based on the eddy current non destructive testing technique. The used eddy current sensor consists of a ferrite torus on which a winding is wound. The torus is of a rectangular section and contains a thin air-gap in which the thin ...
The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia ...
Displacements per atom (DPA) is a widely used damage unit for displacement damage in nuclear materials. Calculating the DPA for SiC irradiated in a particular facility requires a knowledge of the neutron spectrum as well as specific information about displacement damage in that material. In recent years significant improvements in displacement damage information for SiC have been generated, ...
Partial integro-differential equations describing the gas flow in a plane turbine cascade are solved to determine the blading profile which provides a pressure distribution close to a specified form when an ideal gas flows through the stage. The set pressure distribution over the profile contour should satisfy the conditions of the most advantageous flow ...
Polymer degradation occurs when polymer chains are broken under the influence of thermal, mechanical, or chemical energy. Chain-end depolymerization and random- and midpoint-chain scission are mechanisms that have been observed in liquid-phase polymer degradation. Here we develop mathematical models, unified by continuous-mixture kinetics, to show how these different mechanisms affect polymer ...
Recently, multisite delayed feedback stimulation was proposed as a novel method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization. To develop the mathematical background of this technique we propose a continuous medium model of globally coupled phase oscillators in the form of a delayed ...
In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential ...
A reformulation of classical GL(n,c) Yang-Mills theory is presented. The reformulation is in terms of a single matrix-valued function G on a six-dimensional subspace of the space of paths in Minkowski space, M. This subspace is defined as the null paths beginning at each point, (X/sup a/), of M and ending at future null infinity. A convenient parametrization of these paths is to give the Minkowski ...
A theoretical investigation of the breakdown of the viscous wake downstream of a flat plate in supersonic flow is performed in this paper based on the large Reynolds number (Re -> infty ) asymptotic analysis of the Navier Stokes equations. The breakdown is provoked by an oblique shock wave impinging on the wake a small distance l_s downstream of the plate trailing edge. Two ...
The velocity-memory-stress time-domain finite-difference system is a common method of modeling seismic wave propagation in anelastic media. This formulation is based upon the assumption of a standard linear solid rheology which allows the conversion of the original integro-differential system of equations into purely differential ...
For the most general quantum master equations, also called Nakajima-Zwanzig or non-Markovian equations, we first define sufficient conditions [1] on convolution integral kernels and inhomogeneity functions in order to derive with mathematical rigor an upper bound on solutions, as required by the von Neumann conditions. The considered type of ...
Via Carleman's estimates we prove uniqueness and continuous dependence results for solutions to two overdetermined parabolic ill-posed problems, the first being integro-differential, the latter with deviating arguments. The overdetermination is prescribed in an open subset of the (geometric) domain.
We establish in this paper some new Gronwall-Bellman-Bihari type integro-differential inequalities in n variables. These inequalities generalize, in some cases, the existing ones which are known to have a wide range of applications in the study of qualita...
A model for the formation of crystal size distributions (CSDs) in closed magmatic systems such as sills has been presented [1]. The model generates CSDs and properties of suites of CSDs observed in natural rocks. It is, however, a numerical simulation because of the intractable form of the governing differential equation. Ideally, an analytical expression would facilitate a ...
An open system of overdamped, interacting Brownian particles diffusing on a periodic substrate potential U(x+l)=U(x) is studied in terms of an infinite set of coupled partial differential equations describing the time evolution of the relevant many-particle distribution functions. In the mean-field approximation, this hierarchy of equations can be ...
During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than ...
During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion ...
After having briefly reviewed the Hamilton-Jacobi theory of classical point-particle mechanics, its extension to the quantum regime and the formal identity between the Hamilton-Jacobi equation for Hamilton's characteristic function and the eikonal equation of geometrical optics, an eikonal theory for free photons is established. The space-time dynamics of ...
... Abstract : A set of coupled integral equations is derived from the incompressible Navier-Stokes equations and the continuity equation. ...
We build reduced-order dynamical models of a thermal convection loop using the Karhunen-Lo�ve decomposition (KL) methodology, in conjunction with the Galerkin projection technique. The convective loop has the form of a torus and is filled with a water. The loop receives heat in some parts and releases it in others through a known-heat-flow sinusoidal function, thus creating a natural ...
This thesis deals with a coupled-state method for treating the problem of positron-atom collisions. Chapter 1 introduces the processes involved in positron scattering. Chapter 2 describes the coupled-state formulation. From a two-centre expansion for the system wave function in terms of both atom and positronium states, we derive the coupled equations, convert them to partial ...
Non-linear density-wave instabilities are analyzed for two-phase channel flows with nuclear heating; the fluid is homogeneous and enters the channel at saturated conditions. The effect of local pressure losses at the channel inlet and outlet are considered, and a constant pressure drop boundary condition is imposed. The model describes the development of localized instabilities within the core of ...
In this investigation, we are primarily concerned with modeling fluid flow through vertical cracks that were created for the purpose of extracting heat from hot, dry rock masses. The basic equation for the two-dimensional problem of fluid flow through a crack is presented and an approximate solution is found. The basic equation is a non-linear, ...
We consider steady state unsaturated flow in bounded, randomly heterogeneous soils under the influence of random boundary and source terms. Our aim is to predict pressure heads and fluxes without resorting to Monte Carlo simulation, upscaling, or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. We represent this relationship through ...
Dislocations are thought to be the principal mechanism of high ductility of the novel B2 structure intermetallic compounds YAg and YCu. In this paper, the edge dislocation core structures of two primary slip systems <100>{010} and <100>{01bar 11} for YAg and YCu are presented theoretically within the lattice theory of dislocation. The governing dislocation equation ...
The consequences of spontaneously broken translational invariance on the nucleation-rate statistical prefactor in theories of first-order phase transitions are analyzed. A hybrid, semiphenomenological approach based on field-theoretic analyses of condensation and modern density-functional theories of nucleation is adopted to provide a unified prescription for the incorporation of ...
We investigate flows with local vorticity in ideal heavy fluid with free surface in the framework of weakly non-linear theory in two-dimensional spatial representation. Steady flows with a singular structure of the velocity field in the vicinity of a free surface were found in [1] using a quadratic approximation. In the present work, we demonstrate new solutions by taking into account quadratic ...
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence that the population dynamics in the ocean is approximately scale-invariant. We use this invariance in the construction and solution of a size-structured ...
Diffusion is one of the most frequently used assumptions to explain dispersal. Diffusion models and in particular reaction-diffusion equations usually lead to solutions moving at constant speeds, too slow compared to observations. As early as 1899, Reid had found that the rate of spread of tree species migrating to northern environments at the beginning of the Holocene was too ...
The time-dependent description of the dynamics of electron-molecule collision complexes is outlined within the framework of Feshbach's projection-operator formalism. It is shown that the equation of motion for the quantum-mechanical wave packet representing the collision complex contains effective-potential terms which are nonlocal as well as non-Markovian, that is, ...
A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The ...
We study the effect of the non-linear process of ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term behaviour of a non-uniform magnetic field in a one-dimensional geometry. Our main focus is the dissipation of magnetic energy inside neutron stars (particularly magnetars), but our results have a wider application, particularly ...
An electrochemical theory of the glycocalyx surface layer on capillary endothelial cells is developed as a model to study the electrochemical dynamics of anionic molecular transport within capillaries. Combining a constitutive relationship for electrochemical transport, derived from Fick's and Ohm's laws, with the conservation of mass and Gauss's law from electrostatics, a system of three ...
... Title : NOMOGRAM FOR SAHA'S EQUATION. ... Abstract : In the report a nomogram for the solution of Saha's equation is given. ...
... Title : BROADENING IN THE MASTER EQUATION. ... Abstract : Broadening has been introduced into the collision term of the master equation. ...
... Abstract : The Navier-Stokes and the continuity equations are rearranged into a vorticity transport equation and a definition of vorticity equation. ...
... Abstract : The class includes some difference equations, differential-difference equations as well as retarded functional differential equations; that is ...
