Steady Magnetogasdynamic Flow Past a Source

This paper presents an asymptotic solution for the disturbanceat large distance from a source placed in a flow of conductingcompressible fluid in the presence of an applied magnetic field.The solution is obtained by a Fourier transform method usingtechniques developed for magnetohydrodynamic waves by Lighthill(1960). The results are discussed in detail for the cases ofthe undisturbed flow aligned with and perpendicular to the field,although they apply for any angle between the two, and showa Mach cone type of disturbance together with Alfvénwaves.     

An Inner Source in a Transversely Isotropic Elastic Medium

For a homogeneous, transversely isotropic elastic medium excited by a point force acting on the isotropy plane, an exact displacement field is constructed. This field decomposes into P-SV waves and SH waves. For SH waves satisfying the Lamé equations, boundary conditions are established and rather simple expressions are derived. These expressions are compared with the first terms of the ray series. Bibliography: 9 titles.     

Instanton in the Field of a Pointlike Source of a Euclidean Non-Abelian Field

We consider the behavior of an (anti)instanton in the field of a pointlike source of a Euclidean non-Abelian field and investigate (anti)instanton deformations described by variations of its characteristic parameters. We formulate the variational problem of seeking the corresponding “crumpled” topological configurations and solve it algebraically using the Ritz method (of multipole decomposition of deformation fields). We investigate the domain of parameters specific for the instanton liquid model. We propose a simple method of taking contributions of such configurations in the functional integral into account approximately. In the framework of superposition analysis, we obtain an estimate for the mean energy of the source in the instanton liquid, and the estimate increases linearly with distance. In the case of a dipole in the color-singlet state, the energy is a linear function of the distance between the sources with the “strength” coefficient agreeing well with the known model and lattice estimates. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 267–298, February, 2006.     

Reconstruction of a Source from Observational Data

A procedure is described for determining the strength, position, and startup time of a surface force source acting on an elastic half-space from recorded data on the vertical displacements (seismograms) of a linear oscillator (seismograph). The algorithm is based on a previously published analytical solution of the Lamb problem. Special attention is given to the role of the Rayleigh wavefront as a generator of displacements much larger than in the approach of P waves and SV waves to the seismograph, revealing the Rayleigh wave as the primary indicator of a source's space–time position.     

An Obstacle Control Problem with a Source Term

Abstract. An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired profile while the H ¹ norm of the obstacle is not too large. The addition of the source term strongly affects the needed compactness result for the existence of a minimizer.     

An Obstacle Control Problem with a Source Term

   Abstract. An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired profile while the H ¹ norm of the obstacle is not too large. The addition of the source term strongly affects the needed compactness result for the existence of a minimizer.     

Aggregation of a Distributed Source in Morphogen Gradient Formation

In the development of a biological entity, ligands (such as Decapentaplegic (Dpp) along the anterior–posterior axis of the Drosophila wing imaginal disc) are synthesized at a localized source and transported away from the source for binding with cell surface receptors to form concentration gradients of ligand–receptor complexes for cell signaling. Generally speaking, activities such as diffusion and reversible binding with degradable receptors also take place in the region of ligand production. The effects of such morphogen activities in the region of localized distributed ligand source on the ligand–receptor concentration gradient in the entire biological entity have been modeled and analyzed as System F in [ 1 ]. In this paper, we deduce from System F, a related end source model (System A) in which the effects of the distributed ligand source is replaced by an idealized point stimulus at the border between the (posterior) chamber and the ligand production region that simulates the average effects of the ligand activities in the production zone. This aggregated end source model is shown to adequately reproduce the significant implications of System F and to contain the corresponding ad hoc point source model, System R of [ 2 ], as a special case. Because of its simpler mathematical structure and the absence of any limitation on the ligand synthesis rate for the existence of steady-state gradients, System A type models are expected to be used widely. An example of such application is the recent study of the inhibiting effects of the formation of nonsignaling ligand–nonreceptor complexes [ 3 ].     

Motion of a Force Source over an Elastic Surface

The motion of a variable point force P(t) over the free surface of an elastic half-space is investigated with a view toward studying wave processes in an elastic medium. Special attention is given to the determination of surface wavefronts, because the detection of the latter from seismogram data can be utilized to locate the position of a source in space and time. This type of planar problem has been investigated previously, for example, in [1], but the analytical solutions of the problem of a stationary source moving with a constant velocity have been obtained only in the limit t without regard for the transient process of wave propagation.     

Source and coefficient inverse problems for an elliptic equation in a rectangle

The inverse problems of determining the source and coefficient of an elliptic equation in a rectangle are studied. Additional information on the solution to the direct problem (overdetermination) is the trace of its solution on an interval inside the rectangle. Sufficient existence and uniqueness conditions (global) are derived for the inverse problems. The study is performed in the class of continuously differentiable functions whose derivatives satisfy a Hölder condition.     

Determine a Space-Dependent Source Term in a Time Fractional Diffusion-Wave Equation

This paper is devoted to identify a space-dependent source term in a multi-dimensional time fractional diffusion-wave equation from a part of noisy boundary data. Based on the series expression of solution for the direct problem, we improve the regularity of the weak solution for the direct problem under strong conditions. And we obtain the uniqueness of inverse space-dependent source term problem by the Titchmarsh convolution theorem and the Duhamel principle. Further, we use a non-stationary iterative Tikhonov regularization method combined with a finite dimensional approximation to find a stable source term. Numerical examples are provided to show the effectiveness of the proposed method.

     

Influence of a Weak Boundary on the Wave Field of an Approaching Source

The response of a weak interface inside an isotropic elastic medium to an approaching source is considered. It is shown that a strong shear wave arises in the wave field reflected at an angle greater than a critical one. Properties of this wave are studied, and theoretical seismograms describing the contribution of all reflected waves to the total field are presented. Bibliography: 19 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 89–100.     

Aerodynamic Sound Due to a Source Near a Half-Plane

The effect of applying a Kutta-Joukowski condition at the edgeof a semi-infinite plane which is generating noise in a turbulentfluid at low Mach numbers is examined. It is found that in somecircumstances the noise is increased and the intensity of thedistant sound field may depend upon the third power of a typicalfluid velocity. When the sound field is convected the orders of magnitude ofthe acoustic far field are the same whether or not the Kutta-Joukowskicondition is applied, provided that the point of observationis not near the wake. Near the wake there is an acoustic "surface"wave which is much stronger than the distant field elsewhere.     

Source supports in electrostatics

We investigate the inverse source problem of electrostatics in a bounded and convex domain with compactly supported source. We try to extract all information about the unknown source support from the given Cauchy data of the associated potential, adopting by this previous work of Kusiak and Sylvester to the case of electrostatics. We introduce, and for the unit disk we also compute numerically, what we call the discoidal source support, i.e., the smallest set made up by the intersection of disks within the domain, which carries a source compatible with the given data. AMS subject classification (2000)  35R30, 65N21     

On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis

We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation.     

An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model

In this paper, we present a novel approach to determining the steady-state distribution for the number of jobs present in a 2-class, single server preemptive priority queueing model where the low priority source population is finite. Arrivals are assumed to be Poisson with exponential service times. The system investigated is a quasi birth and death process, and the joint distribution is derived via the method of generalized eigenvalues. Using this approach, we are able to obtain all eigenvalues and corresponding eigenvectors explicitly. Furthermore, we link this method to the matrix analytic approach by obtaining an explicit solution for the rate matrix R. Two numerical examples are given to illustrate the procedure and highlight some important computational features.     

The Asymptotic Behaviour of a Curved Line Source Plume within an Enclosure

A line source of heat is situated in an enclosure with inletsand an outlet for the contained fluid. The convection plumeformed must take a curved shape because of the asymmetry ofthe enclosure. We show how boundary-layer theory can be usedto find this shape in the case where the plume's deflectionis small. Two effects govern the shape of the curve; a buoyancyeffect and an inertial effect due to the bounding walls. Bysolving the outer potential flow problem, both effects can beincluded in the model. Finally, a stability analysis is carriedout for steady plumes which shows that any steady solution withan inflection point, as well as several other solutions, isunstable. A comparison is made with previous work which doesnot include all these effects, and with some experimental results.     

On Blowup of a Solution to a Sobolev-Type Equation with a Nonlocal Source

We consider the initial-boundary value problem for a dissipative nonlinear wave equation of the Sobolev type with a nonlocal cubic source. For this problem we obtain a sufficient condition for blowup of a strong generalized solution. Moreover, we obtain a two-sided estimate for the blowup time of the solution.Original Russian Text Copyright © 2005 Korpusov M. O. and Sveshnikov A. G.The authors were supported by the Russian Foundation for Basic Research (Grants 02-01-00253; 02-01-06038) and a grant of the Project Junior Scientists of Russia.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 567–578, May–June, 2005.     

关于一个普遍本源公式及其应用

Here presented is a further investigation on a general source formula(GSF) that has been proved capable of deducing more than 30 special formulas for series expansions and summations in the author's recent paper [On a pair of operator series expansions implying a variety of summation formulas.Anal.Theory Appl.,2015,31(3):260–282].It is shown that the pair of series transformation formulas found and utilized by He,Hsu and Shiue [cf.Disc.Math.,2008,308:3427–3440] is also deducible from the GSF as consequences.Thus it is found that the GSF actually implies more than 50 special series expansions and summation formulas.Finally,several expository remarks relating to the(Σ?D) formula class are given in the closing section.     

Combined Method for Calculating the Field Generated by a Point Source in a Waveguide. II

A two-dimensional problem on the propagation of waves that are excited by a point source in a waveguide is studied. The Dirichlet (Neumann) boundary condition is given on the upper (respectively, lower) boundary of the waveguide. The representation of the exact solution as a sum of geometric-optical waves, normal waves, and a remainder is given. Sufficient conditions on the total amount of detached normal and geometric-optical waves are obtained. The remainder is expressed by a simple formula. Bibliography: 19 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 116–135.     

Aerodynamic Sound due to a Point Source near a Half-plane

In this paper we extend Jones's analysis of the diffractionof sound in three dimensions by a semi-infinite plane with aplane vortex sheet attached in the two cases when the wave equationis in the form for still air and when convection is present.It is found that in so far as the moving medium is concernedthe imposition or otherwise of the Kutta-Joukowski conditiondoes not have much influence on the scattered field away fromthe diffracting plane; when the source is near the edge thefield has the same directionality and order of magnitude. Onthe other hand, near the wake the Kutta-Joukowski conditionproduces a much stronger field than elsewhere even when thesource is not near the edge. We also conclude that the samephenomenon occurs for arbitrary sources and not just for theline source discussed by Jones.