Vasundara Varatharajulu

Bio: Vasundara Varatharajulu is an academic researcher. The author has contributed to research in topics: Surface integral & Matrix (mathematics). The author has an hindex of 2, co-authored 2 publications receiving 349 citations.

Huygens’ principle, radiation conditions, and integral formulas for the scattering of elastic waves

Abstract: Helmholtz‐ and Kirchhoff‐type integral formulas are presented for elastic waves in isotropic and anisotropic solids The displacement vector field at points interior and exterior to a region bounded by a closed surface is expressed in terms of a volume integral of the body sources and a surface integral of the sources on the closed surface, namely, the traction and the displacement The kernels of these integrals are the well‐known Green’s displacement dyadic and a third rank Green’s stress tensor The latter is related to the former by generalized Hooke’s law From these formulas radiation conditions for both steady‐state and transient elastic waves are established in terms of the traction, displacement, and particle velocity In the Kirchhoff‐type formula, the retardation in time for the surface and volume sources is made with respect to the travel times for dilatational and shear waves, respectively This clearly illustrates Huygens’ principle for the two wave fronts of the elastic wave fieldSubject C

Scattering matrix for elastic waves. I. Theory

Abstract: A matrix theory is developed for investigating the scattering of elastic waves in solids by an obstacle of arbitrary shape. The scattering matrix which depends only on the shape and nature of the obstacle relates the scattered field to any type of harmonic incident field. Expressions are obtained for the elements of the scattering matrix in the form of surface integrals around the boundary of the obstacle, which can be evaluated numerically. Using the principle of reciprocity and the conservation of energy, the scattering matrix is shown to be symmetric and unitary. These properties are essential to assure the accuracy of numerical calculations. Both two‐ and three‐dimensional problems are discussed, and the obstacle may be an elastic inclusion, a fluid inclusion, a cavity, or a rigid inclusion of arbitrary shape.Subject Classification: [43]20.15, [43]20.30.

The method of fundamental solutions for elliptic boundary value problems

Abstract: The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.

Green's function representations for seismic interferometry

Abstract: The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

6G and Beyond: The Future of Wireless Communications Systems

Abstract: 6G and beyond will fulfill the requirements of a fully connected world and provide ubiquitous wireless connectivity for all. Transformative solutions are expected to drive the surge for accommodating a rapidly growing number of intelligent devices and services. Major technological breakthroughs to achieve connectivity goals within 6G include: (i) a network operating at the THz band with much wider spectrum resources, (ii) intelligent communication environments that enable a wireless propagation environment with active signal transmission and reception, (iii) pervasive artificial intelligence, (iv) large-scale network automation, (v) an all-spectrum reconfigurable front-end for dynamic spectrum access, (vi) ambient backscatter communications for energy savings, (vii) the Internet of Space Things enabled by CubeSats and UAVs, and (viii) cell-free massive MIMO communication networks. In this roadmap paper, use cases for these enabling techniques as well as recent advancements on related topics are highlighted, and open problems with possible solutions are discussed, followed by a development timeline outlining the worldwide efforts in the realization of 6G. Going beyond 6G, promising early-stage technologies such as the Internet of NanoThings, the Internet of BioNanoThings, and quantum communications, which are expected to have a far-reaching impact on wireless communications, have also been discussed at length in this paper.

Integral Equation Methods for Electromagnetic and Elastic Waves

Abstract: Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods.

The method of fundamental solutions for scattering and radiation problems

Abstract: The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed A brief review of the developments and applications in all areas of the MFS over the last five years is also given Future possible areas of applications in fields related to scattering and radiation problems are identified