Articles de revues : « Unbounded source »

1

Natalini, R. "Unbounded solutions for conservation laws with source." Nonlinear Analysis: Theory, Methods & Applications 21, no. 5 (1993): 349–62. http://dx.doi.org/10.1016/0362-546x(93)90078-7.

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Cox, G., and R. Chitty. "Some Source-Dependent effects of unbounded fires." Combustion and Flame 60, no. 3 (1985): 219–32. http://dx.doi.org/10.1016/0010-2180(85)90027-6.

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Demir, Kaya, and Salih Ergün. "An Analysis of Deterministic Chaos as an Entropy Source for Random Number Generators." Entropy 20, no. 12 (2018): 957. http://dx.doi.org/10.3390/e20120957.

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This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white Gaussian noise source is also sampled regularly to generate random bits. By varying the sampling frequency, and based on the autocorrelation and the approximate entropy analysis of the resulting bit sequences, a comparison is made between bounded chaos, unbounded chaos and Gaussian white noise as an entropy source for random number generators.

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4

ALEKSEEV, G. V. "Multidimensional inverse source problems of underwater acoustics." European Journal of Applied Mathematics 9, no. 6 (1998): 589–605. http://dx.doi.org/10.1017/s0956792598003611.

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We consider linear and nonlinear inverse source problems of sound radiation in an unbounded domain which models an oceanic waveguide. The method for analysing their solvability is based on analytical properties of generalized acoustic potentials and the theory of extremal problems.

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CONAND, NICOLE, and ALICIA DORNADIC. "The Ethnographer Unbounded: Considering open source in corporate environments." Ethnographic Praxis in Industry Conference Proceedings 2012, no. 1 (2012): 88–100. http://dx.doi.org/10.1111/j.1559-8918.2012.00011.x.

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SPEIRS, DAVID C., S. L. McCONVILLE, K. M. GILLESPIE, A. D. R. PHELPS, and K. RONALD. "Numerical simulations of unbounded cyclotron-maser emissions." Journal of Plasma Physics 79, no. 6 (2013): 999–1001. http://dx.doi.org/10.1017/s0022377813001141.

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AbstractNumerical simulations have been conducted to study the spatial growth rate and emission topology of the cyclotron-maser instability responsible for stellar/planetary auroral magnetospheric radio emission and intense non-thermal radio emission in other astrophysical contexts. These simulations were carried out in an unconstrained geometry, so that the conditions existing within the source region of some natural electron cyclotron masers could be more closely modelled. The results have significant bearing on the radiation propagation and coupling characteristics within the source region of such non-thermal radio emissions.

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Wu, Zhen. "Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration." Journal of the Australian Mathematical Society 74, no. 2 (2003): 249–66. http://dx.doi.org/10.1017/s1446788700003281.

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AbstractWe first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.

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Hofmann, Bernd, Peter Mathé, and Heinrich von Weizsäcker. "Regularization in Hilbert space under unbounded operators and general source conditions." Inverse Problems 25, no. 11 (2009): 115013. http://dx.doi.org/10.1088/0266-5611/25/11/115013.

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Rozanov, Yu A. "On Evolution of Random Fields with an Ultra Unbounded Stochastic Source." Theory of Probability & Its Applications 38, no. 2 (1994): 316–29. http://dx.doi.org/10.1137/1138028.

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Marklein, René, Karl J. Langenberg, and Torsten Kaczorowski. "Electromagnetic and elastodynamic point source excitation of unbounded homogeneous anisotropic media." Radio Science 31, no. 6 (1996): 1919–30. http://dx.doi.org/10.1029/96rs02155.

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Carrion, Philip, José Carcione, and Edson E. S. Sampaio. "Radiation patterns: Possibility for monitoring seismic sources." GEOPHYSICS 61, no. 1 (1996): 282–87. http://dx.doi.org/10.1190/1.1443950.

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Recent field measurements of the radiation in boreholes indicate that the radiation patterns of real seismic sources are not always in agreement with those corresponding to the point‐source excitation in unbounded homogeneous and isotropic acoustic or elastic media [we refer the reader to Aki and Richards (1980) for the basic discussion on the radiation patterns in homogeneous media]. This mismatch results from the fact that the point‐source radiation patterns corresponding to homogeneous media are too simplistic to satisfy any experiment in the more realistic Earth environment. A study of radiation patterns is certainly important not only to predict possible seismic events but also to analyze the source performance itself by recording seismic arrivals.

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Pişkin, Erhan. "Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms." Advances in Mathematical Physics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/523254.

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We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

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Halilsoy, M., and A. Ovgun. "Particle Collision Near 1 + 1-Dimensional Horava-Lifshitz Black Hole and Naked Singularity." Advances in High Energy Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/4383617.

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The unbounded center-of-mass (CM) energy of oppositely moving colliding particles near horizon emerges also in 1+1-dimensional Horava-Lifshitz gravity. This theory has imprints of renormalizable quantum gravity characteristics in accordance with the method of simple power counting. Surprisingly the result obtained is not valid for a 1-dimensional Compton-like process between an outgoing photon and an infalling massless/massive particle. It is possible to achieve unbounded CM energy due to collision between infalling photons and particles. The source of outgoing particles may be attributed to an explosive process just outside the horizon for a black hole and the naturally repulsive character for the case of a naked singularity. It is found that absence of angular momenta in 1+1-dimension does not yield unbounded energy for collisions in the vicinity of naked singularities.

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Falconer, Kenneth J., Jiaxin Hu, and Yuhua Sun. "Inhomogeneous parabolic equations on unbounded metric measure spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 5 (2012): 1003–25. http://dx.doi.org/10.1017/s0308210511000539.

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We study the inhomogeneous semilinear parabolic equationwith source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.

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Hijden, J. H. M. T. "Radiation from an impulsive line source in an unbounded homogeneous anisotropic medium." Geophysical Journal International 91, no. 2 (1987): 355–72. http://dx.doi.org/10.1111/j.1365-246x.1987.tb05232.x.

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Tilgner, A. "Oscillatory shear layers in source driven flows in an unbounded rotating fluid." Physics of Fluids 12, no. 5 (2000): 1101–11. http://dx.doi.org/10.1063/1.870364.

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Chen, Zhiming, and Xueshuang Xiang. "A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain." SIAM Journal on Numerical Analysis 51, no. 4 (2013): 2331–56. http://dx.doi.org/10.1137/130917144.

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Krishnan, Gokul P., and David T. Leighton. "Diffusion from a point source in a time‐dependent unbounded extensional flow." Physics of Fluids A: Fluid Dynamics 4, no. 11 (1992): 2327–31. http://dx.doi.org/10.1063/1.858473.

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Povstenko, Yuriy, Martin Ostoja-Starzewski, and Tamara Kyrylych. "Telegraph equation in polar coordinates: Unbounded domain with moving time-harmonic source." International Journal of Heat and Mass Transfer 207 (June 2023): 124013. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2023.124013.

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Dhaliwal, Ranjit S., Samir R. Majumdar, and Jun Wang. "Thermoelastic waves in an infinite solid caused by a line heat source." International Journal of Mathematics and Mathematical Sciences 20, no. 2 (1997): 323–34. http://dx.doi.org/10.1155/s0161171297000434.

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The generalized thermoelasticity theory recently developed by Green and Naghdi is employed to investigate thermoelastic interactions caused by a continuous line heat source in a homogeneous isotropic unbounded solid. Hankel-Laplace transform technique is used to solve the problem. Explicit expressions, for stress and temperature fields, are obtained for small time approximation. Numerical values are displayed graphically. Our results show that this theory predicts an infinite speed for heat propagation in general, and includes the second sound phenomena as a special case.

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21

Poletto, Flavio. "Energy balance of a drill-bit seismic source, part 1: Rotary energy and radiation properties." GEOPHYSICS 70, no. 2 (2005): T13—T28. http://dx.doi.org/10.1190/1.1897038.

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An issue in seismic-while-drilling (SWD) technology is to characterize the dynamic and radiation properties of the drill-bit source working under different operational conditions. The energy requirements, power losses, local crack effects, radiation, and near-field effects associated with rotary drilling are analyzed to quantify the waves produced by an SWD vertical force acting in bounded and unbounded media. Results are expressed in terms of a complex integrated impedance and the equations for rotary drilling. The calculations — extended to the waves in the drill string — are used in part 2 of this paper (Poletto, 2005, this issue) to quantify the performance of actual drill-bit sources.

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Royer, Julien. "Semiclassical measure for the solution of the Helmholtz equation with an unbounded source." Asymptotic Analysis 91, no. 1 (2015): 11–32. http://dx.doi.org/10.3233/asy-141255.

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Hu, Guang-hui, Yavar Kian, and Yue Zhao. "Uniqueness to Some Inverse Source Problems for the Wave Equation in Unbounded Domains." Acta Mathematicae Applicatae Sinica, English Series 36, no. 1 (2019): 134–50. http://dx.doi.org/10.1007/s10255-020-0917-4.

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CAULFIELD, C. P., and ANDREW W. WOODS. "Turbulent gravitational convection from a point source in a non-uniformly stratified environment." Journal of Fluid Mechanics 360 (April 10, 1998): 229–48. http://dx.doi.org/10.1017/s0022112098008623.

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We examine the turbulent gravitational convection which develops above a point source of buoyant fluid in a stably stratified environment in which the buoyancy frequency varies with height according to N2=N2s (z/zs)β. This generalizes the classical model of turbulent buoyant plumes rising through uniform and uniformly stratified environments originally developed by Morton et al. (1956). By analogy, the height of rise of a plume with initial buoyancy flux Fs has the form Hp= Apεp−1/2Fs1/4Ns−3/4hp (λ, β) where εp is the entrainment constant for plume motion, Ap is an O(1) constant, and the non-dimensional plume height, hp is a function of &λ=Apεp−1/2Fs1/4Ns−3/4/zs and β.In the case β>0, the stratification becomes progressively stronger with height, and so plumes are always confined within a finite distance above the origin. Furthermore, the non-dimensional height of rise h decreases with λ. In contrast, in the case β<0, the stratification becomes progressively weaker with height, and so the non-dimensional plume height increases monotonically with λ. For slowly decaying stratification, β>−8/3, the motion is confined within a finite distance above the source. However, for each value of β with β<−8/3, there is a critical value λc(β) such that for λ<λc a plume is confined to a region near the source while for λ[ges ]λc the motion is unbounded. In the unbounded case, the motion asymptotes to the solution for a buoyant plume rising through a uniform environment, with asymptotic buoyancy flux F∞(λ)<Fs. We show that in the limiting case λ=λc, dividing bounded and unbounded motion, as z→∞ the plume asymptotes to a new similarity solution of the second kind which describes the motion of a plume in a non-uniformly stratified environment. These similarity solutions are unstable in the sense that small perturbations to the initial conditions result in very different behaviour far from the source.Analogous results for an instantaneous release of buoyant fluid from a point source, which forms a thermal, are also presented. The model is applied to describe the motion of plumes and thermals in the upper ocean and in naturally ventilated buildings since in both cases the stratification is typically non-uniform.

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Coco, Armando, Gilda Currenti, Ciro Del Negro, and Giovanni Russo. "A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology." Communications in Computational Physics 16, no. 4 (2014): 983–1009. http://dx.doi.org/10.4208/cicp.210713.010414a.

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AbstractWe propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains. The technique is based on a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary geometries are defined by suitable level-set functions. The equations are discretized by classical nine-point stencil on interior points, while boundary conditions and high order reconstructions are used to define the field variables at ghost-points, which are grid nodes external to the domain with a neighbor inside the domain. The linear system arising from such discretization is solved by a multigrid strategy. The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources. The method is suitable to treat problems in which the geometry of the source often changes (explore the effects of different scenarios, or solve inverse problems in which the geometry itself is part of the unknown), since it does not require complex re-meshing when the geometry is modified. Several numerical tests are successfully performed, which asses the effectiveness of the present approach.

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Cragg, Gordon M., and David J. Newman. "Biodiversity: A continuing source of novel drug leads." Pure and Applied Chemistry 77, no. 1 (2005): 7–24. http://dx.doi.org/10.1351/pac200577010007.

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Nature has been a source of medicinal agents for thousands of years and continues to be an abundant source of novel chemotypes and pharmacophores. With only 5 to 15 % of the approximately 250 000 species of higher plants systematically investigated, and the potential of the marine environment barely tapped, these areas will remain a rich source of novel bioactive compounds. Less than 1 % of bacterial and 5 % of fungal species are currently known, and the potential of novel microbial sources, particularly those found in extreme environments, seems unbounded. To these natural sources can be added the potential to investigate the rational design of novel structure types within certain classes of microbial metabolites through genetic engineering. It is apparent that Nature can provide the novel chemical scaffolds for elaboration by combinatorial approaches (chemical and biochemical), thus leading to agents that have been optimized on the basis of their pharmacological activities. The proven natural product drug discovery track record, coupled with the continuing threat to biodiversity through the destruction of terrestrial and marine ecosystems and the current low number of new chemical entities in pharmaceutical industry pipelines, provides a compelling argument in favor of expanded multidisciplinary and international collaboration in the exploration of Nature as a source of novel leads for the development of drugs and other valuable bioactive agents.

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Kahana, Adar, Eli Turkel, and Dan Givoli. "Convective Wave Equation and Time Reversal Process for Source Refocusing." Journal of Theoretical and Computational Acoustics 26, no. 02 (2018): 1850016. http://dx.doi.org/10.1142/s2591728518500160.

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The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to determine the location of the original explosion, given limited spatial observations. We test the effectiveness of this scheme under conditions including dissipation, dispersion, etc. We use finite differences and implement absorbing boundary conditions to simulate an unbounded region.

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Palivos, Theodore, and Dimitrios Varvarigos. "POLLUTION ABATEMENT AS A SOURCE OF STABILIZATION AND LONG-RUN GROWTH." Macroeconomic Dynamics 21, no. 3 (2016): 644–76. http://dx.doi.org/10.1017/s1365100515000632.

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In a two-period overlapping-generations model with production, we consider the damaging impact of environmental degradation on health and consequently life expectancy. Despite the presence of social constant returns to capital, which would otherwise generate unbounded growth, when pollution is left unabated, the economy cannot achieve such a path. Instead, it converges either to a stationary level of capital per worker or to a cycle in which capital per worker oscillates permanently. The government's involvement in environmental preservation proves crucial for both short-term dynamics and long-term prospects of the economy. Particularly, an active policy of pollution abatement emerges as an important engine of long-run economic growth. Furthermore, by eliminating the occurrence of limit cycles, pollution abatement is also a powerful source of stabilization.

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SINAYOKO, SAMUEL, A. AGARWAL, and Z. HU. "Flow decomposition and aerodynamic sound generation." Journal of Fluid Mechanics 668 (December 3, 2010): 335–50. http://dx.doi.org/10.1017/s0022112010004672.

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An approximate decomposition of fluid-flow variables satisfying unbounded compressible Navier–Stokes equations into acoustically radiating and non-radiating components leads to well-defined source terms that can be identified as the physical sources of aerodynamic noise. We show that, by filtering the flow field by means of a linear convolution filter, it is possible to decompose the flow into non-radiating and radiating components. This is demonstrated on two different flows: one satisfying the linearised Euler equations and the other the Navier–Stokes equations. In the latter case, the corresponding sound sources are computed. They are found to be more physical than those computed through classical acoustic analogies in which the flow field is decomposed into a steady mean and fluctuating component.

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Ganapathy, R. "Weak Thermal Vortex Rings." Journal of Fluids Engineering 116, no. 1 (1994): 174–76. http://dx.doi.org/10.1115/1.2910233.

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A simple mathematical model is proposed and a similarity solution is obtained to study the behavior of very weak thermal vortex rings induced by a horizontal line source of thermal energy in an unbounded fluid. The temperature distribution is assumed to be unaffected by the fluid motion, and the Stokes flow approximation is invoked. Streamlines are computed to demonstrate the evolution of the flow field.

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Zenkour, Ashraf M., Daoud S. Mashat, and Ashraf M. Allehaibi. "Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source." Mathematics 10, no. 1 (2021): 9. http://dx.doi.org/10.3390/math10010009.

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The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.

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Simões, Inês, António Tadeu, and Nuno Simões. "Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions." Journal of Applied Mathematics 2016 (2016): 1–22. http://dx.doi.org/10.1155/2016/6439710.

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This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

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Abbas, Ibrahim A. "Thermoelastic interactions in an isotropic unbounded medium due to moving heat source using GNIII model." Latin American Journal of Solids and Structures 12, no. 6 (2015): 1061–73. http://dx.doi.org/10.1590/1679-78251553.

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Xiang, Zhiming Chen and Xueshuang. "A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions." Numerical Mathematics: Theory, Methods and Applications 6, no. 3 (2013): 538–55. http://dx.doi.org/10.4208/nmtma.2013.1217nm.

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Hajarolasvadi, Setare, and Ahmed E. Elbanna. "A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities." Geophysical Journal International 211, no. 2 (2017): 851–64. http://dx.doi.org/10.1093/gji/ggx337.

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Abd-Alla, A. M. "On a generalized thermoelastic interaction in an unbounded body due to a line heat source." Applied Mathematics and Computation 100, no. 2-3 (1999): 285–95. http://dx.doi.org/10.1016/s0096-3003(98)00032-0.

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Lloyd, S. F., C. Jeong, H. N. Gharti, J. Vignola, and J. Tromp. "Spectral-Element Simulations of Acoustic Waves Induced by a Moving Underwater Source." Journal of Theoretical and Computational Acoustics 27, no. 03 (2019): 1850040. http://dx.doi.org/10.1142/s2591728518500408.

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In this study, we model acoustic waves induced by moving acoustic sources in three-dimensional (3D) underwater settings based on a spectral-element method (SEM). Numerical experiments are conducted using the SEM software package SPECFEM3D_Cartesian, which facilitates fluid–solid coupling and absorbing boundary conditions. Examples presented in this paper include an unbounded fluid truncated by using absorbing boundaries, and a shallow-water waveguide modeled as a fluid–solid coupled system based on domain decomposition. In the numerical experiments, the SEM-computed pressures match their analytical counterparts. SEM solutions of pressures at points behind and ahead of modeled moving acoustic sources show a frequency shift, i.e., a Doppler effect, which matches the analytical solution. This paper contributes to the field of passive sonar-based detection of moving acoustic sources, and addresses the challenge of computing wave responses generated by side-scan sonar by using moving sources of continuous signals.

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Hussein, M. S., Daniel Lesnic, Vitaly L. Kamynin, and Andrey B. Kostin. "Direct and inverse source problems for degenerate parabolic equations." Journal of Inverse and Ill-posed Problems 28, no. 3 (2020): 425–48. http://dx.doi.org/10.1515/jiip-2019-0046.

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AbstractDegenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.

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Kudrin, Alexander V., E. Yu Petrov, and T. M. Zaboronkova. "Eigenfunction Expansions of Source-excited Electromagnetic Fields on Open Cylindrical Guiding Structures in Unbounded Gyrotropic Media." PIERS Online 3, no. 8 (2007): 1283–87. http://dx.doi.org/10.2529/piers070317073215.

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Xiong, Xiangtuan, and Junxia Wang. "A Tikhonov-type method for solving a multidimensional inverse heat source problem in an unbounded domain." Journal of Computational and Applied Mathematics 236, no. 7 (2012): 1766–74. http://dx.doi.org/10.1016/j.cam.2011.10.007.

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Das, Payel, and M. Kanoria. "Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source." International Journal of Thermophysics 30, no. 6 (2009): 2098–121. http://dx.doi.org/10.1007/s10765-009-0679-y.

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Şeremet, Victor. "Three-dimensional thermal stresses Green’s functions for an unbounded parallelepiped under an inner point heat source." Journal of Thermal Stresses 40, no. 8 (2017): 973–94. http://dx.doi.org/10.1080/01495739.2017.1319255.

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Baynes, Alexander B., and Oleg A. Godin. "A Semi-Analytic, Numerically Efficient Model for Low-Frequency Sound Scattering by an Infinite Cylinder Located Near a Boundary." Journal of Theoretical and Computational Acoustics 28, no. 04 (2020): 2050010. http://dx.doi.org/10.1142/s2591728520500103.

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Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from the target, with the target being insonified by nearby virtual sources. At low frequencies and for shallow targets, the distance from a virtual source to the target is not necessarily large compared to the acoustic wavelength or the target’s dimensions. Then, multiple orders of scattering make significant contributions and incident wave fields that cannot be approximated as a plane wave. This paper takes advantage of the virtual source concept and recently derived explicit analytic representations of 2D acoustic Green’s functions in unbounded fluids with inclusions of a circular cross-section, to develop a simple, intuitive, and numerically efficient model of multiple scattering. Scattering from soft, hard, and fluid targets is considered. The model is used to study the acoustic field in the vicinity of cylindrical targets near a pressure release surface or a hard bottom.

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HOCKING, G. C., L. K. FORBES, and T. E. STOKES. "A NOTE ON STEADY FLOW INTO A SUBMERGED POINT SINK." ANZIAM Journal 56, no. 2 (2014): 150–59. http://dx.doi.org/10.1017/s1446181114000303.

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AbstractThe steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.

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Jafarsadeghi-Pournaki, Ilgar, Ghader Rezazadeh, Mohammadreza Zamanzadeh, and Rasoul Shabani. "Parametric Thermally Induced Vibration of an Electrostatically Deflected FGM Micro-Beam." International Journal of Applied Mechanics 08, no. 08 (2016): 1650092. http://dx.doi.org/10.1142/s1758825116500927.

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The present paper deals with the study of nonlinear vibration of a functionally graded cantilever micro-beam imposed on a bias DC voltage and superimposed on a sinusoidal heat source. The governing equation of motion is derived extremizing the Lagrange’s equation and Hamilton’s principal under the assumption of Euler–Bernoulli beam theory. The thermo-elastic equation is obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model. Due to the displacement dependency of the electrostatic force and time variability of the heat source, the governing differential equations of the system are nonlinear implicitly parametrically electro-thermo-elastic coupled equations. To evaluate the dynamic response of the micro-beam, the coupled equations are discretized applying a Galerkin-based reduced order model and then integrated numerically by the Runge–Kutta method. By solving the equations, the stable and unstable regions at different bias DC voltages are identified. By picking some special points from these regions and depicting the time history and phase portrait diagrams, their behaviors are investigated in detail. In addition to the classical dynamic pull-in, in which a homoclinic orbit separates stable periodic orbits from the unbounded solutions, a new kind of dynamic pull-in is presented, which separates unstable solutions, due to parametric resonance response, from unbounded rapidly growing solutions owing to the existence of saddle and singular fixed points in the system.

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Procopio, Giuseppe, and Massimiliano Giona. "Bitensorial formulation of the singularity method for Stokes flows." Mathematics in Engineering 5, no. 2 (2022): 1–34. http://dx.doi.org/10.3934/mine.2023046.

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<abstract><p>This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities and hydrodynamic fundamental solutions are multi-point functions, and bitensor calculus provides either the proper geometrical setting, in order to avoid inconsistencies and misunderstandings on the role of the different tensorial indices, or a way for compactly deriving hydrodynamic properties. A first relevant result is to provide a clear definition of the singularities (both bounded and unbounded) in Stokes flow, specifying the associated differential equations and boundary conditions. Using this formalism for bounded flows, we show the existence of an integro-differential operator providing the whole system of hydrodynamic singularities by acting on the unbounded Green function (Stokeslet) at its pole and we derive its explicit representation in terms of moments. In the case of an immersed body in a unbounded fluid, we show that, the operator furnishing the disturbance field of a purely $ n $-th order <italic>ambient</italic> flow, is a generalized $ n $-th order Faxén operator, i.e., it yields the $ n $-th moment on the body if applied to a generic <italic>ambient</italic> flow, and that a generic disturbance field can be expressed by a summation of the generalized $ n $-th order Faxén operators. Furthermore, we find that the operator providing the disturbance of an ambient flow coincides with the reflection operator for the Stokes solutions in the same flow geometry. We apply this result to the paradigmatic case of fundamental singularities for the Stokes flow bounded by a plane. In this way, we obtain in an alternative and easy way the image system for the Sourcelet and the Rotlet (already derived in the literature) and for the Source Doublet and the Strainlet (presented here for the first time).</p></abstract>

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Kopylova, Vera G. "On the Solvability of the Identification Problem for a Source Function in a Quasilinear Parabolic System of Equations in Bounded and Unbounded Domains." Journal of Siberian Federal University. Mathematics & Physics 14, no. 4 (2001): 483–91. http://dx.doi.org/10.17516/1997-1397-2021-14-4-483-491.

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The paper considers the problem of identification for a source function in one of two equations of parabolic quasilinear system. The case of Cauchy data in an unbounded domain and the case of boundary conditions of the first kind in a rectangular domain are considered. The question of the existence and uniqueness of the solution is studied. The proof uses a differential level splitting method known as the weak approximation method. The solution is obtained on a small time interval in the class of sufficiently smooth bounded functions

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Peng, Chengbin, Jung M. Lee, and M. Nafi Toksöz. "Pressure in a fluid‐filled borehole caused by a seismic source in stratified media." GEOPHYSICS 61, no. 1 (1996): 43–55. http://dx.doi.org/10.1190/1.1443955.

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A method for numerically simulating hydrophone vertical seismic profiles (VSP) and crosswell data measured in a fluid‐filled borehole (either open or cased) embedded in stratified media is presented. The method makes use of both the borehole coupling theory and the global matrix formulation for computing synthetic seismograms in a stratified medium. The global matrix formulation is used to calculate the stress field at the borehole location. Borehole coupling theory is then employed to obtain the pressure in the borehole fluid. Comparisons with exact solutions for an open borehole in a homogeneous and unbounded formation show that this method is accurate for frequencies below 2 kHz. This method is used to model the Kent Cliffs hydrophone VSP data, where good agreement between the numerical simulations and the field measurements has been found, in both traveltimes and rms amplitudes of the direct P‐wave. Examples show that this method is efficient and accurate, and can be applied to model VSP and crosswell experiments using an array of hydrophones.

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Deryugin, E. E. "Stress-strain state of the continuum with the source of the shear plastic deformation." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (2022): 29–35. http://dx.doi.org/10.17223/00213411/65/5/29.

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The paper describes a method for constructing a shear plastic band in an elastic plane using the Crouch solution in the problem of a constant discontinuity of displacement on a finite segment of an unbounded plane. Analytical equations are obtained for calculating the stress-strain state (SSS) of a plane with a band of homogeneous plastic deformation for the cases of simple and pure shear. The analysis of SSS was carried out and the features of the field of internal stresses in an elastic plane with a band of plastic deformation shear were revealed. It is shown that a zone of homogeneous plastic shear deformation can be used as an element for constructing a zone of arbitrary geometric shape with a given distribution of plastic shear deformation. In the general case, the proposed approach can also be applied to construct zone with a homogeneous distribution of the normal components of plastic deformation.

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Adimurthi, Aekta Aggarwal, and G. D. Veerappa Gowda. "Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls." Communications in Computational Physics 20, no. 4 (2016): 1071–105. http://dx.doi.org/10.4208/cicp.290615.060516a.

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AbstractWe propose and analyse finite volume Godunov type methods based on discontinuous flux for a 2×2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The problem considered here is the so-called partially open table problem where sand is blocked by a wall (of infinite height) on some part of the boundary of the table. The novelty here is the corresponding modification of boundary conditions for the standing and the rolling layers and generalization of the techniques of the well-balancedness proposed in [1]. Presence of walls may lead to unbounded or discontinuous surface flow density at equilibrium resulting in solutions with singularities propagating from the extreme points of the walls. A scheme has been proposed to approximate efficiently the Hamiltonians with the coefficients which can be unbounded and discontinuous. Numerical experiments are presented to illustrate that the proposed schemes detect these singularities in the equilibrium solutions efficiently and comparisons are made with the previously studied finite difference and Semi-Lagrangian approaches by Finzi Vita et al.

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