Riemann zeta function from wave-packet dynamics
DEFF Research Database (Denmark)
Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.
2010-01-01
We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Ship-induced solitary Riemann waves of depression in Venice Lagoon
International Nuclear Information System (INIS)
Parnell, Kevin E.; Soomere, Tarmo; Zaggia, Luca; Rodin, Artem; Lorenzetti, Giuliano; Rapaglia, John; Scarpa, Gian Marco
2015-01-01
We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope
Ship-induced solitary Riemann waves of depression in Venice Lagoon
Energy Technology Data Exchange (ETDEWEB)
Parnell, Kevin E. [College of Marine and Environmental Sciences and Centre for Tropical Environmental and Sustainability Sciences, James Cook University, Queensland 4811 (Australia); Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Soomere, Tarmo, E-mail: soomere@cs.ioc.ee [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn (Estonia); Zaggia, Luca [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rodin, Artem [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Lorenzetti, Giuliano [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rapaglia, John [Sacred Heart University Department of Biology, 5151 Park Avenue, Fairfield, CT 06825 (United States); Scarpa, Gian Marco [Università Ca' Foscari, Dorsoduro 3246, 30123 Venice (Italy)
2015-03-06
We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope.
Loss of hyperbolicity changes the number of wave groups in Riemann problems
Vítor Matos; Julio D. Silva; Dan Marchesin
2016-01-01
Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve ...
Indian Academy of Sciences (India)
the basis for various fields of mathematics and the general relativity theory of Einstein. In 1857 ... This idea explained the work on algebraic ... theory, Riemann found the key to the problem of the distribution of primes, in that he associated it ...
International Nuclear Information System (INIS)
Rogers, Alice
1990-01-01
A super Riemann surface is a particular kind of (1,1)-dimensional complex analytic supermanifold. From the point of view of super-manifold theory, super Riemann surfaces are interesting because they furnish the simplest examples of what have become known as non-split supermanifolds, that is, supermanifolds where the odd and even parts are genuinely intertwined, as opposed to split supermanifolds which are essentially the exterior bundles of a vector bundle over a conventional manifold. However undoubtedly the main motivation for the study of super Riemann surfaces has been their relevance to the Polyakov quantisation of the spinning string. Some of the papers on super Riemann surfaces are reviewed. Although recent work has shown all super Riemann surfaces are algebraic, some areas of difficulty remain. (author)
Riemann, topology, and physics
Monastyrsky, Michael I
2008-01-01
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...
Balsara, Dinshaw S.; Nkonga, Boniface
2017-10-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.
International Nuclear Information System (INIS)
Pokhozhaev, Stanislav I
2011-01-01
The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.
Solution of Riemann problem for ideal polytropic dusty gas
International Nuclear Information System (INIS)
Nath, Triloki; Gupta, R.K.; Singh, L.P.
2017-01-01
Highlights : • A direct approach is used to solve the Riemann problem for dusty ideal polytropic gas. • An analytical solution to the Riemann problem for dusty gas flow is obtained. • The existence and uniqueness of the solution in dusty gas is discussed. • Properties of elementary wave solutions of Riemann problem are discussed. • Effect of mass fraction of solid particles on the solution is presented. - Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.
International Nuclear Information System (INIS)
Arnlind, Joakim; Hofer, Laurent; Hoppe, Jens; Bordemann, Martin; Shimada, Hidehiko
2009-01-01
We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.
International Nuclear Information System (INIS)
Manakov, S V; Santini, P M
2008-01-01
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking
Energy Technology Data Exchange (ETDEWEB)
Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)
2008-02-08
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.
Deformations of super Riemann surfaces
International Nuclear Information System (INIS)
Ninnemann, H.
1992-01-01
Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.)
Deformations of super Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Ninnemann, H [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
1992-11-01
Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).
Riemann solvers and undercompressive shocks of convex FPU chains
International Nuclear Information System (INIS)
Herrmann, Michael; Rademacher, Jens D M
2010-01-01
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions
Conformal mapping on Riemann surfaces
Cohn, Harvey
2010-01-01
The subject matter loosely called ""Riemann surface theory"" has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five pans. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in
Computational approach to Riemann surfaces
Klein, Christian
2011-01-01
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first...
Directory of Open Access Journals (Sweden)
Xuefeng Wei
2016-12-01
Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.
Transformation optics with artificial Riemann sheets
Xu, Lin; Chen, Huanyang
2013-11-01
The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777-80 and Pendry et al 2006 Science 312 1780-2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110-12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.
Transformation optics with artificial Riemann sheets
International Nuclear Information System (INIS)
Xu, Lin; Chen, Huanyang
2013-01-01
The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results. (paper)
Supermanifolds and super Riemann surfaces
International Nuclear Information System (INIS)
Rabin, J.M.
1986-09-01
The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary modular group. Super moduli space is shown to be the gauge-fixing slice for the fermionic string path integral
Riemann surfaces with boundaries and string theory
International Nuclear Information System (INIS)
Morozov, A.Yu.; Roslyj, A.A.
1989-01-01
A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
Exploring the Riemann zeta function 190 years from Riemann's birth
Nikeghbali, Ashkan; Rassias, Michael
2017-01-01
This book is concerned with the Riemann Zeta Function, its generalizations, and various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis and Probability Theory. Eminent experts in the field illustrate both old and new results towards the solution of long-standing problems and include key historical remarks. Offering a unified, self-contained treatment of broad and deep areas of research, this book will be an excellent tool for researchers and graduate students working in Mathematics, Mathematical Physics, Engineering and Cryptography.
Functionals of finite Riemann surfaces
Schiffer, Menahem
1954-01-01
This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
A Polyakov action on Riemann surfaces
International Nuclear Information System (INIS)
Zucchini, R.
1991-02-01
A calculation of the effective action for induced conformal gravity on higher genus Riemann surfaces is presented. Our expression, generalizing Polyakov's formula, depends holomorphically on the Beltrami and integrates the diffeomorphism anomaly. A solution of the conformal Ward identity on an arbitrary compact Riemann surfaces without boundary is presented, and its remarkable properties are studied. (K.A.) 16 refs., 2 figs
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Directory of Open Access Journals (Sweden)
José Manuel Sánchez Muñoz
2011-10-01
Full Text Available En el mes de noviembre de 1859, durante la presentación mensual de losinformes de la Academia de Berlín, el alemán Bernhard Riemann presentóun trabajo que cambiaría los designios futuros de la ciencia matemática. El tema central de su informe se centraba en los números primos, presentando el que hoy día, una vez demostrada la Conjetura de Poincaré, puede ser considerado el problema matemático abierto más importante. El presente artículo muestra en su tercera sección una traducción al castellano de dicho trabajo.
Conformal algebra of Riemann surfaces
International Nuclear Information System (INIS)
Vafa, C.
1988-01-01
It has become clear over the last few years that 2-dimensional conformal field theories are a crucial ingredient of string theory. Conformal field theories correspond to vacuum solutions of strings; or more precisely we know how to compute string spectrum and scattering amplitudes by starting from a formal theory (with a proper value of central charge of the Virasoro algebra). Certain non-linear sigma models do give rise to conformal theories. A lot of progress has been made in the understanding of conformal theories. The author discusses a different view of conformal theories which was motivated by the development of operator formalism on Riemann surfaces. The author discusses an interesting recent work from this point of view
Super differential forms on super Riemann surfaces
International Nuclear Information System (INIS)
Konisi, Gaku; Takahasi, Wataru; Saito, Takesi.
1994-01-01
Line integral on the super Riemann surface is discussed. A 'super differential operator' which possesses both properties of differential and of differential operator is proposed. With this 'super differential operator' a new theory of differential form on the super Riemann surface is constructed. We call 'the new differentials on the super Riemann surface' 'the super differentials'. As the applications of our theory, the existency theorems of singular 'super differentials' such as 'super abelian differentials of the 3rd kind' and of a super projective connection are examined. (author)
Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
Chiodaroli, Elisabetta; Kreml, Ondřej
2018-04-01
We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.
Riemann problems and their application to ultra-relativistic heavy ion collisions
International Nuclear Information System (INIS)
Plohr, B.J.; Sharp, D.H.
1986-07-01
Heavy ion collisions at sufficiently high energies to form quark-gluon plasma are considered. The phase transformation from a quark-gluon phase to hadrons as the nuclear matter cools is modeled as a hydrodynamical flow. Nonlinear waves are the predominant feature of this type of flow and the Riemann problem of a relativistic gas undergoing a phase transformation is explored as a method to numerically model this phase transition process in nuclear matter. The solution of the Riemann problem is outlined and results of preliminary numerical computations of the flow are presented. 10 refs., 2 figs
Lectures on the Riemann zeta function
Iwaniec, H
2014-01-01
The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. Th...
Quantum Hall effect on Riemann surfaces
Tejero Prieto, Carlos
2009-06-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Quantum Hall effect on Riemann surfaces
International Nuclear Information System (INIS)
Tejero Prieto, Carlos
2009-01-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Numerical implication of Riemann problem theory for fluid dynamics
International Nuclear Information System (INIS)
Menikoff, R.
1988-01-01
The Riemann problem plays an important role in understanding the wave structure of fluid flow. It is also crucial step in some numerical algorithms for accurately and efficiently computing fluid flow; Godunov method, random choice method, and from tracking method. The standard wave structure consists of shock and rarefaction waves. Due to physical effects such as phase transitions, which often are indistinguishable from numerical errors in an equation of state, anomalkous waves may occur, ''rarefaction shocks'', split waves, and composites. The anomalous waves may appear in numerical calculations as waves smeared out by either too much artificial viscosity or insufficient resolution. In addition, the equation of state may lead to instabilities of fluid flow. Since these anomalous effects due to the equation of state occur for the continuum equations, they can be expected to occur for all computational algorithms. The equation of state may be characterized by three dimensionless variables: the adiabatic exponent γ, the Grueneisen coefficient Γ, and the fundamental derivative G. The fluid flow anomalies occur when inequalities relating these variables are violated. 18 refs
Chiral bosonization on a Riemann surface
International Nuclear Information System (INIS)
Eguchi, Tohru; Ooguri, Hirosi
1987-01-01
We point out that the basic addition theorem of θ-functions, Fay's identity, implies an equivalence between bosons and chiral fermions on Riemann surfaces with arbitrary genus. We present a rule for a bosonized calculation of correlation functions. We also discuss ghost systems of n and (1-n) tensors and derive formulas for their chiral determinants. (orig.)
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Conformal deformation of Riemann space and torsion
International Nuclear Information System (INIS)
Pyzh, V.M.
1981-01-01
Method for investigating conformal deformations of Riemann spaces using torsion tensor, which permits to reduce the second ' order equations for Killing vectors to the system of the first order equations, is presented. The method is illustrated using conformal deformations of dimer sphere as an example. A possibility of its use when studying more complex deformations is discussed [ru
Study Paths, Riemann Surfaces, and Strebel Differentials
Buser, Peter; Semmler, Klaus-Dieter
2017-01-01
These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…
Hysteresis rarefaction in the Riemann problem
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
2008-01-01
Roč. 138, - (2008), s. 1-10 ISSN 1742-6588. [International Workshop on Multi-Rate Processes and Hysteresis. Cork , 31.03.2008-05.04.2008] Institutional research plan: CEZ:AV0Z10190503 Keywords : Preisach hysteresis * Riemann problem Subject RIV: BA - General Mathematics http://iopscience.iop.org/1742-6596/138/1/012010
Generalized Riemann problem for reactive flows
International Nuclear Information System (INIS)
Ben-Artzi, M.
1989-01-01
A generalized Riemann problem is introduced for the equations of reactive non-viscous compressible flow in one space dimension. Initial data are assumed to be linearly distributed on both sides of a jump discontinuity. The resolution of the singularity is studied and the first-order variation (in time) of flow variables is given in exact form. copyright 1989 Academic Press, Inc
Shao, Zhiqiang
2018-04-01
The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.
A New Riemann Type Hydrodynamical Hierarchy and its Integrability Analysis
International Nuclear Information System (INIS)
Golenia, Jolanta Jolanta; Bogolubov, Nikolai N. Jr.; Popowicz, Ziemowit; Pavlov, Maxim V.; Prykarpatsky, Anatoliy K.
2009-12-01
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations for the special cases N = 2, 3 and N = 4 are constructed. (author)
On Lovelock analogs of the Riemann tensor
Camanho, Xián O.; Dadhich, Naresh
2016-03-01
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.
The KZB equations on Riemann surfaces
Felder, Giovanni
1996-01-01
In this paper, based on the author's lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universa...
Stability of the isentropic Riemann solutions of the full multidimensional Euler system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Kreml, Ondřej; Vasseur, A.
2015-01-01
Roč. 47, č. 3 (2015), s. 2416-2425 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * isentropic solutions * Riemann problem * rarefaction wave Subject RIV: BA - General Mathematics Impact factor: 1.486, year: 2015 http://epubs.siam.org/doi/abs/10.1137/140999827
Post-Quantum Cryptography: Riemann Primitives and Chrysalis
Malloy, Ian; Hollenbeck, Dennis
2018-01-01
The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors relying on the Gauss Circle Problem within the Riemann sphere. The principle security reduction proposed by this novel cryptographic scheme applies c...
Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis
International Nuclear Information System (INIS)
Khuri, N. N.
2002-01-01
It is well known that the s-wave Jost function for a potential, λV, is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the 'coupling constant', λ, will all be real and negative, λ n (0) n n =1/2+iγ n . Thus, finding a repulsive V whose coupling constant spectrum coincides with the Riemann zeros will establish the Riemann hypothesis, but this will be a very difficult and unguided search.In this paper we make a significant enlargement of the class of potentials needed for a generalization of the above idea. We also make this new class amenable to construction via inverse scattering methods. We show that all one needs is a one parameter class of potentials, U(s;x), which are analytic in the strip, 0≤Res≤1, Ims>T 0 , and in addition have an asymptotic expansion in powers of [s(s-1)] -1 , i.e. U(s;x)=V 0 (x)+gV 1 (x)+g 2 V 2 (x)+...+O(g N ), with g=[s(s-1)] -1 . The potentials V n (x) are real and summable. Under suitable conditions on the V n 's and the O(g N ) term we show that the condition, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx≠0, where f 0 is the zero energy and g=0 Jost function for U, is sufficient to guarantee that the zeros g n are real and, hence, s n =1/2+iγ n , for γ n ≥T 0 .Starting with a judiciously chosen Jost function, M(s,k), which is constructed such that M(s,0) is Riemann's ξ(s) function, we have used inverse scattering methods to actually construct a U(s;x) with the above properties. By necessity, we had to generalize inverse methods to deal with complex potentials and a nonunitary S-matrix. This we have done at least for the special cases under consideration.For our specific example, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx=0 and, hence, we get no restriction on Img n or Res n . The reasons for the vanishing of the above integral are given, and they give us hints on what one needs to proceed further. The problem
Operator bosonization on Riemann surfaces: new vertex operators
International Nuclear Information System (INIS)
Semikhatov, A.M.
1989-01-01
A new formalism is proposed for the construction of an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the theory of closed strings). The operators of the bc system are expressed in terms of operators of the bosonic conformal theory on a Riemann surface. In contrast to the standard bosonization formulas, which have meaning only locally, operator Baker-Akhiezer functions, which are well defined globally on a Riemann surface of arbitrary genus, are introduced. The operator algebra of the Baker-Akhiezer functions generates explicitly the algebraic-geometric τ function and correlation functions of bc systems on Riemann surfaces
The concept of a Riemann surface
Weyl, Hermann
2009-01-01
This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment
Riemann monodromy problem and conformal field theories
International Nuclear Information System (INIS)
Blok, B.
1989-01-01
A systematic analysis of the use of the Riemann monodromy problem for determining correlators (conformal blocks) on the sphere is presented. The monodromy data is constructed in terms of the braid matrices and gives a constraint on the noninteger part of the conformal dimensions of the primary fields. To determine the conformal blocks we need to know the order of singularities. We establish a criterion which tells us when the knowledge of the conformal dimensions of primary fields suffice to determine the blocks. When zero modes of the extended algebra are present the analysis is more difficult. In this case we give a conjecture that works for the SU(2) WZW case. (orig.)
Quantum field theory on higher-genus Riemann surfaces
International Nuclear Information System (INIS)
Kubo, Reijiro; Yoshii, Hisahiro; Ojima, Shuichi; Paul, S.K.
1989-07-01
Quantum field theory for b-c systems is formulated on Riemann surfaces with arbitrary genus. We make use of the formalism recently developed by Krichever and Novikov. Hamiltonian is defined properly, and the Ward-Takahashi identities are derived on higher-genus Riemann surfaces. (author)
Non-abelian bosonization in higher genus Riemann surfaces
International Nuclear Information System (INIS)
Koh, I.G.; Yu, M.
1988-01-01
We propose a generalization of the character formulas of the SU(2) Kac-Moody algebra to higher genus Riemann surfaces. With this construction, we show that the modular invariant partition funciton of the SO(4) k = 1 Wess-Zumino model is equivalent, in arbitrary genus Riemann surfaces, to that of free fermion theory. (orig.)
Collisionless analogs of Riemann S ellipsoids with halo
International Nuclear Information System (INIS)
Abramyan, M.G.
1987-01-01
A spheroidal halo ensures equilibrium of the collisionless analogs of the Riemann S ellipsoids with oscillations of the particles along the direction of their rotation. Sequences of collisionless triaxial ellipsoids begin and end with dynamically stable members of collisionless embedded spheroids. Both liquid and collisionless Riemann S ellipsoids with weak halo have properties that resemble those of bars of SB galaxies
A Riemann problem with small viscosity and dispersion
Directory of Open Access Journals (Sweden)
Kayyunnapara Thomas Joseph
2006-09-01
Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.
Getting superstring amplitudes by degenerating Riemann surfaces
International Nuclear Information System (INIS)
Matone, Marco; Volpato, Roberto
2010-01-01
We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansaetze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu-Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space-time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.
Balsara, Dinshaw S.; Dumbser, Michael
2015-04-01
Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we
Ice cream and orbifold Riemann-Roch
International Nuclear Information System (INIS)
Buckley, Anita; Reid, Miles; Zhou Shengtian
2013-01-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
E-string theory on Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Kim, Hee-Cheol; Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University, Cambridge, MA (United States); Razamat, Shlomo S. [Physics Department, Technion, Haifa (Israel); Zafrir, Gabi [Kavli IPMU (WPI), UTIAS, the University of Tokyo, Kashiwa, Chiba (Japan)
2018-01-15
We study compactifications of the 6d E-string theory, the theory of a small E{sub 8} instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E{sub 8} flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Moduli of Riemann surfaces, transcendental aspects
International Nuclear Information System (INIS)
Hain, R.
2000-01-01
These notes are an informal introduction to moduli spaces of compact Riemann surfaces via complex analysis, topology and Hodge Theory. The prerequisites for the first lecture are just basic complex variables, basic Riemann surface theory up to at least the Riemann-Roch formula, and some algebraic topology, especially covering space theory. The first lecture covers moduli in genus 0 and genus 1 as these can be understood using relatively elementary methods, but illustrate many of the points which arise in higher genus. The notes cover more material than was covered in the lectures, and sometimes the order of topics in the notes differs from that in the lectures. We have seen in genus 1 case that M 1 is the quotient Γ 1 /X 1 of a contractible complex manifold X 1 = H by a discrete group Γ 1 = SL 2 (Z). The action of Γ 1 on X 1 is said to be virtually free - that is, Γ 1 has a finite index subgroup which acts (fixed point) freely on X 1 . In this section we will generalize this to all g >= 1 - we will sketch a proof that there is a contractible complex manifold Xg, called Teichmueller space, and a group Γ g , called the mapping class group, which acts virtually freely on X g . The moduli space of genus g compact Riemann surfaces is the quotient: M g = Γ g /X g . This will imply that M g has the structure of a complex analytic variety with finite quotient singularities. Teichmueller theory is a difficult and technical subject. Because of this, it is only possible to give an overview. In this lecture, we compute the orbifold Picard group of M g for all g >= 1. Recall that an orbifold line bundle over M g is a holomorphic line bundle L over Teichmueller space X g together with an action of the mapping class group Γ g on it such that the projection L → X g is Γ g -equivariant. An orbifold section of this line bundle is a holomorphic Γ g -equivariant section X g → L of L. This is easily seen to be equivalent to fixing a level l>= 3 and considering holomorphic
Ice cream and orbifold Riemann-Roch
Buckley, Anita; Reid, Miles; Zhou, Shengtian
2013-06-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
From Riemann to differential geometry and relativity
Papadopoulos, Athanase; Yamada, Sumio
2017-01-01
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities
International Nuclear Information System (INIS)
Beccantini, A.
2001-01-01
This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)
Interpolating and sampling sequences in finite Riemann surfaces
Ortega-Cerda, Joaquim
2007-01-01
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
The exchange algebra for Liouville theory on punctured Riemann sphere
International Nuclear Information System (INIS)
Shen Jianmin; Sheng Zhengmao
1991-11-01
We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs
Meromorphic functions and cohomology on a Riemann surface
International Nuclear Information System (INIS)
Gomez-Mont, X.
1989-01-01
The objective of this set of notes is to introduce a series of concepts of Complex Analytic Geometry on a Riemann Surface. We motivate the introduction of cohomology groups through the analysis of meromorphic functions. We finish by showing that the set of infinitesimal deformations of a Riemann surface (the tangent space to Teichmueller space) may be computed as a Cohomology group. (author). 6 refs
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Riemann surfaces, Clifford algebras and infinite dimensional groups
International Nuclear Information System (INIS)
Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.
1990-01-01
We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)
BRST quantization of superconformal theories on higher genus Riemann surfaces
International Nuclear Information System (INIS)
Leman Kuang
1992-01-01
A complex contour integral method is constructed and applied to the Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of string theories on higher genus Riemann surfaces with N=0 and 1 Krichever-Novikov (KN) algebras. This method makes calculations very simple. It is shown that the critical spacetime dimension of the string theories on a genus-g Riemann surface equals that of the string theories on a genus-zero Riemann surface, and that the 'Regge intercepts' in the genus-g case are α(g)=1-3/4g-9/8g 2 and 1/2-3/4g-17/16g 2 for bosonic strings and superstrings, respectively. (orig.)
Compact Riemann surfaces an introduction to contemporary mathematics
Jost, Jürgen
2006-01-01
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
The sewing technique and correlation functions on arbitrary Riemann surfaces
International Nuclear Information System (INIS)
Di Vecchia, P.
1989-01-01
We describe in the case of free bosonic and fermionic theories the sewing procedure, that is a very convenient way for constructing correlation functions of these theories on an arbitrary Riemann surface from their knowledge on the sphere. The fundamental object that results from this construction is the N-point g-loop vertex. It summarizes the information of all correlation functions of the theory on an arbitrary Riemann surface. We then check explicitly the bosonization rules and derive some useful formulas. (orig.)
Line operators from M-branes on compact Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Amariti, Antonio [Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY 10031 (United States); Orlando, Domenico [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Reffert, Susanne, E-mail: sreffert@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
2016-12-15
In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. The latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.
On Riemann zeroes, lognormal multiplicative chaos, and Selberg integral
International Nuclear Information System (INIS)
Ostrovsky, Dmitry
2016-01-01
Rescaled Mellin-type transforms of the exponential functional of the Bourgade–Kuan–Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot–Bacry–Muzy. The conjecture implies that a non-trivial, log-infinitely divisible probability distribution is associated with Riemann zeroes. For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic extension of the Selberg integral. (paper)
Integrability of Liouville system on high genus Riemann surface: Pt. 1
International Nuclear Information System (INIS)
Chen Yixin; Gao Hongbo
1992-01-01
By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface
On an isospectrality question over compact Riemann surfaces
International Nuclear Information System (INIS)
Srinivas Rau, S.
1990-01-01
It is proved that for a generic compact Riemann surface X of genus g>1,(i) there are at most 2 2g unitary characters of π 1 (X) whose associated line bundles have laplacians of identical spectrum, (ii) generating cycles for π 1 (X) can be chosen to be closed geodesics whose length multiplicity is 1. (author). 5 refs
Quantum Riemann surfaces. Pt. 2; The discrete series
Energy Technology Data Exchange (ETDEWEB)
Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))
1992-02-01
We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).
Colliding holes in Riemann surfaces and quantum cluster algebras
Chekhov, Leonid; Mazzocco, Marta
2018-01-01
In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.
Weyl transforms associated with the Riemann-Liouville operator
Directory of Open Access Journals (Sweden)
N. B. Hamadi
2006-01-01
Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.
Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2007-01-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established
Toeplitz operators on higher Cauchy-Riemann spaces
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Zhang, G.
2017-01-01
Roč. 22, č. 22 (2017), s. 1081-1116 ISSN 1431-0643 Institutional support: RVO:67985840 Keywords : Toeplitz operator * Hankel operator * Cauchy-Riemann operators Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 0.800, year: 2016 https://www. math .uni-bielefeld.de/documenta/vol-22/32.html
The beauty of the Riemann-Silberstein vector
International Nuclear Information System (INIS)
Bialynicki-Birula, I.
2005-01-01
Beams of light carrying angular momentum have recently been widely studied theoretically and experimentally. In my talk I will show that the description of these beams in terms of the Riemann-Silberstein vector offers many advantages. In particular, it provides a natural bridge between the classical and the quantum description. (author)
Energy Technology Data Exchange (ETDEWEB)
Beccantini, A
2001-07-01
This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)
Riemann-Theta Boltzmann Machine arXiv
Krefl, Daniel; Haghighat, Babak; Kahlen, Jens
A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.
Exploration and extension of an improved Riemann track fitting algorithm
Strandlie, A.; Frühwirth, R.
2017-09-01
Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.
Pseudo-periodic maps and degeneration of Riemann surfaces
Matsumoto, Yukio
2011-01-01
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Extended Riemann-Liouville type fractional derivative operator with applications
Directory of Open Access Journals (Sweden)
Agarwal P.
2017-12-01
Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
Quantum field theory on higher-genus Riemann surfaces, 2
International Nuclear Information System (INIS)
Kubo, Reijiro; Ojima, Shuichi.
1990-08-01
Quantum field theory for closed bosonic string systems is formulated on arbitrary higher-genus Riemann surfaces in global operator formalism. Canonical commutation relations between bosonic string field X μ and their conjugate momenta P ν are derived in the framework of conventional quantum field theory. Problems arising in quantizing bosonic systems are considered in detail. Applying the method exploited in the preceding paper we calculate Ward-Takahashi identities. (author)
A contribution to the great Riemann solver debate
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
Directory of Open Access Journals (Sweden)
Jolanta Golenia
2010-01-01
Full Text Available Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N=3 are constructed.
Submaximal Riemann-Roch expected curves and symplectic packing.
Directory of Open Access Journals (Sweden)
Wioletta Syzdek
2007-06-01
Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.
Conformal scalar fields and chiral splitting on super Riemann surfaces
International Nuclear Information System (INIS)
D'Hoker, E.; Phong, D.H.
1989-01-01
We provide a complete description of correlation functions of scalar superfields on a super Riemann surface, taking into account zero modes and non-trivial topology. They are built out of chirally split correlation functions, or conformal blocks at fixed internal momenta. We formulate effective rules which determine these completely in terms of geometric invariants of the super Riemann surface. The chirally split correlation functions have non-trivial monodromy and produce single-valued amplitudes only upon integration over loop momenta. Our discussion covers the even spin structure as well as the odd spin structure case which had been the source of many difficulties in the past. Super analogues of Green's functions, holomorphic spinors, and prime forms emerge which should pave the way to function theory on super Riemann surfaces. In superstring theories, chirally split amplitudes for scalar superfields are crucial in enforcing the GSO projection required for consistency. However one really knew how to carry this out only in the operator formalism to one-loop order. Our results provide a way of enforcing the GSO projection to any loop. (orig.)
Method of construction of the Riemann function for a second-order hyperbolic equation
Aksenov, A. V.
2017-12-01
A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.
Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral
Directory of Open Access Journals (Sweden)
Weijing Zhao
2014-01-01
Full Text Available The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.
Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law
Wei Cai; Yanyan Zhang
2016-01-01
We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.
On the $a$-points of the derivatives of the Riemann zeta function
Onozuka, Tomokazu
2016-01-01
We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta function. The second result is on certain exponential sum involving $a$-points. The third result is an analogue of the zero density theorem. We count the $a$-points of the derivatives of the Riemann zeta function in $1/2-(\\log\\log T)^2/\\log T
Integrable systems twistors, loop groups, and Riemann surfaces
Hitchin, NJ; Ward, RS
2013-01-01
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu
Bosonization in a two-dimensional Riemann Cartan geometry
International Nuclear Information System (INIS)
Denardo, G.; Spallucci, E.
1987-01-01
We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)
The Riemann zeta-function theory and applications
Ivic, Aleksandar
2003-01-01
""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim
Riemann-Roch Spaces and Linear Network Codes
DEFF Research Database (Denmark)
Hansen, Johan P.
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal...... number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\\cite{DBLP:journals/tit/KoetterK08} introduced...... in the above metric making them suitable for linear network coding....
Extended KN algebras and extended conformal field theories over higher genus Riemann surfaces
International Nuclear Information System (INIS)
Ceresole, A.; Huang Chaoshang
1990-01-01
A global operator formalism for extended conformal field theories over higher genus Riemann surfaces is introduced and extended KN algebra are obtained by means of the KN bases. The BBSS construction of the spin-3 operator is carried out for Kac-Moody algebra A 2 over a Riemann surface of arbitrary genus. (orig.)
Superconformal structures and holomorphic 1/2-superdifferentials on N=1 super Riemann surfaces
International Nuclear Information System (INIS)
Kachkachi, H.; Kachkachi, M.
1992-07-01
Using the Super Riemann-Roch theorem we give a local expression for a holomorphic 1/2-superdifferential in a superconformal structure parametrized by special isothermal coordinates on an N=1 Super Riemann Surface (SRS). This construction is done by choosing a suitable origin for these coordinates. The holomorphy of the latter with respect to super Beltrami differentials is proven. (author). 26 refs
Superconformal algebra on meromorphic vector fields with three poles on super-Riemann sphere
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-07-01
Based upon the Riemann-Roch theorem, we construct superconformal algebra of meromorphic vector fields with three poles and the relevant abelian differential of the third kind on super Riemann sphere. The algebra includes two Ramond sectors as subalgebra, and implies a picture of interaction of three superstrings. (author). 14 refs
Two-Loop Scattering Amplitudes from the Riemann Sphere
Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr
2016-01-01
The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.
Poisson sigma model with branes and hyperelliptic Riemann surfaces
International Nuclear Information System (INIS)
Ferrario, Andrea
2008-01-01
We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions
Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis
Castro, C
2004-01-01
The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...
Large chiral diffeomorphisms on Riemann surfaces and W-algebras
International Nuclear Information System (INIS)
Bandelloni, G.; Lazzarini, S.
2006-01-01
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims
Polynomials, Riemann surfaces, and reconstructing missing-energy events
Gripaios, Ben; Webber, Bryan
2011-01-01
We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.
Supersymmetric Dirac particles in Riemann-Cartan space-time
International Nuclear Information System (INIS)
Rumpf, H.
1981-01-01
A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of h/2π and thus complete the partial results of previous WKB calculations. The author also considers such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass. (Auth.)
The Picard group of the moduli space of r-Spin Riemann surfaces
DEFF Research Database (Denmark)
Randal-Williams, Oscar
2012-01-01
An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford...... conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles....
International Nuclear Information System (INIS)
Sierra, Germán
2014-01-01
We construct a Hamiltonian H R whose discrete spectrum contains, in a certain limit, the Riemann zeros. H R is derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1 + 1 dimensions, which has a boundary given by the world line of a uniformly accelerated observer. The action contains a sum of delta function potentials that can be viewed as partially reflecting moving mirrors. An appropriate choice of the accelerations of the mirrors, provide primitive periodic orbits that are associated with the prime numbers p, whose periods, as measured by the observer's clock, are logp. Acting on the chiral components of the fermion χ ∓ , H R becomes the Berry–Keating Hamiltonian ±(x p-hat + p-hat x)/2, where x is identified with the Rindler spatial coordinate and p-hat with the conjugate momentum. The delta function potentials give the matching conditions of the fermion wave functions on both sides of the mirrors. There is also a phase shift e iϑ for the reflection of the fermions at the boundary where the observer sits. The eigenvalue problem is solved by transfer matrix methods in the limit where the reflection amplitudes become infinitesimally small. We find that, for generic values of ϑ, the spectrum is a continuum where the Riemann zeros are missing, as in the adelic Connes model. However, for some values of ϑ, related to the phase of the zeta function, the Riemann zeros appear as discrete eigenvalues that are immersed in the continuum. We generalize this result to the zeros of Dirichlet L-functions, which are associated to primitive characters, that are encoded in the reflection coefficients of the mirrors. Finally, we show that the Hamiltonian associated to the Riemann zeros belongs to class AIII, or chiral GUE, of the Random Matrix Theory. (paper)
On membrane interactions and a three-dimensional analog of Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Kovacs, Stefano [Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); ICTP South American Institute for Fundamental Research, IFT-UNESP,São Paulo, SP 01440-070 (Brazil); Sato, Yuki [National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwartersrand,Wits 2050 (South Africa); Shimada, Hidehiko [Okayama Institute for Quantum Physics,Okayama (Japan)
2016-02-08
Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ{sup 3} connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.
On membrane interactions and a three-dimensional analog of Riemann surfaces
International Nuclear Information System (INIS)
Kovacs, Stefano; Sato, Yuki; Shimada, Hidehiko
2016-01-01
Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ"3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Directory of Open Access Journals (Sweden)
Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
National Research Council Canada - National Science Library
Derbyshire, John
2003-01-01
.... Is the hypothesis true or false?Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence...
Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition
Directory of Open Access Journals (Sweden)
Ge-Feng Yang
2012-01-01
differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.
A variational approach to closed bosonic strings on bordered Riemann surfaces
International Nuclear Information System (INIS)
Ohrndorf, T.
1987-01-01
Polyakov's path integral for bosonic closed strings defined on a bordered Riemann surface is investigated by variational methods. It is demonstrated that boundary variations are generated by the Virasoro operators. The investigation is performed for both, simply connected Riemann surfaces as well as ringlike domains. It is shown that the form of the variational operator is the same on both kinds of surfaces. The Virasoro algebra arises as a consistency condition for the variation. (orig.)
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
Biane, P.; Pitman, J.; Yor, M.
1999-01-01
This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.
Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.
The Euler–Riemann gases, and partition identities
International Nuclear Information System (INIS)
Chair, Noureddine
2013-01-01
The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ 4 , and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t) 2 ) . Finally, we propose two formulas which brings
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
Bernard, Julien
2018-02-01
I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.
Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
International Nuclear Information System (INIS)
Ernst, Frederick J
2007-01-01
metric tensor components. The first two chapters of this book are devoted to some basic ideas: in the introductory chapter 1 the authors discuss the concept of integrability, comparing the integrability of the vacuum Ernst equation with the integrability of nonlinear equations of Korteweg-de Vries (KdV) type, while in chapter 2 they describe various circumstances in which the vacuum Ernst equation has been determined to be relevant, not only in connection with gravitation but also, for example, in the construction of solutions of the self-dual Yang-Mills equations. It is also in this chapter that one of several equivalent linear systems for the Ernst equation is described. The next two chapters are devoted to Dmitry Korotkin's concept of algebro-geometric solutions of a linear system: in chapter 3 the structure of such solutions of the vacuum Ernst equation, which involve Riemann theta functions of hyperelliptic algebraic curves of any genus, is contrasted with the periodic structure of such solutions of the KdV equation. How such solutions can be obtained, for example, by solving a matrix Riemann-Hilbert problem and how the metric tensor of the associated spacetime can be evaluated is described in detail. In chapter 4 the asymptotic behaviour and the similarity structure of the general algebro-geometric solutions of the Ernst equation are described, and the relationship of such solutions to the perhaps more familiar multi-soliton solutions is discussed. The next three chapters are based upon the authors' own published research: in chapter 5 it is shown that a problem involving counter-rotating infinitely thin disks of matter can be solved in terms of genus two Riemann theta functions, while in chapter 6 the authors describe numerical methods that facilitate the construction of such solutions, and in chapter 7 three-dimensional graphs are displayed that depict all metrical fields of the associated spacetime. Finally, in chapter 8, the difficulties associated with
Minimal models on Riemann surfaces: The partition functions
International Nuclear Information System (INIS)
Foda, O.
1990-01-01
The Coulomb gas representation of the A n series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius) 2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)
Minimal models on Riemann surfaces: The partition functions
Energy Technology Data Exchange (ETDEWEB)
Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)
1990-06-04
The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).
Conformal fields. From Riemann surfaces to integrable hierarchies
International Nuclear Information System (INIS)
Semikhatov, A.M.
1991-01-01
I discuss the idea of translating ingredients of conformal field theory into the language of hierarchies of integrable differential equations. Primary conformal fields are mapped into (differential or matrix) operators living on the phase space of the hierarchy, whereas operator insertions of, e.g., a current or the energy-momentum tensor, become certain vector fields on the phase space and thus acquire a meaning independent of a given Riemann surface. A number of similarities are observed between the structures arising on the hierarchy and those of the theory on the world-sheet. In particular, there is an analogue of the operator product algebra with the Cauchy kernel replaced by its 'off-shell' hierarchy version. Also, hierarchy analogues of certain operator insertions admit two (equivalent, but distinct) forms, resembling the 'bosonized' and 'fermionized' versions respectively. As an application, I obtain a useful reformulation of the Virasoro constraints of the type that arise in matrix models, as a system of equations on dressing (or Lax) operators (rather than correlation functions, i.e., residues or traces). This also suggests an interpretation in terms of a 2D topological field theory, which might be extended to a correspondence between Virasoro-constrained hierarchies and topological theories. (orig.)
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
Deduction of Einstein equation from homogeneity of Riemann spacetime
Ni, Jun
2012-03-01
The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).
DEFF Research Database (Denmark)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many...... times smaller it remains very high. For example, whilst there is enough potential wave power off the UK to supply the electricity demands several times over, the economically recoverable resource for the UK is estimated at 25% of current demand; a lot less, but a very substantial amount nonetheless....
High-Order Wave Propagation Algorithms for Hyperbolic Systems
Ketcheson, David I.; Parsani, Matteo; LeVeque, Randall J.
2013-01-01
of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law
Directory of Open Access Journals (Sweden)
Wei Cai
2016-01-01
Full Text Available We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.
The continuous determination of spacetime geometry by the Riemann curvature tensor
International Nuclear Information System (INIS)
Rendall, A.D.
1988-01-01
It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)
Quantized Dirac field in curved Riemann--Cartan background. I. Symmetry properties, Green's function
International Nuclear Information System (INIS)
Nieh, H.T.; Yan, M.L.
1982-01-01
In the present series of papers, we study the properties of quantized Dirac field in curved Riemann--Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann--Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann--Cartan background, using the Schwinger--DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background
International Nuclear Information System (INIS)
Zolotarev, Vladimir A
2009-01-01
Functional models are constructed for commutative systems {A 1 ,A 2 } of bounded linear non-self-adjoint operators which do not contain dissipative operators (which means that ξ 1 A 1 +ξ 2 A 2 is not a dissipative operator for any ξ 1 , ξ 2 element of R). A significant role is played here by the de Branges transform and the function classes occurring in this context. Classes of commutative systems of operators {A 1 ,A 2 } for which such a construction is possible are distinguished. Realizations of functional models in special spaces of meromorphic functions on Riemann surfaces are found, which lead to reasonable analogues of de Branges spaces on these Riemann surfaces. It turns out that the functions E(p) and E-tilde(p) determining the order of growth in de Branges spaces on Riemann surfaces coincide with the well-known Baker-Akhiezer functions. Bibliography: 11 titles.
Explicit solution of Riemann-Hilbert problems for the Ernst equation
Klein, C.; Richter, O.
1998-01-01
Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.
SO(N) WZNW models on higher-genus Riemann surfaces
International Nuclear Information System (INIS)
Alimohammadi, M.; Arfaei, H.; Bonn Univ.
1993-08-01
With the help of the string functions and fusion rules of SO(2N) 1 , we show that the results on SU(N) 1 correlators on higher-genus Riemann surfaces (HGRS) can be extended to the SO(2N) 1 and other level-one simply-laced WZNW models. Using modular invariance and factorization properties of Green functions we find multipoint correlators of primary and descendant fields of SO(2N+1) 1 WZNW models on higher genus Riemann surfaces. (orig.)
Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus
International Nuclear Information System (INIS)
Miao Li; Ming Yu.
1989-05-01
We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies
Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul
2018-03-01
This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.
Reassessing Riemann's paper on the number of primes less than a given magnitude
Dittrich, Walter
2018-01-01
In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.
Local Extrema of the $\\Xi(t)$ Function and The Riemann Hypothesis
Kobayashi, Hisashi
2016-01-01
In the present paper we obtain a necessary and sufficient condition to prove the Riemann hypothesis in terms of certain properties of local extrema of the function $\\Xi(t)=\\xi(\\tfrac{1}{2}+it)$. First, we prove that positivity of all local maxima and negativity of all local minima of $\\Xi(t)$ form a necessary condition for the Riemann hypothesis to be true. After showing that any extremum point of $\\Xi(t)$ is a saddle point of the function $\\Re\\{\\xi(s)\\}$, we prove that the above properties o...
Reduction of 4-dim self dual super Yang-Mills onto super Riemann surfaces
International Nuclear Information System (INIS)
Mendoza, A.; Restuccia, A.; Martin, I.
1990-05-01
Recently self dual super Yang-Mills over a super Riemann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of 4-dim Euclidean self dual super Yang-Mills in terms of constraints on the supercurvature. By dimensional reduction we obtain the same set of superconformal field equations which define self dual connections on a super Riemann surface. (author). 10 refs
Super-quasi-conformal transformation and Schiffer variation on super-Riemann surface
International Nuclear Information System (INIS)
Takahasi, Wataru
1990-01-01
A set of equations which characterizes the super-Teichmueller deformations is proposed. It is a supersymmetric extension of the Beltrami equation. Relations between the set of equations and the Schiffer variations with the KN bases are discussed. This application of the KN bases shows the powerfulness of the KN theory in the study of super-Riemann surfaces. (author)
The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals
Sealey, Vicki; Engelke, Nicole
2012-01-01
The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…
Riemann type algebraic structures and their differential-algebraic integrability analysis
Directory of Open Access Journals (Sweden)
Prykarpatsky A.K.
2010-06-01
Full Text Available The differential-algebraic approach to studying the Lax type integrability of generalized Riemann type equations is devised. The differentiations and the associated invariant differential ideals are analyzed in detail. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-12-01
The superconformal algebras of meromorphic vector fields with multipoles, the central extension and the relevant abelian differential of the third kind on super Riemann sphere were constructed. The background of our theory is concerned with the interaction of closed superstrings. (author). 9 refs
Seeley-De Witt coefficients in a Riemann-Cartan manifold
International Nuclear Information System (INIS)
Cognola, G.; Zerbini, S.; Istituto Nazionale di Fisica Nucleare, Povo
1988-01-01
A new derivation of the first two coefficients of the heat kernel expansion for a second-order elliptic differential operator on a Riemann-Cartan manifold with arbitrary torsion is given. The expressions are presented in a very compact and tractable form useful for physical applications. Comparisons with other similar results that appeared in the literature are briefly discussed. (orig.)
Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
Bender, Carl M.; Brody, Dorje C.
2018-04-01
The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.
International Nuclear Information System (INIS)
Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.
1984-09-01
The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)
Representation theory of current algebra and conformal field theory on Riemann surfaces
International Nuclear Information System (INIS)
Yamada, Yasuhiko
1989-01-01
We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)
International Nuclear Information System (INIS)
Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.
1995-01-01
The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented
Moser, Jan
2015-01-01
In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\\sigma=\\frac 12$ into a butterfly (=infinite series of M\\" obius functions in the region of absolute convergence $\\sigma>1$).
Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)
International Nuclear Information System (INIS)
Shen Jianmin; Sheng Zhengmao; Wang Zhonghua
1992-02-01
We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs
Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere
International Nuclear Information System (INIS)
Sabbah, C
2004-01-01
It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin
Rosatti, Giorgio; Zugliani, Daniel
2015-03-01
In a two-phase free-surface flow, the transition from a mobile-bed condition to a fixed-bed one (and vice versa) occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly. This leads to the possibility of conceiving a new type of Riemann Problem (RP), which we have called Composite Riemann Problem (CRP), where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity. In this paper, we present a strategy for solving a CRP by reducing it to a standard RP of a single, composite system of equations. This can be obtained by combining the two original systems by means of a suitable weighting function, namely the erodibility variable, and the introduction of an appropriate differential equation for this quantity. In this way, the CRP problem can be analyzed theoretically with standard methods, and the features of the solutions can be clearly identified. In particular, a stationary contact wave is able to correctly describe the sharp transition between mobile- and fixed-bed conditions. A finite volume scheme based on the Multiple Averages Generalized Roe approach (Rosatti and Begnudelli (2013) [22]) was used to numerically solve the fixed-mobile CRP. Several test cases demonstrate the effectiveness, exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model.
Directory of Open Access Journals (Sweden)
Meina Sun
2016-05-01
Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.
Asymptotic Behavior of Periodic Wave Solution to the Hirota—Satsuma Equation
International Nuclear Information System (INIS)
Wu Yong-Qi
2011-01-01
The one- and two-periodic wave solutions for the Hirota—Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure. (general)
Directory of Open Access Journals (Sweden)
Kyncl Martin
2017-01-01
Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some
International Nuclear Information System (INIS)
Bolte, J.
1992-08-01
The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)
International Nuclear Information System (INIS)
Stachel, J.
1977-01-01
A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Energy Technology Data Exchange (ETDEWEB)
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
Riemann-Hilbert treatment of Liouville theory on the torus: the general case
International Nuclear Information System (INIS)
Menotti, Pietro
2011-01-01
We extend the previous treatment of Liouville theory on the torus to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equations on a Riemann surface to the two-point function on the torus in which one source is arbitrary and the other small. As a byproduct, we give in terms of quadratures the exact Green function on the square and on the rhombus with opening angle 2π/6 in the background of the field generated by an arbitrary charge.
Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface
Gulden, Tobias; Janas, Michael; Kamenev, Alex
2015-02-01
Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchy’s integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.
Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics
Laugwitz, Detlef
2008-01-01
The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...
Averages of ratios of the Riemann zeta-function and correlations of divisor sums
Conrey, Brian; Keating, Jonathan P.
2017-10-01
Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.
Flux quantization and quantum mechanics on Riemann surfaces in an external magnetic field
International Nuclear Information System (INIS)
Bolte, J.; Steiner, F.
1990-10-01
We investigate the possibility to apply an external constant magnetic field to a quantum mechanical system consisting of a particle moving on a compact or non-compact two-dimensional manifold of constant negative Gaussian curvature and of finite volume. For the motion on compact Riemann surfaces we find that a consistent formulation is only possible if the magnetic flux is quantized, as it is proportional to the (integrated) first Chern class of a certain complex line bundle over the manifold. In the case of non-compact surfaces of finite volume we obtain the striking result that the magnetic flux has to vanish identically due to the theorem that any holomorphic line bundle over a non-compact Riemann surface is holomorphically trivial. (orig.)
International Nuclear Information System (INIS)
van Nieuwenhuizen, P.; Wu, C.C.
1977-01-01
The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss--Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when R/sub μ//sub ν/=0, viz., ∫ (-g) 1 / 2 (R/sub b//sub β//sub μ//sub ν/R/sup μ//sup ν//sup rho//sup sigma/R/sub rho//sub sigma/ /sup α//sup β/).It is explicitly shown that this invariant does not vanish, even when R/sub μ//sub ν/=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes
From Euclidean to Minkowski space with the Cauchy-Riemann equations
International Nuclear Information System (INIS)
Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.
2008-01-01
We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich
2018-01-01
The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.
Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy
Neagu, Mircea
2007-01-01
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.
Temperature duality on Riemann surface and cosmological solutions for genus g = 1 and 2
International Nuclear Information System (INIS)
Yan Jun; Wang Shunjin
1999-01-01
A bosonic string model at finite temperature on the gravitation g μν and the dilaton φ background field is examined. Moreover, the duality relation of energy momentum tensor on high genus Riemann surface is derived. At the same time, the temperature duality invariance for the action of string gas matter is proved in 4-D Robertson-Walker metric, the string cosmological solutions and temperature duality of the equations of motion for genus g = 1 and 2 are also investigated
Codomains for the Cauchy-Riemann and Laplace operators in ℝ2
Directory of Open Access Journals (Sweden)
Lloyd Edgar S. Moyo
2008-01-01
Full Text Available A codomain for a nonzero constant-coefficient linear partial differential operator P(∂ with fundamental solution E is a space of distributions T for which it is possible to define the convolution E*T and thus solving the equation P(∂S=T. We identify codomains for the Cauchy-Riemann operator in ℝ2 and Laplace operator in ℝ2 . The convolution is understood in the sense of the S′-convolution.
Representation of symmetric metric connection via Riemann-Christoffel curvature tensor
International Nuclear Information System (INIS)
Selikhov, A.V.
1989-01-01
Bivector σ-bar μ ν ' which is the Jacoby matrix of the transformation to the Riemanian coordinates is considered in the paper. Basing on the dual nature of σ-bar μ ν ' the representation of metric connection (Christoffel symbols) have been obtained at the Riemanian coordinates via Riemann-Christoffel curvature tensor; the covariant conserved four-momentum in the general theory of relativity have been constructed. 11 refs
International Nuclear Information System (INIS)
Tan, Zhiqiang; Wilson, D.; Varghese, P.L.
1997-01-01
We consider an extension of the ordinary Riemann problem and present an efficient approximate solution that can be used to improve the calculations of aerodynamic forces on an accelerating body. The method is demonstrated with one-dimensional examples where the Euler equations and the body motion are solved in the non-inertial co-ordinate frame fixed to the accelerating body. 8 refs., 6 figs
Fermions on a Riemann surface and the Kadomtsev-Petviashvili equation
International Nuclear Information System (INIS)
Zabrodin, A.V.
1989-01-01
It is shown that the S matrix of free massless fermions on a Riemann surface of finite genus generates quasiperiodic solutions of the Kadomtsev-Petviashvili equation. An operator that changes the genus of a solution is constructed, and the law of composition of such operators is discussed. The construction is a generalization of the well-known operator approach in the case of soliton solutions to the general case of quasiperiodic τ functions
A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces
International Nuclear Information System (INIS)
Soda, Jiro
1991-02-01
We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)
Cálculo de áreas mediante la suma de Riemann con la TI-83
Lupiáñez, José Luis
2002-01-01
En este artículo presentamos una actividad para introducir el cálculo del área que encierra una curva, basada en la Suma de Riemann, y que puede realizarse con la calculadora TI-83. El planteamiento de la actividad permite estudiar varias funciones sin perder tiempo en tediosos cálculos, con idea de observar lo acertado de este método de aproximación.
Riemann zeros and phase transitions via the spectral operator on fractal strings
International Nuclear Information System (INIS)
Herichi, Hafedh; Lapidus, Michel L
2012-01-01
The spectral operator was introduced by Lapidus and van Frankenhuijsen (2006 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings) in their reinterpretation of the earlier work of Lapidus and Maier (1995 J. Lond. Math. Soc. 52 15–34) on inverse spectral problems and the Riemann hypothesis. In essence, it is a map that sends the geometry of a fractal string onto its spectrum. In this review, we present the rigorous functional analytic framework given by Herichi and Lapidus (2012) and within which to study the spectral operator. Furthermore, we give a necessary and sufficient condition for the invertibility of the spectral operator (in the critical strip) and therefore obtain a new spectral and operator-theoretic reformulation of the Riemann hypothesis. More specifically, we show that the spectral operator is quasi-invertible (or equivalently, that its truncations are invertible) if and only if the Riemann zeta function ζ(s) does not have any zeros on the vertical line Re(s) = c. Hence, it is not invertible in the mid-fractal case when c= 1/2 , and it is quasi-invertible everywhere else (i.e. for all c ∈ (0, 1) with c≠ 1/2 ) if and only if the Riemann hypothesis is true. We also show the existence of four types of (mathematical) phase transitions occurring for the spectral operator at the critical fractal dimension c= 1/2 and c = 1 concerning the shape of the spectrum, its boundedness, its invertibility as well as its quasi-invertibility. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)
Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem
International Nuclear Information System (INIS)
Gato, B.; Massachusetts Inst. of Tech., Cambridge
1990-01-01
We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)
Czech Academy of Sciences Publication Activity Database
Chiodaroli, E.; Kreml, Ondřej
2018-01-01
Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/ article /10.1088/1361-6544/aaa10d/meta
Czech Academy of Sciences Publication Activity Database
Chiodaroli, E.; Kreml, Ondřej
2018-01-01
Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aaa10d/meta
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Soft Gravitons & the Memory Effect for Plane Gravitational Waves
Zhang, P. -M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.
2017-01-01
The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constr...
International Nuclear Information System (INIS)
Toumi, I.
1990-04-01
This thesis is devoted to the study of the Riemann problem and the construction of Godunov type numerical schemes for one or two dimensional two-phase flow models. In the first part, we study the Riemann problem for the well-known Drift-Flux, model which has been widely used for the analysis of thermal hydraulics transients. Then we use this study to construct approximate Riemann solvers and we describe the corresponding Godunov type schemes for simplified equation of state. For computation of complex two-phase flows, a weak formulation of Roe's approximate Riemann solver, which gives a method to construct a Roe-averaged jacobian matrix with a general equation of state, is proposed. For two-dimensional flows, the developed methods are based upon an approximate solver for a two-dimensional Riemann problem, according to Harten-Lax-Van Leer principles. The numerical results for standard test problems show the good behaviour of these numerical schemes for a wide range of flow conditions [fr
Fractional parts and their relations to the values of the Riemann zeta function
Alabdulmohsin, Ibrahim
2017-09-06
A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.
Fractional parts and their relations to the values of the Riemann zeta function
Alabdulmohsin, Ibrahim
2017-01-01
A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.
Harada, Hiromitsu; Mouchet, Amaury; Shudo, Akira
2017-10-01
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.
The motion of a classical spinning point particle in a Riemann-Cartan space-time
International Nuclear Information System (INIS)
Amorim, R.
1983-01-01
A consistent set of equations of motion for classical charged point particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a generalized Lagrangean formalism. The equations avoid the spurius free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are paralell in this theory, where the condition of orthogonality between the spin and the 4-velocity is treated as a non-holonomic one. (Author) [pt
Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function
Directory of Open Access Journals (Sweden)
Saker SamirH
2010-01-01
Full Text Available On the hypothesis that the th moments of the Hardy -function are correctly predicted by random matrix theory and the moments of the derivative of are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the zeros of the Riemann zeta-function by employing some Wirtinger-type inequalities. In particular, it is obtained that which means that consecutive nontrivial zeros often differ by at least 6.1392 times the average spacing.
A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line
Its, A.; Sukhanov, V.
2016-05-01
The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.
The transition from regular to irregular motions, explained as travel on Riemann surfaces
International Nuclear Information System (INIS)
Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M
2005-01-01
We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a three-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology-illustrating the onset in a deterministic context of irregular motions-is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. Here only some of our main findings are reported, without detailing their proofs: a more complete presentation will be published elsewhere
Riemann-Hilbert approach to the time-dependent generalized sine kernel
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)
Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.
2013-06-01
A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.
International Nuclear Information System (INIS)
Li Jiequan; Li Qibing; Xu Kun
2011-01-01
The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an
Towards a theory of chaos explained as travel on Riemann surfaces
International Nuclear Information System (INIS)
Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M
2009-01-01
We investigate the dynamics defined by a set of three coupled first-order ODEs. It is shown that the system can be reduced to quadratures which can be expressed in terms of elementary functions. Despite the integrable character of the model, the general solution is a multiple-valued function of time (considered as a complex variable), and we investigate the position and nature of its branch points. In the semi-symmetric case (g 1 = g 2 ≠ g 3 ), for rational values of the coupling constants the system is isochronous and explicit formulae for the period of the solutions can be given. For irrational values, the motions are confined but feature aperiodic motion with sensitive dependence on initial conditions. The system shows a rich dynamical behaviour that can be understood in quantitative detail since a global description of the Riemann surface associated with the solutions can be achieved. The details of the description of the Riemann surface are postponed to a forthcoming publication. This toy model is meant to provide a paradigmatic first step towards understanding a certain novel kind of chaotic behaviour
Do extended objects move along the geodesics in the Riemann space-time
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.
1981-01-01
Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru
Non-supersymmetric matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces
International Nuclear Information System (INIS)
Billo, M.; D'Adda, A.; Provero, P.
2000-01-01
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S N and U(1) N . By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon
Indian Academy of Sciences (India)
and that this should be true, no matter how the in- terval [a, b] is subdivided. ..... Moreover, J: 1 is the unique number with this property. We do not know which ..... as some of our previous demonstrations illustrate, the details of the argument ...
Zou, Li; Tian, Shou-Fu; Feng, Lian-Li
2017-12-01
In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.
The computation of pressure waves in shock tubes by a finite difference procedure
International Nuclear Information System (INIS)
Barbaro, M.
1988-09-01
A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)
Energy Technology Data Exchange (ETDEWEB)
Toumi, I.; Kumbaro, A.; Paillere, H
1999-07-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
Energy Technology Data Exchange (ETDEWEB)
Prykarpatsky, Anatoliy K [Department of Mining Geodesy, AGH University of Science and Technology, Cracow 30059 (Poland); Artemovych, Orest D [Department of Algebra and Topology, Faculty of Mathematics and Informatics of the Vasyl Stefanyk Pre-Carpathian National University, Ivano-Frankivsk (Ukraine); Popowicz, Ziemowit [Institute of Theoretical Physics, University of Wroclaw (Poland); Pavlov, Maxim V, E-mail: pryk.anat@ua.f, E-mail: artemo@usk.pk.edu.p, E-mail: ziemek@ift.uni.wroc.p, E-mail: M.V.Pavlov@lboro.ac.u [Department of Mathematical Physics, P.N. Lebedev Physical Institute, 53 Leninskij Prospekt, Moscow 119991 (Russian Federation)
2010-07-23
A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.
International Nuclear Information System (INIS)
Prykarpatsky, Anatoliy K; Artemovych, Orest D; Popowicz, Ziemowit; Pavlov, Maxim V
2010-01-01
A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.
Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol
2013-01-01
This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.
Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction
Sauloy, Jacques
2017-01-01
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...
A boundary-fitted staggered difference method for incompressible flow using Riemann geometry
International Nuclear Information System (INIS)
Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.
1990-01-01
A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)
Riemann-Liouville integrals of fractional order and extended KP hierarchy
International Nuclear Information System (INIS)
Kamata, Masaru; Nakamula, Atsushi
2002-01-01
An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators
A Riemann-Hilbert formulation for the finite temperature Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)
2015-06-03
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.
Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira
2014-06-01
Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.
Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach
DEFF Research Database (Denmark)
Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel
2016-01-01
This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell with an ap......This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell...... with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...
Riemann surfaces and algebraic curves a first course in Hurwitz theory
Cavalieri, Renzo
2016-01-01
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering
Pelinovsky, Dmitry E.; Sulem, Catherine
A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.
Lapidus, Michel L
2015-08-06
This research expository article not only contains a survey of earlier work but also contains a main new result, which we first describe. Given c≥0, the spectral operator [Formula: see text] can be thought of intuitively as the operator which sends the geometry onto the spectrum of a fractal string of dimension not exceeding c. Rigorously, it turns out to coincide with a suitable quantization of the Riemann zeta function ζ=ζ(s): a=ζ(∂), where ∂=∂(c) is the infinitesimal shift of the real line acting on the weighted Hilbert space [Formula: see text]. In this paper, we establish a new asymmetric criterion for the Riemann hypothesis (RH), expressed in terms of the invertibility of the spectral operator for all values of the dimension parameter [Formula: see text] (i.e. for all c in the left half of the critical interval (0,1)). This corresponds (conditionally) to a mathematical (and perhaps also, physical) 'phase transition' occurring in the midfractal case when [Formula: see text]. Both the universality and the non-universality of ζ=ζ(s) in the right (resp., left) critical strip [Formula: see text] (resp., [Formula: see text]) play a key role in this context. These new results are presented here. We also briefly discuss earlier joint work on the complex dimensions of fractal strings, and we survey earlier related work of the author with Maier and with Herichi, respectively, in which were established symmetric criteria for the RH, expressed, respectively, in terms of a family of natural inverse spectral problems for fractal strings of Minkowski dimension D∈(0,1), with [Formula: see text], and of the quasi-invertibility of the family of spectral operators [Formula: see text] (with [Formula: see text]). © 2015 The Author(s) Published by the Royal Society. All rights reserved.
High-Order Wave Propagation Algorithms for Hyperbolic Systems
Ketcheson, David I.
2013-01-22
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.
Uniqueness of rarefaction waves in multidimensional compressible Euler system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Kreml, Ondřej
2015-01-01
Roč. 12, č. 3 (2015), s. 489-499 ISSN 0219-8916 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler system * uniqueness * rarefaction wave * Riemann problem Subject RIV: BA - General Mathematics Impact factor: 0.556, year: 2015 http://www.worldscientific.com/doi/abs/10.1142/S0219891615500149
Shock and Rarefaction Waves in a Heterogeneous Mantle
Jordan, J.; Hesse, M. A.
2012-12-01
We explore the effect of heterogeneities on partial melting and melt migration during active upwelling in the Earth's mantle. We have constructed simple, explicit nonlinear models in one dimension to examine heterogeneity and its dynamic affects on porosity, temperature and the magnesium number in a partially molten, porous medium comprised of olivine. The composition of the melt and solid are defined by a closed, binary phase diagram for a simplified, two-component olivine system. The two-component solid solution is represented by a phase loop where concentrations 0 and 1 to correspond to fayalite and forsterite, respectively. For analysis, we examine an advective system with a Riemann initial condition. Chromatographic tools and theory have primarily been used to track large, rare earth elements as tracers. In our case, we employ these theoretical tools to highlight the importance of the magnesium number, enthalpy and overall heterogeneity in the dynamics of melt migration. We calculate the eigenvectors and eigenvalues in the concentration-enthalpy space in order to glean the characteristics of the waves emerging the Riemann step. Analysis on Riemann problems of this nature shows us that the composition-enthalpy waves can be represented by self-similar solutions. The eigenvalues of the composition-enthalpy system represent the characteristic wave propagation speeds of the compositions and enthalpy through the domain. Furthermore, the corresponding eigenvectors are the directions of variation, or ``pathways," in concentration-enthalpy space that the characteristic waves follow. In the two-component system, the Riemann problem yields two waves connected by an intermediate concentration-enthalpy state determined by the intersections of the integral curves of the eigenvectors emanating from both the initial and boundary states. The first wave, ``slow path," and second wave, ``fast path," follow the aformentioned pathways set by the eigenvectors. The slow path wave
International Nuclear Information System (INIS)
Gomez Martinez, Silvina Paola; Madriz Aguilar, Jose Edgar; Bellini, Mauricio
2007-01-01
We study gravitational waves generated during the inflationary epoch in presence of a decaying cosmological parameter on a 5D geometrical background which is Riemann flat. Two examples are considered, one with a constant cosmological parameter and the second with a decreasing one
Implicit approximate Riemann solver for two fluid two phase flow models
International Nuclear Information System (INIS)
Raymond, P.; Toumi, I.; Kumbaro, A.
1993-01-01
This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by
Saka, Takashi
2016-05-01
The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.
Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem
Gaydashev, D G
2006-01-01
The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Approximate Riemann solvers and flux vector splitting schemes for two-phase flow
International Nuclear Information System (INIS)
Toumi, I.; Kumbaro, A.; Paillere, H.
1999-01-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
A geometric construction of the Riemann scalar curvature in Regge calculus
McDonald, Jonathan R.; Miller, Warner A.
2008-10-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.
International Nuclear Information System (INIS)
Loubere, Raphael; Maire, Pierre-Henri; Vachal, Pavel
2013-01-01
The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids. The classical compatible discretization is used; namely, momentum equation is discretized using the fundamental concept of subcell forces. Specific internal energy equation is obtained using total energy conservation. The subcell force is derived by invoking the Galilean invariance and thermodynamic consistency. A general form of the subcell force is provided so that a cell entropy inequality is satisfied. The subcell force consists of a classical pressure term plus a tensorial viscous contribution proportional to the difference between the node velocity and the cell-centered velocity. This cell-centered velocity is an extra degree of freedom solved with a cell-centered approximate Riemann solver. The second law of thermodynamics is satisfied by construction of the local positive definite subcell tensor involved in the viscous term. A particular expression of this tensor is proposed. A more accurate extension of this discretization both in time and space is also provided using a piecewise linear reconstruction of the velocity field and a predictor-corrector time discretization. Numerical tests are presented in order to assess the efficiency of this approach in 3D. Sanity checks show that the 3D extension of the 2D approach reproduces 1D and 2D results. Finally, 3D problems such as Sedov, Noh, and Saltzman are simulated. (authors)
A geometric construction of the Riemann scalar curvature in Regge calculus
International Nuclear Information System (INIS)
McDonald, Jonathan R; Miller, Warner A
2008-01-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas
On the properties of torsions in Riemann-Cartan space-times
International Nuclear Information System (INIS)
Baker, W.M.; Atkins, W.K.; Davis, W.R.
1978-01-01
This paper is the first paper in a series of three papers dealing with the physical properties of torsions in Riemann-Cartan space-times (U 4 ). Paper one deals with the particular types of torsion that can be associated with the U 4 reinterpretation of a special class of null electromagnetic solutions of the standard form of Einstein's equations. In particular, for plane null electromagnetic solutions, three types of torsion solutions are associated with this type of reinterpretation. Two of these solutions, the trivector and semi-symmetric torsions, although rather special, serve as examples of what could be done to find the associated torsions in terms of simple requirements on identities in U 4 . The third class is obtained by relating the contorsion to the Lanczos ''spin'' tensor. Paper two, dealing with gravitational radiation, provides the proper background relating to the physical significance of the Lanczos tensor. This series of papers is primarily concerned with the question of the possible physical role of all types of torsion, compatible with an extension or an U 4 reinterpretation of Einstein's theory, consistent with the broadest possible interpretation of the present form of the Einstein-Cartan-Sciama-Kibble theory. However, in paper three some consideration will be given on theories with simpler metrical generalizations of U 4 and the related types of torsion. We emphasize that the content of paper one and two should be viewed mainly as special formal results that introduce the more general considerations of paper three
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
Energy Technology Data Exchange (ETDEWEB)
Duca, Vittorio Del [Institute for Theoretical Physics, ETH Zürich,Hönggerberg, 8093 Zürich (Switzerland); Druc, Stefan; Drummond, James [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Duhr, Claude [Theoretical Physics Department, CERN,Route de Meyrin, CH-1211 Geneva 23 (Switzerland); Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Dulat, Falko [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Marzucca, Robin [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Papathanasiou, Georgios [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Verbeek, Bram [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium)
2016-08-25
We show that scattering amplitudes in planar N=4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L+4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.
AdS5 solutions from M5-branes on Riemann surface and D6-branes sources
Energy Technology Data Exchange (ETDEWEB)
Bah, Ibrahima [Department of Physics and Astronomy, University of Southern California,Los Angeles, CA 90089 (United States); Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France)
2015-09-24
We describe the gravity duals of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a punctured Riemann surface. The internal geometry, normal to the AdS{sub 5} factor, generically preserves two U(1)s, with generators (J{sup +},J{sup −}), that are fibered over the Riemann surface. The metric is governed by a single potential that satisfies a version of the Monge-Ampère equation. The spectrum of N=1 punctures is given by the set of supersymmetric sources of the potential that are localized on the Riemann surface and lead to regular metrics near a puncture. We use this system to study a class of punctures where the geometry near the sources corresponds to M-theory description of D6-branes. These carry a natural (p,q) label associated to the circle dual to the killing vector pJ{sup +}+qJ{sup −} which shrinks near the source. In the generic case the world volume of the D6-branes is AdS{sub 5}×S{sup 2} and they locally preserve N=2 supersymmetry. When p=−q, the shrinking circle is dual to a flavor U(1). The metric in this case is non-degenerate only when there are co-dimension one sources obtained by smearing M5-branes that wrap the AdS{sub 5} factor and the circle dual the superconformal R-symmetry. The D6-branes are extended along the AdS{sub 5} and on cups that end on the co-dimension one branes. In the special case when the shrinking circle is dual to the R-symmetry, the D6-branes are extended along the AdS{sub 5} and wrap an auxiliary Riemann surface with an arbitrary genus. When the Riemann surface is compact with constant curvature, the system is governed by a Monge-Ampère equation.
On spherical harmonic representation of transient waves in dispersive media
International Nuclear Information System (INIS)
Borisov, Victor V
2003-01-01
Axisymmetric transient solutions to the inhomogeneous telegraph equation are constructed in terms of spherical harmonics. Explicit solutions of the initial-value problem are derived in the spacetime domain by means of the Smirnov method of incomplete separation of variables and the Riemann formula. The corresponding Riemann function is constructed with the help of the Olevsky theorem. Solutions for some source distributions on a sphere expanding with a velocity greater than the wavefront velocity are obtained. This allows an analogous solution in the case of a circle belonging to a sphere expanding with the wavefront velocity to be written at once. Application of the scalar solution to a description of electromagnetic waves is also discussed
Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics
International Nuclear Information System (INIS)
Kraczek, B.; Miller, S.T.; Haber, R.B.; Johnson, D.D.
2010-01-01
We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in
Shock waves and rarefaction waves in magnetohydrodynamics. Pt. 1: A model system
International Nuclear Information System (INIS)
Myong, R.S.; Roe, P.L.
1997-01-01
The present study consists of two parts. Here in Part I, a model set of conservation laws exactly preserving the MHD hyperbolic singularities is investigated to develop the general theory of the nonlinear evolution of MHD shock waves. Great emphasis is placed on shock admissibility conditions. By developing the viscosity admissibility condition, it is shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. In contrast, it turns out that the evolutionary condition is inappropriate for determining physically relevant MHD, shocks. In the general non-planar case, by studying canonical cases, we show that the solution of the Riemann problem is not necessarily unique - in particular, that it depends not only on reference states but also on the associated internal structure. Finally, the stability of intermediate shocks is discussed, and a theory of their nonlinear evolution is proposed. In Part 2, the theory of nonlinear waves developed for the model is applied to the MHD problem. It is shown that the topology of the MHD Hugoniot and wave curves is identical to that of the model problem. (Author)
Zeros da função zeta de Riemann e o teorema dos números primos
Oliveira, Willian Diego [UNESP
2013-01-01
We studied various properties of the Riemann’s zeta function. Three proofs of the Prime Number Theorem were provides. Classical results on zero-free region of the zeta function, as well as their relation to the error term in the Prime Number Theorem, were studied in details Estudamos várias propriedades da função zeta de Riemann. Três provas do Teorema dos Números Primos foram fornecidas. Resultados clássicos sobre regiões livres de zeros da função zeta, bem como sua relação com o termo do...
International Nuclear Information System (INIS)
Le Mehaute, Alain; El Kaabouchi, Abdelaziz; Nivanen, Laurent
2008-01-01
Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function 1/(ζ(s)) =Σ n=1 ∞ (μ(n))/(n s ) in the gap [0, 1], is characterized by s=1/2 (1+2iθ). This conjecture can be understood as a consequence of 1/2-order fractional differential characteristics of automorph dynamics upon opened punctuated torus with an angle at infinity equal to π/4. This physical interpretation suggests new opportunities for revisiting the cryptographic methodologies
Directory of Open Access Journals (Sweden)
Rahmatullah
2018-03-01
Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation
Bui-Thanh, T.; Girolami, M.
2014-11-01
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint
On the theory of waves in Chew-Goldberger-Low relativistic magnetohydrodynamics
International Nuclear Information System (INIS)
Shikin, I.S.
1976-01-01
A relativistic invariant form of equations of the Chew-Goldberger-Low magnetic hydrodynamics with longitudinal and transverse pressures has been considered. Fundamental equations, nonlinear riemann waves and ratios on nonremovable discontinuities have been studied. The evolution conditions and the discontinuities ''switching on'' and ''switching off'' the transverse magnetic field have been discussed; a possible presence of jumps is shown after which the transverse pressure decreases
THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION
Çenesiz, Yücel; Kurt, Ali
2015-01-01
– In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...
International Nuclear Information System (INIS)
Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho
2016-01-01
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is
Energy Technology Data Exchange (ETDEWEB)
Balsara, Dinshaw S., E-mail: dbalsara@nd.edu [Physics Department, University of Notre Dame (United States); Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, Tokyo 113-0033 (Japan); Garain, Sudip, E-mail: sgarain@nd.edu [Physics Department, University of Notre Dame (United States); Kim, Jinho, E-mail: jkim46@nd.edu [Physics Department, University of Notre Dame (United States)
2016-08-01
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is
Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion
International Nuclear Information System (INIS)
Wabnitz, Stefan
2013-01-01
In analogy with ocean waves running up towards the beach, shoaling of pre-chirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion. (paper)
International Nuclear Information System (INIS)
Minkowski, P.
1986-01-01
The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)
Pioline, Boris
2016-01-01
The Kawazumi-Zhang invariant $\\varphi$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known behavior of $\\varphi$ in the non-separating degeneration limit, it is shown that $\\varphi$ is equal to the Theta lift of the unique (up to normalization) weak Jacobi form of weight $-2$. This identification provides the complete Fourier-Jacobi expansion of $\\varphi$ near the non-separating node, gives full control on the asymptotics of $\\varphi$ in the various degeneration limits, and provides a efficient numerical procedure to evaluate $\\varphi$ to arbitrary accuracy. It also reveals a mock-type holomorphic Siegel modular form of weight $-2$ underlying $\\varphi$. From the general relation between the Faltings invariant, the Kawazumi-Zhang invariant and the discriminant for hyperelliptic Riemann surfaces, a Theta lift representation for the Faltings invariant in genus two ...
La notion husserlienne de multiplicité : au-delà de Cantor et Riemann
Directory of Open Access Journals (Sweden)
Carlo Ierna
2012-04-01
Full Text Available En raison du rôle changeant qu’il joue dans les différents ouvrages de Husserl, le concept de Mannigfaltigkeit afait l’objet de nombreuses interprétations. La présence de ce terme a notamment induit en erreur plusieurs commentateurs, qui ont cru en déterminer l’origine dans les années de Halle, à l’époque où Husserl, ami et collègue de Cantor, rédigeait la Philosophie de l’arithmétique. Mais force est de constater qu’à cette époque Husserl s’était déjà ouvertement éloigné de la définition cantorienne de Mannigfaltigkeit en s’approchant plutôt de Riemann, comme le montrent les nombreuses études et leçons qui lui sont consacrées. La Mannigfaltigkeitslehre de Husserl semble donc plus proche de la topologie que de la théorie des ensembles de Cantor. Ainsi, dans les Prolégomènes, Husserl introduit l’idée d’une Mannigfaltigkeitslehre pure en tant qu’entreprise méta-théorique dont le but est d’étudier les relations entre théories, à savoir la manière par laquelle une théorie est dérivée ou fondée à partir d’une autre. Dès lors, lorsque Husserl affirme que le meilleur exemple d’une telle théorie pure des multiplicités se trouve dans les mathématiques, cela risque donc de prêter à confusion. En effet, la théorie pure des théories ne saurait être simplement identifiée aux mathématiques qui relèvent de la topologie, mais considérée en tant que mathesis universalis. Bien qu’une telle position ne fût sans doute pas entièrement claire en 1900-01, Husserl ne tardera pas à relier explicitement théorie des multiplicités et mathesis universalis.En ce sens, la mathesis universalis, théorie des théories en général, est une discipline formelle, apriori et analytique qui a pour but l’analyse des catégories sémantiques suprêmes et des catégories d’objets qui leur sont corrélées. Dans cet article j’essayerai de comprendre le développement de la notion de
Gravitational waves and electrodynamics: new perspectives.
Cabral, Francisco; Lobo, Francisco S N
2017-01-01
Given the recent direct measurement of gravitational waves (GWs) by the LIGO-VIRGO collaboration, the coupling between electromagnetic fields and gravity have a special relevance since it opens new perspectives for future GW detectors and also potentially provides information on the physics of highly energetic GW sources. We explore such couplings using the field equations of electrodynamics on (pseudo) Riemann manifolds and apply it to the background of a GW, seen as a linear perturbation of Minkowski geometry. Electric and magnetic oscillations are induced that propagate as electromagnetic waves and contain information as regards the GW which generates them. The most relevant results are the presence of longitudinal modes and dynamical polarization patterns of electromagnetic radiation induced by GWs. These effects might be amplified using appropriate resonators, effectively improving the signal to noise ratio around a specific frequency. We also briefly address the generation of charge density fluctuations induced by GWs and the implications for astrophysics.
Gravitational waves and electrodynamics: new perspectives
Energy Technology Data Exchange (ETDEWEB)
Cabral, Francisco; Lobo, Francisco S.N. [Faculdade de Ciencias da Universidade de Lisboa, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal)
2017-04-15
Given the recent direct measurement of gravitational waves (GWs) by the LIGO-VIRGO collaboration, the coupling between electromagnetic fields and gravity have a special relevance since it opens new perspectives for future GW detectors and also potentially provides information on the physics of highly energetic GW sources. We explore such couplings using the field equations of electrodynamics on (pseudo) Riemann manifolds and apply it to the background of a GW, seen as a linear perturbation of Minkowski geometry. Electric and magnetic oscillations are induced that propagate as electromagnetic waves and contain information as regards the GW which generates them. The most relevant results are the presence of longitudinal modes and dynamical polarization patterns of electromagnetic radiation induced by GWs. These effects might be amplified using appropriate resonators, effectively improving the signal to noise ratio around a specific frequency. We also briefly address the generation of charge density fluctuations induced by GWs and the implications for astrophysics. (orig.)
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel; Ketcheson, David I.
2013-01-01
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel
2013-07-14
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Balsara, Dinshaw S.; Dumbser, Michael
2015-10-01
Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on
Carraro, F.; Valiani, A.; Caleffi, V.
2018-03-01
Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.
2016-06-08
Ideal Magnetohydrodynamics,” J. Com- put. Phys., Vol. 153, No. 2, 1999, pp. 334–352. [14] Tang, H.-Z. and Xu, K., “A high-order gas -kinetic method for...notwithstanding any other provision of law , no person shall be subject to any penalty for failing to comply with a collection of information if it does...Riemann-solver-free spacetime discontinuous Galerkin method for general conservation laws to solve compressible magnetohydrodynamics (MHD) equations. The
Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films
Janantha, P. A. Praveen; Sprenger, Patrick; Hoefer, Mark A.; Wu, Mingzhong
2017-07-01
The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic Y3Fe5O12 thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.
Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.
Liu, Yichao; Sun, Fei; He, Sailing
2018-01-11
In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.
Directory of Open Access Journals (Sweden)
Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
Wave propagation in metamaterials mimicking the topology of a cosmic string
Fernández-Núñez, Isabel; Bulashenko, Oleg
2018-04-01
We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string—a topological defect with curvature singularity. The phenomenon may look like a gravitational analogue of the Aharonov-Bohm effect, since the light propagates in a region where the Riemann tensor vanishes, being nonetheless affected by the non-zero curvature confined to the string core. We carry out the full-wave numerical simulation of the metamaterial medium and give the analytical interpretation of the results by use of the asymptotic theory of diffraction, which turns out to be in excellent agreement. In particular, we show that the main features of wave propagation in a medium with conical singularity can be explained by four-wave interference involving two geometrical optics and two diffracted waves.
Baez, Joao-Joan; Lapidaryus, Michelle; Siegel, Edward Carl-Ludwig
2013-03-01
Riemann-hypothesis physics-proof combines: Siegel-Antono®-Smith[AMS Joint Mtg.(2002)- Abs.973-03-126] digits on-average statistics HIll[Am. J. Math 123, 3, 887(1996)] logarithm-function's (1,0)- xed-point base =units =scale-invariance proven Newcomb [Am. J. Math. 4, 39(1881)]-Weyl[Goett. Nachr.(1914); Math. Ann.7, 313(1916)]-Benford[Proc. Am. Phil. Soc. 78, 4, 51(1938)]-law [Kac,Math. of Stat.-Reasoning(1955); Raimi, Sci. Am. 221, 109(1969)] algebraic-inversion to ONLY Bose-Einstein quantum-statistics(BEQS) with digit d = 0 gapFUL Bose-Einstein Condensation(BEC) insight that digits are quanta are bosons because bosons are and always were quanta are and always were digits, via Siegel-Baez category-semantics tabular list-format matrix truth-table analytics in Plato-Aristotle classic ''square-of-opposition'' : FUZZYICS =CATEGORYICS/Category-Semantics, with Goodkind Bose-Einstein Condensation (BEC) ABOVE ground-state with/and Rayleigh(cut-limit of ''short-cut method''1870)-Polya(1922)-''Anderson''(1958) localization [Doyle and Snell,Random-Walks and Electrical-Networks, MAA(1981)-p.99-100!!!] in Brillouin[Wave-Propagation in Periodic-Structures(1946) Dover(1922)]-Hubbard-Beeby[J.Phys.C(1967)] Siegel[J.Nonxline-Sol.40,453(1980)] generalized-disorder collective-boson negative-dispersion mode-softening universality-principle(G...P) first use of the ``square-of-opposition'' in physics since Plato and Aristote!!!
The Equation Δ u + ∇φ· ∇u = 8πc(1-heu) on a Riemann Surface
International Nuclear Information System (INIS)
Wang Meng
2009-12-01
Let M be a compact Riemann surface, h(x) a positive smooth function on M, and φ(x) a smooth function on M which satisfies that ∫ M e φ dV g = 1. In this paper, we consider the functional J(u) = 2 1 ∫ M |∇u| 2 e φ dV g +8πc ∫ M ue φ dV g -8πclog ∫ M he u+φ dV g . We give a sufficient condition under which J achieves its minimum for c ≤ inf xelement ofM Φ(x). (author)
Kittell, D. E.; Yarrington, C. D.; Lechman, J. B.; Baer, M. R.
2018-05-01
A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.
Swanson, DG
1989-01-01
Plasma Waves discusses the basic development and equations for the many aspects of plasma waves. The book is organized into two major parts, examining both linear and nonlinear plasma waves in the eight chapters it encompasses. After briefly discussing the properties and applications of plasma wave, the book goes on examining the wave types in a cold, magnetized plasma and the general forms of the dispersion relation that characterize the waves and label the various types of solutions. Chapters 3 and 4 analyze the acoustic phenomena through the fluid model of plasma and the kinetic effects. Th
Heat Waves Dangers we face during periods of very high temperatures include: Heat cramps: These are muscular pains and spasms due ... that the body is having trouble with the heat. If a heat wave is predicted or happening… - ...
DEFF Research Database (Denmark)
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star.......Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star....
Energy Technology Data Exchange (ETDEWEB)
Miller, Jonah Maxwell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-10-18
This report has slides on Gravitational Waves; Pound and Rebka: A Shocking Fact; Light is a Ruler; Gravity is the Curvature of Spacetime; Gravitational Waves Made Simple; How a Gravitational Wave Affects Stuff Here; LIGO; This Detection: Neutron Stars; What the Gravitational Wave Looks Like; The Sound of Merging Neutron Stars; Neutron Star Mergers: More than GWs; The Radioactive Cloud; The Kilonova; and finally Summary, Multimessenger Astronomy.
Towne, Dudley H
1988-01-01
This excellent undergraduate-level text emphasizes optics and acoustics, covering inductive derivation of the equation for transverse waves on a string, acoustic plane waves, boundary-value problems, polarization, three-dimensional waves and more. With numerous problems (solutions for about half). ""The material is superbly chosen and brilliantly written"" - Physics Today. Problems. Appendices.
DEFF Research Database (Denmark)
This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis......, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, etc....
DEFF Research Database (Denmark)
Kofoed, Jens Peter; Frigaard, Peter; Sørensen, H. C.
1998-01-01
This paper concerns with the development of the wave energy converter (WEC) Wave Dragon. This WEC is based on the overtopping principle. An overview of the performed research done concerning the Wave Dragon over the past years is given, and the results of one of the more comprehensive studies, co...
Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests
Ciolek, Glenn E.; Roberge, Wayne G.
2013-05-01
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are Lt magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.
MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS
International Nuclear Information System (INIS)
Ciolek, Glenn E.; Roberge, Wayne G.
2013-01-01
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.
Jaffe, Lionel F
2008-04-12
Waves through living systems are best characterized by their speeds at 20 degrees C. These speeds vary from those of calcium action potentials to those of ultraslow ones which move at 1-10 and/or 10-20 nm s(-1). All such waves are known or inferred to be calcium waves. The two classes of calcium waves which include ones with important morphogenetic effects are slow waves that move at 0.2-2 microm s(-1) and ultraslow ones. Both may be propagated by cycles in which the entry of calcium through the plasma membrane induces subsurface contraction. This contraction opens nearby stretch-sensitive calcium channels. Calcium entry through these channels propagates the calcium wave. Many slow waves are seen as waves of indentation. Some are considered to act via cellular peristalsis; for example, those which seem to drive the germ plasm to the vegetal pole of the Xenopus egg. Other good examples of morphogenetic slow waves are ones through fertilizing maize eggs, through developing barnacle eggs and through axolotl embryos during neural induction. Good examples of ultraslow morphogenetic waves are ones during inversion in developing Volvox embryos and across developing Drosophila eye discs. Morphogenetic waves may be best pursued by imaging their calcium with aequorins.
Energy Technology Data Exchange (ETDEWEB)
Nazarenko, Sergey [Warwick Univ., Coventry (United Kingdom). Mathematics Inst.
2011-07-01
Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as ''frozen'' turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field. (orig.)
Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun
2018-03-01
Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a
CERN. Geneva
2005-01-01
We will present a brief introduction to the physics of gravitational waves and their properties. We will review potential astrophysical sources of gravitational waves, and the physics and astrophysics that can be learned from their study. We will survey the techniques and technologies for detecting gravitational waves for the first time, including bar detectors and broadband interferometers, and give a brief status report on the international search effort, with special emphasis on the LIGO detectors and search results.
National Research Council Canada - National Science Library
Swanson, D. G
1989-01-01
... Swanson, D.G. (Donald Gary), D a t e - Plasma waves. Bibliography: p. Includes index. 1. Plasma waves. QC718.5.W3S43 1989 ISBN 0-12-678955-X I. Title. 530.4'4 88-34388 Printed in the United Sta...
DEFF Research Database (Denmark)
Tedd, James; Kofoed, Jens Peter; Friis-Madsen, Erik
2008-01-01
Since March 2003 a prototype of Wave Dragon has been tested in an inland sea in Denmark. This has been a great success with all subsystems tested and improved through working in an offshore environment. The project has proved the Wave Dragon device and has enabled the next stage, a production sized...
DEFF Research Database (Denmark)
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star.......Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star....
International Nuclear Information System (INIS)
Beklaryan, Leva A
2011-01-01
A finite difference analogue of the wave equation with potential perturbation is investigated, which simulates the behaviour of an infinite rod under the action of an external longitudinal force field. For a homogeneous rod, describing solutions of travelling wave type is equivalent to describing the full space of classical solutions to an induced one-parameter family of functional differential equations of point type, with the characteristic of the travelling wave as parameter. For an inhomogeneous rod, the space of solutions of travelling wave type is trivial, and their 'proper' extension is defined as solutions of 'quasitravelling' wave type. By contrast to the case of a homogeneous rod, describing the solutions of quasitravelling wave type is equivalent to describing the quotient of the full space of impulsive solutions to an induced one-parameter family of point-type functional differential equations by an equivalence relation connected with the definition of solutions of quasitravelling wave type. Stability of stationary solutions is analyzed. Bibliography: 9 titles.
DEFF Research Database (Denmark)
Kramer, Morten; Frigaard, Peter
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star....
DEFF Research Database (Denmark)
Kramer, Morten; Andersen, Thomas Lykke
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star....
DEFF Research Database (Denmark)
Tedd, James; Kofoed, Jens Peter; Knapp, W.
2006-01-01
Wave Dragon is a floating wave energy converter working by extracting energy principally by means of overtopping of waves into a reservoir. A 1:4.5 scale prototype has been sea tested for 20 months. This paper presents results from testing, experiences gained and developments made during this ext......Wave Dragon is a floating wave energy converter working by extracting energy principally by means of overtopping of waves into a reservoir. A 1:4.5 scale prototype has been sea tested for 20 months. This paper presents results from testing, experiences gained and developments made during...... this extended period. The prototype is highly instrumented. The overtopping characteristic and the power produced are presented here. This has enabled comparison between the prototype and earlier results from both laboratory model and computer simulation. This gives the optimal operating point and the expected...... power of the device. The project development team has gained much soft experience from working in the harsh offshore environment. In particular the effect of marine growth in the draft tubes of the turbines has been investigated. The control of the device has been a focus for development as is operates...
DEFF Research Database (Denmark)
Frigaard, Peter; Høgedal, Michael; Christensen, Morten
The intention of this manual is to provide some formulas and techniques which can be used for generating waves in hydraulic laboratories. Both long crested waves (2-D waves) and short crested waves (3-D waves) are considered.......The intention of this manual is to provide some formulas and techniques which can be used for generating waves in hydraulic laboratories. Both long crested waves (2-D waves) and short crested waves (3-D waves) are considered....
Study of nonlinear waves described by the cubic Schroedinger equation
International Nuclear Information System (INIS)
Walstead, A.E.
1980-01-01
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables
Study of nonlinear waves described by the cubic Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Walstead, A.E.
1980-03-12
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.
Initial-value problem for the 1-D wave equation in an inhomogeneous medium
International Nuclear Information System (INIS)
Sedlacek, Z.; Roberts, B.; Adam, J.A.
1986-03-01
A complete mathematical analysis of oscillations of an inhomogeneous medium described by a wave equation with a space-dependent coefficient is given. The initial-value problem is solved both by the Laplace transform and by normal-mode analysis and the equivalency of both approaches is demonstrated. The Green function of the problem is a double-valued function of the complex frequency, analytic in the upper and lower halves of the complex frequency plane (the ''physical'' sheet of its Riemann surface) with discontinuity on the whole real axis, corresponding to the continuous frequency spectrum of the physical system in question. The Green function has complex poles on analytic continuation onto the ''unphysical'' sheet of its Riemann surface. This makes it possible, by inverting the Laplace transform, to interpret the solution of the initial-value problem in terms of ''damped'' eigenmodes. The continuum eigenmodes can be constructed directly and are also recovered by integrating the Green function in the complex frequency plane along a closed contour enclosing the spectrum. Their orthogonality and completeness is proved. The solution of the initial-value problem synthesized from the continuum eigenmodes can be interpreted in terms of travelling disturbances scattered by inhomogeneity. (author)
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J
, steep nonsymmetric cnoidal waves, solitons and random waves. They have different properties too. Any wave form has a wave period (T), wave height (H) and speed (C) which depends on T. Still another type of waves are breaking waves near a coast...
International Nuclear Information System (INIS)
Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.
2007-01-01
We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3
International Nuclear Information System (INIS)
Connes, A.; Kreimer, D.
2000-01-01
This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)
Wave fronts of electromagnetic cyclotron harmonic waves
International Nuclear Information System (INIS)
Ohnuma, T.; Watanabe, T.
1982-01-01
In an inhomogeneous high-density magnetized plasma, the spatial properties of the wave fronts and ray trajectories of electromagnetic ordinary and extraordinary cyclotron harmonic waves are investigated. Those waves which are radiated from a local source are found to have wave fronts which are almost parallel to the magnetic field. Also, the reflective properties of the electromagnetic cyclotron harmonic waves are confirmed
International Nuclear Information System (INIS)
Red'kov, V.M.; Ovsiyuk, E.M.; Ishkhanyan, A.M.
2013-01-01
The Schrodinger particle on the background of the 2D space of the constant positive curvature S 2 , a sphere in the 3D Euclidean space, is considered in the external magnetic field. By analogy with the case of the hyperbolic Lobachevsky plane H 2 , where quasi-Cartesian coordinates exist with the realization of H 2 as the Poincare half-plane, a specific system of quasi-Cartesian coordinates (x, y) in S 2 is introduced. It turns out that it is possible only if the two coordinates are complex and obey an additional restriction in order to present a real 2D space. The Schrodinger equation is solved using the method of separation of the variables in the both coordinate systems, cylindrical and quasi-Cartesian, the energy spectrum is the same. For parametrization of the space S 2 , one can use the coordinates (x, x*) or (y, y*), however, in this case the separability of the variables in the wave functions is lost. Constructed solutions may be of interest for describing charged particles in magnetic fields in the context of cosmological models, and for simulating the behavior of the particles in a specific field-configuration in the nano-physics. (authors)
DEFF Research Database (Denmark)
Kramer, Morten; Frigaard, Peter
På foranledning af Löwenmark F.R.I, er der udført numeriske beregninger af Wave Dragons (herefter WD) armes effektivitet for forskellige geometriske udformninger. 5 geometriske modeller, hvor WD's arme er forkortet/forlænget er undersøgt for 3 forskellige drejninger af armene. I alt er 15...
Impact of Wave Dragon on Wave Climate
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Tedd, James; Kramer, Morten
This report is an advisory paper for use in determining the wave dragon effects on hydrography, by considering the effect on the wave climate in the region of a wave dragon. This is to be used in the impact assessment for the Wave Dragon pre-commercial demonstrator.......This report is an advisory paper for use in determining the wave dragon effects on hydrography, by considering the effect on the wave climate in the region of a wave dragon. This is to be used in the impact assessment for the Wave Dragon pre-commercial demonstrator....
Energy Technology Data Exchange (ETDEWEB)
Whittaker, T.J.T. (Queen' s Univ., Belfast, Northern Ireland (UK)); White, P.R.S. (Lanchester Polytechnic, Coventry (UK)); Baker, A.C.J. (Binnie and Partners, London (UK))
1988-10-01
An informal discussion on various wave energy converters is reported. These included a prototype oscillating water column (OWC) device being built on the Isle of Islay in Scotland; the SEA Clam; a tapering channel device (Tapchan) raising incoming waves into a lagoon on a Norwegian island and an OWC device on the same island. The Norwegian devices are delivering electricity at about 5.5p/KWh and 4p/KWh respectively with possibilities for reduction to 2.5-3p/KWh and 3p/KWh under favourable circumstances. The discussion ranged over comparisons with progress in wind power, engineering aspects, differences between inshore and offshore devices, tidal range and energy storage. (UK).
Ciufolini, I; Moschella, U; Fre, P
2001-01-01
Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.
DEFF Research Database (Denmark)
Kramer, Morten; Frigaard, Peter; Brorsen, Michael
Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004.......Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004....
Jiang, Z
2005-01-01
The International Symposium on Shock Waves (ISSW) is a well established series of conferences held every two years in a different location. A unique feature of the ISSW is the emphasis on bridging the gap between physicists and engineers working in fields as different as gas dynamics, fluid mechanics and materials sciences. The main results presented at these meetings constitute valuable proceedings that offer anyone working in this field an authoritative and comprehensive source of reference.
Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar
2018-03-01
We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.
2015-10-30
Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can
Tripathi, B. B.; Espíndola, D.; Pinton, G. F.
2017-11-01
The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.
Efficient Wave Energy Amplification with Wave Reflectors
DEFF Research Database (Denmark)
Kramer, Morten Mejlhede; Frigaard, Peter Bak
2002-01-01
Wave Energy Converters (WEC's) extract wave energy from a limited area, often a single point or line even though the wave energy is generally spread out along the wave crest. By the use of wave reflectors (reflecting walls) the wave energy is effectively focused and increased to approximately 130......-140%. In the paper a procedure for calculating the efficiency and optimizing the geometry of wave reflectors are described, this by use of a 3D boundary element method. The calculations are verified by laboratory experiments and a very good agreement is found. The paper gives estimates of possible power benifit...... for different geometries of the wave reflectors and optimal geometrical design parameters are specified. On this basis inventors of WEC's can evaluate whether a specific WEC possible could benefit from wave reflectors....
Frashure, K. M.; Chen, R. F.; Stephen, R. A.; Bolmer, T.; Lavin, M.; Strohschneider, D.; Maichle, R.; Micozzi, N.; Cramer, C.
2007-01-01
Demonstrating wave processes quantitatively in the classroom using standard classroom tools (such as Slinkys and wave tanks) can be difficult. For example, waves often travel too fast for students to actually measure amplitude or wavelength. Also, when teaching propagating waves, reflections from the ends set up standing waves, which can confuse…
Indian Academy of Sciences (India)
IAS Admin
wavelength, they are called shallow water waves. In the ... Deep and intermediate water waves are dispersive as the velocity of these depends on wavelength. This is not the ..... generation processes, the finite amplitude wave theories are very ...
International Nuclear Information System (INIS)
Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar
2010-01-01
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.
Dynamics on the Riemann Sphere
DEFF Research Database (Denmark)
Petersen, Carsten Lunde
Collection of research papers on holomorphic dynamical systems with an introduction to Bodil Branners works on the field. Contributions: John Milnor: On Lattès Maps. Carsten Lunde Petersen and Tan Lei: Branner-Hubbard motions and attracting dynamics. Artur Avila and Mikhail Lyubich: Examples...
National Research Council Canada - National Science Library
Pritchard, David
1999-01-01
Matter wave interferometers, in which de Broglie waves are coherently split and then recombined to produce interference fringes, have opened exciting new possibilities for precision and fundamental...
International Nuclear Information System (INIS)
Yan Zhenya
2010-01-01
We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These rogue wave solutions may he used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
Hierarchical wave functions revisited
International Nuclear Information System (INIS)
Li Dingping.
1997-11-01
We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasi electron excitation on a torus, is also solved in this paper. (author)
Temiz, Burak Kagan; Yavuz, Ahmet
2015-01-01
This study was done to develop a simple and inexpensive wave driver that can be used in experiments on string waves. The wave driver was made using a battery-operated toy car, and the apparatus can be used to produce string waves at a fixed frequency. The working principle of the apparatus is as follows: shortly after the car is turned on, the…
Balsara, Dinshaw S.; Garain, Sudip; Taflove, Allen; Montecinos, Gino
2018-02-01
The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability to satisfy the constraints in Maxwell's equations. Even so, in the previous paper of this series we were able to present a second order accurate Godunov scheme for computational electrodynamics (CED) which satisfied all the same constraints and simultaneously retained all the traditional advantages of Godunov schemes. In this paper we extend the Finite Volume Time Domain (FVTD) schemes for CED in material media to better than second order of accuracy. From the FDTD method, we retain a somewhat modified staggering strategy of primal variables which enables a very beneficial constraint-preservation for the electric displacement and magnetic induction vector fields. This is accomplished with constraint-preserving reconstruction methods which are extended in this paper to third and fourth orders of accuracy. The idea of one-dimensional upwinding from Godunov schemes has to be significantly modified to use the multidimensionally upwinded Riemann solvers developed by the first author. In this paper, we show how they can be used within the context of a higher order scheme for CED. We also report on advances in timestepping. We show how Runge-Kutta IMEX schemes can be adapted to CED even in the presence of stiff source terms brought on by large conductivities as well as strong spatial variations in permittivity and permeability. We also formulate very efficient ADER timestepping strategies to endow our method with sub-cell resolving capabilities. As a result, our method can be stiffly-stable and resolve significant sub-cell variation in the material properties within a zone. Moreover, we present ADER schemes that are applicable to all hyperbolic PDEs with stiff source terms and at all orders of accuracy. Our new ADER formulation offers a treatment of stiff source terms that is much more efficient than previous ADER
Effective gravitational wave stress-energy tensor in alternative theories of gravity
International Nuclear Information System (INIS)
Stein, Leo C.; Yunes, Nicolas
2011-01-01
The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.
Fovargue, Daniel E; Mitran, Sorin; Smith, Nathan B; Sankin, Georgy N; Simmons, Walter N; Zhong, Pei
2013-08-01
A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model.
Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
El, G. A.; Nguyen, L. T. K.; Smyth, N. F.
2018-04-01
We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.
Energy Technology Data Exchange (ETDEWEB)
Muller, Norbert; Piechna, Janusz; Sun, Guangwei; Parraga, Pablo-Francisco
2018-01-02
A wave disc engine apparatus is provided. A further aspect employs a constricted nozzle in a wave rotor channel. A further aspect provides a sharp bend between an inlet and an outlet in a fluid pathway of a wave rotor, with the bend being spaced away from a peripheral edge of the wave rotor. A radial wave rotor for generating electricity in an automotive vehicle is disclosed in yet another aspect.
Bialynicki-Birula, Iwo
2005-01-01
Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, t...
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.
Electromagnetic waves in gravitational wave spacetimes
International Nuclear Information System (INIS)
Haney, M.; Bini, D.; Ortolan, A.; Fortini, P.
2013-01-01
We have considered the propagation of electromagnetic waves in a space-time representing an exact gravitational plane wave and calculated the induced changes on the four-potential field Aμ of a plane electromagnetic wave. By choosing a suitable photon round-trip in a Michelson interferometer, we have been able to identify the physical effects of the exact gravitational wave on the electromagnetic field, i.e. phase shift, change of the polarization vector, angular deflection and delay. These results have been exploited to study the response of an interferometric gravitational wave detector beyond the linear approximation of the general theory of relativity. A much more detailed examination of this problem can be found in our paper recently published in Classical and Quantum Gravity (28 (2011) 235007).
International Nuclear Information System (INIS)
Pinheiro, R.
1979-01-01
The properties and production of gravitational radiation are described. The prospects for their detection are considered including the Weber apparatus and gravity-wave telescopes. Possibilities of gravity-wave astronomy are noted
Electromagnetic ultrasonic guided waves
Huang, Songling; Li, Weibin; Wang, Qing
2016-01-01
This book introduces the fundamental theory of electromagnetic ultrasonic guided waves, together with its applications. It includes the dispersion characteristics and matching theory of guided waves; the mechanism of production and theoretical model of electromagnetic ultrasonic guided waves; the effect mechanism between guided waves and defects; the simulation method for the entire process of electromagnetic ultrasonic guided wave propagation; electromagnetic ultrasonic thickness measurement; pipeline axial guided wave defect detection; and electromagnetic ultrasonic guided wave detection of gas pipeline cracks. This theory and findings on applications draw on the author’s intensive research over the past eight years. The book can be used for nondestructive testing technology and as an engineering reference work. The specific implementation of the electromagnetic ultrasonic guided wave system presented here will also be of value for other nondestructive test developers.
Fuster, A.; Pabst, C.
2015-01-01
In this work we present a Finslerian version of the well-known pp-waves, which generalizes the very special relativity (VSR) line element. Our Finsler pp-waves are an exact solution of Finslerian Einstein's equations in vacuum.
National Research Council Canada - National Science Library
Pritchard, David
2000-01-01
Long-term research objective: Matter wave interferometers, in which de Broglie waves are coherently split and then recombined to produce interference fringes, have opened exciting new possibilities for precision and fundamental...
Coronal Waves and Oscillations
Directory of Open Access Journals (Sweden)
Nakariakov Valery M.
2005-07-01
Full Text Available Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations (standing kink, sausage and longitudinal modes, propagating slow waves and fast wave trains, the search for torsional waves, theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma - MHD coronal seismology - is discussed and the applicability of this method for the estimation of coronal magnetic field, transport coefficients, fine structuring and heating function is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-14
The Zel’dovich-von Neumann-Doering (ZND) profile of a detonation wave is derived. Two basic assumptions are required: i. An equation of state (EOS) for a partly burned explosive; P(V, e, λ). ii. A burn rate for the reaction progress variable; d/dt λ = R(V, e, λ). For a steady planar detonation wave the reactive flow PDEs can be reduced to ODEs. The detonation wave profile can be determined from an ODE plus algebraic equations for points on the partly burned detonation loci with a specified wave speed. Furthermore, for the CJ detonation speed the end of the reaction zone is sonic. A solution to the reactive flow equations can be constructed with a rarefaction wave following the detonation wave profile. This corresponds to an underdriven detonation wave, and the rarefaction is know as a Taylor wave.
Electromagnetic wave matching device
International Nuclear Information System (INIS)
Hirata, Yosuke; Mitsunaka, Yoshika; Hayashi, Ken-ichi; Ito, Yasuyuki.
1997-01-01
The present invention provides an electromagnetic wave matching capable of reducing a cost for the transmission system in a system of using electromagnetic waves for plasma heating of a thermonuclear reactor. Namely, incident electromagnetic waves are reflected by using a plurality of phase correction mirrors. The reflected electromagnetic waves are connected to an external transmission system through an exit. The phase correction mirrors have such a shape to receive a plurality of beam-like electromagnetic waves and output electromagnetic waves by the number different from the number of the received electromagnetic wave beams having a predetermined distribution. Further, at least two of the phase correction mirrors have such a shape to change the phase of the electromagnetic waves beams incident to the reflection surface of the phase correction mirrors by a predetermined amount corresponding to the position of the reflection surface. Then, the cost for transmission system can greatly be reduced. (I.S.)
Wiley, Scott
2008-01-01
This viewgraph document reviews some mountain wave turbulence and operational hazards while soaring. Maps, photographs, and satellite images of the meteorological phenomena are included. Additionally, photographs of aircraft that sustained mountain wave damage are provided.
A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation
Terrana, S.; Vilotte, J. P.; Guillot, L.
2018-04-01
We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm
Wave Equation Inversion of Skeletonized SurfaceWaves
Zhang, Zhendong; Liu, Yike; Schuster, Gerard T.
2015-01-01
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve
International Nuclear Information System (INIS)
Lambert, A.J.D.
1979-01-01
A review of linear and weakly non-linear theory of electron waves, ion waves and electromagnetic waves in plasmas is presented. The author restricts the discussion to an infinitely extended, homogeneous and isotropic plasma, not affected by external fields and described by Vlasov's and Maxwell's equations. (Auth.)
DEFF Research Database (Denmark)
Kofoed, Jens Peter; Frigaard, Peter
Wave Dragon is a wave energy converter of the overtopping type. The device has been thoroughly tested on a 1:51.8 scale model in wave laboratories and a 1:4.5 scale model deployed in Nissum Bredning, a large inland waterway in Denmark. Based on the experience gained a full scale, multi MW prototype...
Electromagnetic cyclotron harmonic waves
International Nuclear Information System (INIS)
Ohnuma, T.; Watanabe, T.; Hamamatsu, K.
1981-09-01
Electromagnetic electron cyclotron harmonic waves just below the electron cyclotron harmonics are investigated numerically and experimentally. Backward waves which are observed to propagate nearly perpendicular to the magnetic field just below the electron cyclotron frequency in a high density magnetoplasma are confirmed to be in accord with the theoretical electromagnetic cyclotron waves. (author)
Directory of Open Access Journals (Sweden)
Andreas Spiegelberg
2016-12-01
With the still unmet need for a clinically acceptable method for acquiring intracranial compliance, and the revival of ICP waveform analysis, B-waves are moving back into the research focus. Herein we provide a concise review of the literature on B-waves, including a critical assessment of non-invasive methods for obtaining B-wave surrogates.
Energy Technology Data Exchange (ETDEWEB)
Degasperis, Antonio [Dipartimento di Fisica, “Sapienza” Università di Roma, P.le A. Moro 2, 00185 Roma (Italy); Wabnitz, Stefan, E-mail: stefan.wabnitz@unibs.it [Dipartimento di Ingegneria dell' Informazione, Università degli Studi di Brescia and INO-CNR, via Branze 38, 25123 Brescia (Italy); Aceves, Alejandro B. [Southern Methodist University, Dallas (United States)
2015-06-12
We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing may lead to extreme waves at extremely low powers.
Fundamentals of wave phenomena
Hirose, Akira
2010-01-01
This textbook provides a unified treatment of waves that either occur naturally or can be excited and propagated in various media. This includes both longitudinal and transverse waves. The book covers both mechanical and electrical waves, which are normally covered separately due to their differences in physical phenomena.
International Nuclear Information System (INIS)
Goree, J.; Ono, M.; Colestock, P.; Horton, R.; McNeill, D.; Park, H.
1985-07-01
Fast wave current drive is demonstrated in the Princeton ACT-I toroidal device. The fast Alfven wave, in the range of high ion-cyclotron harmonics, produced 40 A of current from 1 kW of rf power coupled into the plasma by fast wave loop antenna. This wave excites a steady current by damping on the energetic tail of the electron distribution function in the same way as lower-hybrid current drive, except that fast wave current drive is appropriate for higher plasma densities
DEFF Research Database (Denmark)
Sørensen, H. C.; Hansen, R.; Friis-Madsen, E.
2000-01-01
The Wave Dragon is an offshore wave energy converter of the overtopping type, utilizing a patented wave reflector design to focus the waves towards a ramp, and the overtopping is used for electricity production through a set of Kaplan/propeller hydro turbines. During the last 2 years, excessive...... design an testing has been performed on a scale 1:50 model of the Wave Dragon, and on a scale 1:3:5 model turbine. Thus survivability, overtopping, hydraulic response, turbine performance and feasibility have been verified....
Elmore, William C
1985-01-01
Because of the increasing demands and complexity of undergraduate physics courses (atomic, quantum, solid state, nuclear, etc.), it is often impossible to devote separate courses to the classic wave phenomena of optics, acoustics, and electromagnetic radiation. This brief comprehensive text helps alleviate the problem with a unique overview of classical wave theory in one volume.By examining a sequence of concrete and specific examples (emphasizing the physics of wave motion), the authors unify the study of waves, developing abstract and general features common to all wave motion. The fundam
Bed Evolution under Rapidly Varying Flows by a New Method for Wave Speed Estimation
Directory of Open Access Journals (Sweden)
Khawar Rehman
2016-05-01
Full Text Available This paper proposes a sediment-transport model based on coupled Saint-Venant and Exner equations. A finite volume method of Godunov type with predictor-corrector steps is used to solve a set of coupled equations. An efficient combination of approximate Riemann solvers is proposed to compute fluxes associated with sediment-laden flow. In addition, a new method is proposed for computing the water depth and velocity values along the shear wave. This method ensures smooth solutions, even for flows with high discontinuities, and on domains with highly distorted grids. The numerical model is tested for channel aggradation on a sloping bottom, dam-break cases at flume-scale and reach-scale with flat bottom configurations and varying downstream water depths. The proposed model is tested for predicting the position of hydraulic jump, wave front propagation, and for predicting magnitude of bed erosion. The comparison between results based on the proposed scheme and analytical, experimental, and published numerical results shows good agreement. Sensitivity analysis shows that the model is computationally efficient and virtually independent of mesh refinement.
Lambrecht, L.; Lamert, A.; Friederich, W.; Möller, T.; Boxberg, M. S.
2018-03-01
A nodal discontinuous Galerkin (NDG) approach is developed and implemented for the computation of viscoelastic wavefields in complex geological media. The NDG approach combines unstructured tetrahedral meshes with an element-wise, high-order spatial interpolation of the wavefield based on Lagrange polynomials. Numerical fluxes are computed from an exact solution of the heterogeneous Riemann problem. Our implementation offers capabilities for modelling viscoelastic wave propagation in 1-D, 2-D and 3-D settings of very different spatial scale with little logistical overhead. It allows the import of external tetrahedral meshes provided by independent meshing software and can be run in a parallel computing environment. Computation of adjoint wavefields and an interface for the computation of waveform sensitivity kernels are offered. The method is validated in 2-D and 3-D by comparison to analytical solutions and results from a spectral element method. The capabilities of the NDG method are demonstrated through a 3-D example case taken from tunnel seismics which considers high-frequency elastic wave propagation around a curved underground tunnel cutting through inclined and faulted sedimentary strata. The NDG method was coded into the open-source software package NEXD and is available from GitHub.
Data on the electromagnetic pion form factor and p-wave
International Nuclear Information System (INIS)
Dubnicka, S.; Meshcheryakov, V.A.; Milko, J.
1980-01-01
The pion form factor absolute value data (free of the omega meson contribution) are unified with the P-wave isovector ππ phase shift. The resultant real and imaginary parts of the pion form factor are described by means of the Pade approximation. All the data, which involve the pion form factor experimental points from the range of momenta - 0.8432 GeV 2 2 , the pion charge radius, and the P-wave isovector ππ phase shift in the elastic region (including also the generally accepted value of the scattering length) are mutually consistent. The data themselves through the Pade approximation reveal that the aforementioned consistency can be achieved only if the pion form factor left-hand cut from the second Riemann sheet is taken into account. Almost in all of the considered Pade approximations one stable pion form factor zero is found in the space-like region, which might indicate the existence of a diffraction minimum in the differential cross section for elastic e - π scattering as a consequence of the constituent structure of the pion like in the case of the electron elastic scattering on nuclei
Linear waves and instabilities
International Nuclear Information System (INIS)
Bers, A.
1975-01-01
The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)
Engelbrecht, Jüri
2015-01-01
This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Magnetohydrodynamic waves, electrohydrodynamic waves and photons
International Nuclear Information System (INIS)
Carstoin, J.
1984-01-01
Two new subjects have lately attracted increased attention: the magnetohydrodynamics (m.h.d.) and the theory of lasers. Equally important is the subject of electrohydrodynamics (e.h.d.). Now, clearly, all electromagnetic waves carry photons; it is the merit of Louis de Broglie to have had reconciled the validity of the Maxwell equations with existence of the latter. I have, recently, derived L. de Broglie's equations from the equations C. It seems natural to assume that the m.h.d. waves carry also photons, but how to reconcile the m.h.d axioms with the existence of photons ... a problem which has, so far, escaped the notice of physicists. In the lines which follows, an attempt is made to incorporate the photons in the m.h.d. waves, re e.h.d. waves in a rather simple fashion
Wave Overtopping Characteristics of the Wave Dragon
DEFF Research Database (Denmark)
Tedd, James; Kofoed, Jens Peter
Simulation work has been used extensively with the Wave dragon and other overtopping devices to analyse the power production performance of them and to optimise the structural design and the control strategy. A time domain approach to this is well documented in Jakobsen & Frigaard 1999. Using...... measurements taken from the Wave Dragon Nissum Bredning prototype, some of the previous assumptions have been slightly modified and improved upon, so that the simulation method better represents the reality of what is occurring....
Cycloidal Wave Energy Converter
Energy Technology Data Exchange (ETDEWEB)
Stefan G. Siegel, Ph.D.
2012-11-30
This program allowed further advancing the development of a novel type of wave energy converter, a Cycloidal Wave Energy Converter or CycWEC. A CycWEC consists of one or more hydrofoils rotating around a central shaft, and operates fully submerged beneath the water surface. It operates under feedback control sensing the incoming waves, and converts wave power to shaft power directly without any intermediate power take off system. Previous research consisting of numerical simulations and two dimensional small 1:300 scale wave flume experiments had indicated wave cancellation efficiencies beyond 95%. The present work was centered on construction and testing of a 1:10 scale model and conducting two testing campaigns in a three dimensional wave basin. These experiments allowed for the first time for direct measurement of electrical power generated as well as the interaction of the CycWEC in a three dimensional environment. The Atargis team successfully conducted two testing campaigns at the Texas A&M Offshore Technology Research Center and was able to demonstrate electricity generation. In addition, three dimensional wave diffraction results show the ability to achieve wave focusing, thus increasing the amount of wave power that can be extracted beyond what was expected from earlier two dimensional investigations. Numerical results showed wave cancellation efficiencies for irregular waves to be on par with results for regular waves over a wide range of wave lengths. Using the results from previous simulations and experiments a full scale prototype was designed and its performance in a North Atlantic wave climate of average 30kW/m of wave crest was estimated. A full scale WEC with a blade span of 150m will deliver a design power of 5MW at an estimated levelized cost of energy (LCOE) in the range of 10-17 US cents per kWh. Based on the new results achieved in the 1:10 scale experiments these estimates appear conservative and the likely performance at full scale will
Wave Dragon Wave Energy Converters Used as Coastal Protection
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Kofoed, Jens Peter
2011-01-01
This paper deals with wave energy converters used to reduce the wave height along shorelines. For this study the Wave Dragon wave energy converter is chosen. The wave height reduction from a single device has been evaluated from physical model tests in scale 1:51.8 of the 260 x 150 m, 24 kW/m model...... Spain, to evaluate the potential for reducing wave heights close the shore by means of Wave Dragons....
Kuznetsov, N.; Maz'ya, V.; Vainberg, B.
2002-08-01
This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'
Electromagnetic wave matching device
International Nuclear Information System (INIS)
Hirata, Yosuke; Mitsunaka, Yoshika; Hayashi, Ken-ichi; Ito, Yasuyuki.
1997-01-01
The present invention provides a matching device capable of increasing an efficiency of combining beams of electromagnetic waves outputted from an output window of a gyrotron which is expected for plasma heating of a thermonuclear reactor and an electromagnetic wave transmission system as high as possible. Namely, an electromagnetic wave matching device reflects beams of electromagnetic waves incident from an inlet by a plurality of phase correction mirrors and combines them to an external transmission system through an exit. In this case, the phase correction mirrors change the phase of the beams of electromagnetic waves incident to the phase correction mirrors by a predetermined amount corresponding to the position of the reflection mirrors. Then, the beams of electromagnetic waves outputted, for example, from a gyrotron can properly be shaped as desired for the intensity and the phase. As a result, combination efficiency with the transmission system can be increased. (I.S.)
DEFF Research Database (Denmark)
Frigaard, Peter; Andersen, Thomas Lykke
The present book describes the most important aspects of wave analysis techniques applied to physical model tests. Moreover, the book serves as technical documentation for the wave analysis software WaveLab 3, cf. Aalborg University (2012). In that respect it should be mentioned that supplementary...... to the present technical documentation exists also the online help document describing the WaveLab software in detail including all the inputs and output fields. In addition to the two main authors also Tue Hald, Jacob Helm-Petersen and Morten Møller Jakobsen have contributed to the note. Their input is highly...... acknowledged. The outline of the book is as follows: • Chapter 2 and 3 describes analysis of waves in time and frequency domain. • Chapter 4 and 5 describes the separation of incident and reflected waves for the two-dimensional case. • Chapter 6 describes the estimation of the directional spectra which also...
CERN. Geneva
2016-01-01
In the past year, the LIGO-Virgo Collaboration announced the first secure detection of gravitational waves. This discovery heralds the beginning of gravitational wave astronomy: the use of gravitational waves as a tool for studying the dense and dynamical universe. In this talk, I will describe the full spectrum of gravitational waves, from Hubble-scale modes, through waves with periods of years, hours and milliseconds. I will describe the different techniques one uses to measure the waves in these bands, current and planned facilities for implementing these techniques, and the broad range of sources which produce the radiation. I will discuss what we might expect to learn as more events and sources are measured, and as this field matures into a standard part of the astronomical milieu.
Ockendon, Hilary
2016-01-01
Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications. New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises. Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, ...
International Nuclear Information System (INIS)
Gregg, D.W.; Kidder, R.E.; Biehl, A.T.
1975-01-01
A method is described for generating a traveling wave laser pulse of almost unlimited energy content wherein a gain medium is pumped into a traveling wave mode, the traveling wave moving at essentially the velocity of light to generate an amplifying region or zone which moves through the medium at the velocity of light in the presence of directed stimulating radiation, thereby generating a traveling coherent, directed radiation pulse moving with the amplification zone through the gain medium. (U.S.)
Kinesthetic Transverse Wave Demonstration
Pantidos, Panagiotis; Patapis, Stamatis
2005-09-01
This is a variation on the String and Sticky Tape demonstration "The Wave Game," suggested by Ron Edge. A group of students stand side by side, each one holding a card chest high with both hands. The teacher cues the first student to begin raising and lowering his card. When he starts lowering his card, the next student begins to raise his. As succeeding students move their cards up and down, a wave such as that shown in the figure is produced. To facilitate the process, students' motions were synchronized with the ticks of a metronome (without such synchronization it was nearly impossible to generate a satisfactory wave). Our waves typically had a frequency of about 1 Hz and a wavelength of around 3 m. We videotaped the activity so that the students could analyze the motions. The (17-year-old) students had not received any prior instruction regarding wave motion and did not know beforehand the nature of the exercise they were about to carry out. During the activity they were asked what a transverse wave is. Most of them quickly realized, without teacher input, that while the wave propagated horizontally, the only motion of the transmitting medium (them) was vertical. They located the equilibrium points of the oscillations, the crests and troughs of the waves, and identified the wavelength. The teacher defined for them the period of the oscillations of the motion of a card to be the total time for one cycle. The students measured this time and then several asserted that it was the same as the wave period. Knowing the length of the waves and the number of waves per second, the next step can easily be to find the wave speed.
DEFF Research Database (Denmark)
Takayama, Osamu; Crasovan, Lucian Cornel; Johansen, Steffen Kjær
2008-01-01
The interface of two semi-infinite media, where at least one of them is a birefringent crystal, supports a special type of surface wave that was predicted theoretically by D'yakonov in 1988. Since then, the properties of such waves, which exist in transparent media only under very special......, the existence of these surface waves in specific material examples is analyzed, discussing the challenge posed by their experimental observation....
CERN. Geneva HR-RFA
2006-01-01
We will present a brief introduction to the physics of gravitational waves and their properties. We will review potential astrophysical sources of gravitational waves, and the physics and astrophysics that can be learned from their study. We will survey the techniques and technologies for detecting gravitational waves for the first time, including bar detectors and broadband interferometers, and give a brief status report on the international search effort.
Wave reflections from breakwaters
Dickson, William S.
1994-01-01
A new method is presented for estimating the reflection of a random, multi-directional sea from a coastal structure. The technique is applicable to an array of wave gauges of arbitrary geometry deployed seaward of the reflector. An expansion for small oblique wave incidence angles is used to derive an approximate relationship between measured array cross-spectra and a small number of parameters that describe the incident wave properties and the reflectivity of the structure. Model tests with ...
CERN. Geneva
2006-01-01
Gravitational wave astronomy is expected to become an observational field within the next decade. First direct detection of gravitational waves is possible with existing terrestrial-based detectors, and highly probable with proposed upgrades. In this three-part lecture series, we give an overview of the field, including material on gravitional wave sources, detection methods, some details of interferometric detectors, data analysis methods, and current results from observational data-taking runs of the LIGO and GEO projects.
Thorpe, S. A.
1980-01-01
The physical processes which control the transfer of gases between the atmosphere and oceans or lakes are poorly understood. Clouds of micro-bubbles have been detected below the surface of Loch Ness when the wind is strong enough to cause the waves to break. The rate of transfer of gas into solution from these bubbles is estimated to be significant if repeated on a global scale. We present here further evidence that the bubbles are caused by breaking waves, and discuss the relationship between the mean frequency of wave breaking at a fixed point and the average distance between breaking waves, as might be estimated from an aerial photograph.
DEFF Research Database (Denmark)
Østergaard, Claus Møller; Rosenstand, Claus Andreas Foss; Gertsen, Frank
2012-01-01
Building on previous well-argued work by Jon Sundbo (1995a), on how innovation has evolved in three phases or waves since 1880, this paper’s contribution is extending the historical line, by offering arguments and explanations for two additional waves of innovation that explain the most recent...... developments. The paper also adds new interpretations of the previous work by Sundbo (1995a) in suggesting that the waves are triggered by societal and economic crisis. The result is a new theoretical and historical framework, proposing five waves of innovation triggered by societal and economic crises...
DEFF Research Database (Denmark)
Kofoed, Jens Peter
2017-01-01
This Handbook for Ocean Wave Energy aims at providing a guide into the field of ocean wave energy utilization. The handbook offers a concise yet comprehensive overview of the main aspects and disciplines involved in the development of wave energy converters (WECs). The idea for the book has been...... shaped by the development, research, and teaching that we have carried out at the Wave Energy Research Group at Aalborg University over the past decades. It is our belief and experience that it would be useful writing and compiling such a handbook in order to enhance the understanding of the sector...
International Nuclear Information System (INIS)
Gregg, D.W.; Kidder, R.E.; Biehl, A.T.
1975-01-01
The invention broadly involves a method and means for generating a traveling wave laser pulse and is basically analogous to a single pass light amplifier system. However, the invention provides a traveling wave laser pulse of almost unlimited energy content, wherein a gain medium is pumped in a traveling wave mode, the traveling wave moving at essentially the velocity of light to generate an amplifying region or zone which moves through the medium at the velocity of light in the presence of directed stimulating radiation, thereby generating a traveling coherent, directed radiation pulse moving with the amplification zone through the gain medium. (U.S.)
David, P
2013-01-01
Propagation of Waves focuses on the wave propagation around the earth, which is influenced by its curvature, surface irregularities, and by passage through atmospheric layers that may be refracting, absorbing, or ionized. This book begins by outlining the behavior of waves in the various media and at their interfaces, which simplifies the basic phenomena, such as absorption, refraction, reflection, and interference. Applications to the case of the terrestrial sphere are also discussed as a natural generalization. Following the deliberation on the diffraction of the "ground? wave around the ear
Pizzo, Nick
2017-11-01
A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497-503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.
Hernandez-Figueroa, Hugo E; Recami, Erasmo
2013-01-01
This continuation and extension of the successful book ""Localized Waves"" by the same editors brings together leading researchers in non-diffractive waves to cover the most important results in their field and as such is the first to present the current state.The well-balanced presentation of theory and experiments guides readers through the background of different types of non-diffractive waves, their generation, propagation, and possible applications. The authors include a historical account of the development of the field, and cover different types of non-diffractive waves, including Airy
Wave Mechanics or Wave Statistical Mechanics
International Nuclear Information System (INIS)
Qian Shangwu; Xu Laizi
2007-01-01
By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
Reflectors to Focus Wave Energy
DEFF Research Database (Denmark)
Kramer, Morten; Frigaard, Peter
2005-01-01
Wave Energy Converters (WEC’s) extract wave energy from a limited area, often a single point or line even though the wave energy is generally spread out along the wave crest. By the use of wave reflectors (reflecting walls) the wave energy is effectively focused and increased by approximately 30......-50%. Clearly longer wave reflectors will focus more wave energy than shorter wave reflectors. Thus the draw back is the increased wave forces for the longer wave reflectors. In the paper a procedure for calculating the energy efficiency and the wave forces on the reflectors are described, this by use of a 3D...... boundary element method. The calculations are verified by laboratory experiments and a very good agreement is found. The paper gives estimates of possible power benefit for different wave reflector geometries and optimal geometrical design parameters are specified. On this basis inventors of WEC’s can...
Making waves: visualizing fluid flows
Zweers, Wout; Zwart, Valerie; Bokhove, Onno
2013-01-01
We explore the visualization of violent wave dynamics and erosion by waves and jets in laser-cut reliefs, laser engravings, and three-dimensional printing. For this purpose we built table-top experiments to cast breaking waves, and also explored the creation of extreme or rogue waves in larger wave
DEFF Research Database (Denmark)
Burcharth, H. F.; Larsen, Brian Juul
The investigation concerns the design of a new internal breakwater in the main port of Ibiza. The objective of the model tests was in the first hand to optimize the cross section to make the wave reflection low enough to ensure that unacceptable wave agitation will not occur in the port. Secondly...
Newman, J. N.
1979-01-01
Discussed is the utilization of surface ocean waves as a potential source of power. Simple and large-scale wave power devices and conversion systems are described. Alternative utilizations, environmental impacts, and future prospects of this alternative energy source are detailed. (BT)
International Nuclear Information System (INIS)
Shawhan, S.D.
1977-01-01
A brief history of plasma wave observations in the Earth's magnetosphere is recounted and a classification of the identified plasma wave phenomena is presented. The existence of plasma waves is discussed in terms of the characteristic frequencies of the plasma, the energetic particle populations and the proposed generation mechanisms. Examples are given for which plasmas waves have provided information about the plasma parameters and particle characteristics once a reasonable theory has been developed. Observational evidence and arguments by analogy to the observed Earth plasma wave processes are used to identify plasma waves that may be significant in other planetary magnetospheres. The similarities between the observed characteristics of the terrestrial kilometric radiation and radio bursts from Jupiter, Saturn and possibly Uranus are stressed. Important scientific problems concerning plasma wave processes in the solar system and beyond are identified and discussed. Models for solar flares, flare star radio outbursts and pulsars include elements which are also common to the models for magnetospheric radio bursts. Finally, a listing of the research and development in terms of instruments, missions, laboratory experiments, theory and computer simulations needed to make meaningful progress on the outstanding scientific problems of plasma wave research is given. (Auth.)
Those Elusive Gravitational Waves
MOSAIC, 1976
1976-01-01
The presence of gravitational waves was predicted by Einstein in his theory of General Relativity. Since then, scientists have been attempting to develop a detector sensitive enough to measure these cosmic signals. Once the presence of gravitational waves is confirmed, scientists can directly study star interiors, galaxy cores, or quasars. (MA)
Directory of Open Access Journals (Sweden)
Zheng-Johansson J. X.
2006-10-01
Full Text Available The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity v, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed c between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength Λd=vcΛ and phase velocity c2/v+v which resembles directly L. de Broglie’s hypothetic phase wave. This phase wave in terms of transmitting the particle mass at the speed v and angular frequency Ωd= 2πv/Λd, with Λd and Ωd obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schrödinger equation of an identical system.
Langfellner, Jan; Birch, Aaron; Gizon, Laurent
2017-08-01
Solar supergranules remain a mysterious phenomenon, half a century after their discovery. One particularly interesting aspect of supergranulation is its wave-like nature detected in Fourier space. Using SDO/HMI local helioseismology and granulation tracking, we provide new evidence for supergranular waves. We also discuss their influence on the evolution of the network magnetic field using cork simulations.
International Nuclear Information System (INIS)
Yan, Zhenya
2011-01-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black–Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields. -- Highlights: ► We investigate the coupled nonlinear volatility and option pricing model. ► We analytically present vector financial rogue waves. ► The vector financial rogue waves may be used to describe the extreme events in financial markets. ► This results may excite the relative researches and potential applications of vector rogue waves.
Gravitational waves from inflation
International Nuclear Information System (INIS)
Guzzetti, M.C.; Bartolo, N.; Liguori, M.; Matarrese, S.
2016-01-01
The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio r and tensor spectral index ηT. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.
Parametric analysis of change in wave number of surface waves
Directory of Open Access Journals (Sweden)
Tadić Ljiljana
2015-01-01
Full Text Available The paper analyzes the dependence of the change wave number of materials soil constants, ie the frequency of the waves. The starting point in this analysis cosists of wave equation and dynamic stiffness matrix of soil.
International Nuclear Information System (INIS)
Kho, T.H.; Lin, A.T.
1988-01-01
Cyclotron masers such as Gyrotrons and the Autoresonance Masers, are fast wave devices: the electromagnetic wave's phase velocity v rho , is greater than the electron beam velocity, v b . To be able to convert the beam kinetic energy into radiation in these devices the beam must have an initial transverse momentum, usually obtained by propagating the beam through a transverse wiggler magnet, or along a nonuniform guide magnetic field before entry into the interaction region. Either process introduces a significant amount of thermal spread in the beam which degrades the performance of the maser. However, if the wave phase velocity v rho v b , the beam kinetic energy can be converted directly into radiation without the requirement of an initial transverse beam momentum, making a slow wave cyclotron maser a potentially simpler and more compact device. The authors present the linear and nonlinear physics of the slow wave cyclotron maser and examine its potential for practical application
Parsimonious Surface Wave Interferometry
Li, Jing
2017-10-24
To decrease the recording time of a 2D seismic survey from a few days to one hour or less, we present a parsimonious surface-wave interferometry method. Interferometry allows for the creation of a large number of virtual shot gathers from just two reciprocal shot gathers by crosscoherence of trace pairs, where the virtual surface waves can be inverted for the S-wave velocity model by wave-equation dispersion inversion (WD). Synthetic and field data tests suggest that parsimonious wave-equation dispersion inversion (PWD) gives S-velocity tomograms that are comparable to those obtained from a full survey with a shot at each receiver. The limitation of PWD is that the virtual data lose some information so that the resolution of the S-velocity tomogram can be modestly lower than that of the S-velocity tomogram inverted from a conventional survey.
International Nuclear Information System (INIS)
Booker, H.G.
1984-01-01
The book aims to present current knowledge concerning the propagation of electromagnetic waves in a homogeneous magnetoplasma for which temperature effects are unimportant. It places roughly equal emphasis on the radio and the hydromagnetic parts of the electromagnetic spectrum. The dispersion properties of a magnetoplasma are treated as a function both of wave frequency (assumed real) and of ionization density. The effect of collisions is included only in so far as this can be done with simplicity. The book describes how pulses are radiated from both small and large antennas embedded in a homogeneous magnetoplasma. The power density radiated from a type of dipole antenna is studied as a function of direction of radiation in all bands of wave frequency. Input reactance is not treated, but the dependence of radiation resistance on wave frequency is described for the entire electromagnetic spectrum. Also described is the relation between beaming and guidance for Alfven waves. (Auth.)
Electromagnetic wave energy converter
Bailey, R. L. (Inventor)
1973-01-01
Electromagnetic wave energy is converted into electric power with an array of mutually insulated electromagnetic wave absorber elements each responsive to an electric field component of the wave as it impinges thereon. Each element includes a portion tapered in the direction of wave propagation to provide a relatively wideband response spectrum. Each element includes an output for deriving a voltage replica of the electric field variations intercepted by it. Adjacent elements are positioned relative to each other so that an electric field subsists between adjacent elements in response to the impinging wave. The electric field results in a voltage difference between adjacent elements that is fed to a rectifier to derive dc output power.
Parsimonious Surface Wave Interferometry
Li, Jing; Hanafy, Sherif; Schuster, Gerard T.
2017-01-01
To decrease the recording time of a 2D seismic survey from a few days to one hour or less, we present a parsimonious surface-wave interferometry method. Interferometry allows for the creation of a large number of virtual shot gathers from just two reciprocal shot gathers by crosscoherence of trace pairs, where the virtual surface waves can be inverted for the S-wave velocity model by wave-equation dispersion inversion (WD). Synthetic and field data tests suggest that parsimonious wave-equation dispersion inversion (PWD) gives S-velocity tomograms that are comparable to those obtained from a full survey with a shot at each receiver. The limitation of PWD is that the virtual data lose some information so that the resolution of the S-velocity tomogram can be modestly lower than that of the S-velocity tomogram inverted from a conventional survey.
Directory of Open Access Journals (Sweden)
Jin Lan (兰金
2015-12-01
Full Text Available A diode, a device allowing unidirectional signal transmission, is a fundamental element of logic structures, and it lies at the heart of modern information systems. The spin wave or magnon, representing a collective quasiparticle excitation of the magnetic order in magnetic materials, is a promising candidate for an information carrier for the next-generation energy-saving technologies. Here, we propose a scalable and reprogrammable pure spin-wave logic hardware architecture using domain walls and surface anisotropy stripes as waveguides on a single magnetic wafer. We demonstrate theoretically the design principle of the simplest logic component, a spin-wave diode, utilizing the chiral bound states in a magnetic domain wall with a Dzyaloshinskii-Moriya interaction, and confirm its performance through micromagnetic simulations. Our findings open a new vista for realizing different types of pure spin-wave logic components and finally achieving an energy-efficient and hardware-reprogrammable spin-wave computer.
Ion Acoustic Waves in the Presence of Electron Plasma Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Pécseli, Hans; Juul Rasmussen, Jens
1977-01-01
Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave.......Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave....
Investigation of Wave Transmission from a Floating Wave Dragon Wave Energy Converter
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke
2012-01-01
This paper focuses on the calibration of the MIKE21BW model against the measured wave height reduction behind a 24 kW/m Wave Dragon (WD) wave energy converter. A numerical model is used to determine the wave transmission through the floating WD in varying wave conditions. The transmission obtained...
Directional spectrum of ocean waves
Digital Repository Service at National Institute of Oceanography (India)
Fernandes, A.A; Gouveia, A; Nagarajan, R.
This paper describes a methodology for obtaining the directional spectrum of ocean waves from time series measurement of wave elevation at several gauges arranged in linear or polygonal arrays. Results of simulated studies using sinusoidal wave...
revivals of Rydberg wave packets
International Nuclear Information System (INIS)
Bluhm, R.; Kostelecky, V.A.; Tudose, B.
1998-01-01
We examine the revival structure of Rydberg wave packets. The effects of quantum defects on wave packets in alkali-metal atoms and a squeezed-state description of the initial wave packets are also described. We then examine the revival structure of Rydberg wave packets in the presence of an external electric field, i.e., the revival structure of Stark wave packets. These wave packets have energies that depend on two quantum numbers and exhibit new types of interference behaviour
MONOTONIC DERIVATIVE CORRECTION FOR CALCULATION OF SUPERSONIC FLOWS WITH SHOCK WAVES
Directory of Open Access Journals (Sweden)
P. V. Bulat
2015-07-01
Full Text Available Subject of Research. Numerical solution methods of gas dynamics problems based on exact and approximate solution of Riemann problem are considered. We have developed an approach to the solution of Euler equations describing flows of inviscid compressible gas based on finite volume method and finite difference schemes of various order of accuracy. Godunov scheme, Kolgan scheme, Roe scheme, Harten scheme and Chakravarthy-Osher scheme are used in calculations (order of accuracy of finite difference schemes varies from 1st to 3rd. Comparison of accuracy and efficiency of various finite difference schemes is demonstrated on the calculation example of inviscid compressible gas flow in Laval nozzle in the case of continuous acceleration of flow in the nozzle and in the case of nozzle shock wave presence. Conclusions about accuracy of various finite difference schemes and time required for calculations are made. Main Results. Comparative analysis of difference schemes for Euler equations integration has been carried out. These schemes are based on accurate and approximate solution for the problem of an arbitrary discontinuity breakdown. Calculation results show that monotonic derivative correction provides numerical solution uniformity in the breakdown neighbourhood. From the one hand, it prevents formation of new points of extremum, providing the monotonicity property, but from the other hand, causes smoothing of existing minimums and maximums and accuracy loss. Practical Relevance. Developed numerical calculation method gives the possibility to perform high accuracy calculations of flows with strong non-stationary shock and detonation waves. At the same time, there are no non-physical solution oscillations on the shock wave front.
Undamped electrostatic plasma waves
Energy Technology Data Exchange (ETDEWEB)
Valentini, F.; Perrone, D.; Veltri, P. [Dipartimento di Fisica and CNISM, Universita della Calabria, 87036 Rende (CS) (Italy); Califano, F.; Pegoraro, F. [Dipartimento di Fisica and CNISM, Universita di Pisa, 56127 Pisa (Italy); Morrison, P. J. [Institute for Fusion Studies and Department of Physics, University of Texas at Austin, Austin, Texas 78712-1060 (United States); O' Neil, T. M. [Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)
2012-09-15
Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named corner modes. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the (k,{omega}{sub R}) plane ({omega}{sub R} being the real part of the wave frequency and k the wavenumber), away from the well-known 'thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower k-values and chopping the tail shifts them toward higher k-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.
Undamped electrostatic plasma waves
International Nuclear Information System (INIS)
Valentini, F.; Perrone, D.; Veltri, P.; Califano, F.; Pegoraro, F.; Morrison, P. J.; O'Neil, T. M.
2012-01-01
Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named corner modes. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the (k,ω R ) plane (ω R being the real part of the wave frequency and k the wavenumber), away from the well-known “thumb curve” for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower k-values and chopping the tail shifts them toward higher k-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.
Robust Wave Resource Estimation
DEFF Research Database (Denmark)
Lavelle, John; Kofoed, Jens Peter
2013-01-01
density estimates of the PDF as a function both of Hm0 and Tp, and Hm0 and T0;2, together with the mean wave power per unit crest length, Pw, as a function of Hm0 and T0;2. The wave elevation parameters, from which the wave parameters are calculated, are filtered to correct or remove spurious data....... An overview is given of the methods used to do this, and a method for identifying outliers of the wave elevation data, based on the joint distribution of wave elevations and accelerations, is presented. The limitations of using a JONSWAP spectrum to model the measured wave spectra as a function of Hm0 and T0......;2 or Hm0 and Tp for the Hanstholm site data are demonstrated. As an alternative, the non-parametric loess method, which does not rely on any assumptions about the shape of the wave elevation spectra, is used to accurately estimate Pw as a function of Hm0 and T0;2....
Borcherdt, R. D.
2007-12-01
General theoretical solutions for Rayleigh- and Love-Type surface waves in viscoelastic media describe physical characteristics of the surface waves in elastic as well as anelastic media with arbitrary amounts of intrinsic absorption. In contrast to corresponding physical characteristics for Rayleigh waves in elastic media, Rayleigh- Type surface waves in anelastic media demonstrate; 1) tilt of the particle motion orbit that varies with depth, and 2) amplitude and volumetric strain distributions with superimposed sinusoidal variations that decay exponentially with depth. Each characteristic is dependent on the amount of intrinsic absorption and the chosen model of viscoelasticity. Distinguishing characteristics of anelastic Love-Type surface waves include: 1) dependencies of the wave speed and absorption coefficient on the chosen model and amount of intrinsic absorption and frequency, and 2) superimposed sinusoidal amplitude variations with an exponential decay with depth. Numerical results valid for a variety of viscoelastic models provide quantitative estimates of the physical characteristics of both types of viscoelastic surface waves appropriate for interpretations pertinent to models of earth materials ranging from low-loss in the crust to moderate- and high-loss in water-saturated soils.
Stress wave focusing transducers
Energy Technology Data Exchange (ETDEWEB)
Visuri, S.R., LLNL
1998-05-15
Conversion of laser radiation to mechanical energy is the fundamental process behind many medical laser procedures, particularly those involving tissue destruction and removal. Stress waves can be generated with laser radiation in several ways: creation of a plasma and subsequent launch of a shock wave, thermoelastic expansion of the target tissue, vapor bubble collapse, and ablation recoil. Thermoelastic generation of stress waves generally requires short laser pulse durations and high energy density. Thermoelastic stress waves can be formed when the laser pulse duration is shorter than the acoustic transit time of the material: {tau}{sub c} = d/c{sub s} where d = absorption depth or spot diameter, whichever is smaller, and c{sub s} = sound speed in the material. The stress wave due to thermoelastic expansion travels at the sound speed (approximately 1500 m/s in tissue) and leaves the site of irradiation well before subsequent thermal events can be initiated. These stress waves, often evolving into shock waves, can be used to disrupt tissue. Shock waves are used in ophthalmology to perform intraocular microsurgery and photodisruptive procedures as well as in lithotripsy to fragment stones. We have explored a variety of transducers that can efficiently convert optical to mechanical energy. One such class of transducers allows a shock wave to be focused within a material such that the stress magnitude can be greatly increased compared to conventional geometries. Some transducer tips could be made to operate regardless of the absorption properties of the ambient media. The size and nature of the devices enable easy delivery, potentially minimally-invasive procedures, and precise tissue- targeting while limiting thermal loading. The transducer tips may have applications in lithotripsy, ophthalmology, drug delivery, and cardiology.
Mandal, Birendra Nath
2015-01-01
The theory of water waves is most varied and is a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers, and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special configurations that are of interest to ocean engineers. Unfortunately, even the apparently simple problems appear to be difficult to tackle mathematically unless some simplified assumptions are made. Fortunately, one can assume water to be an incompressible, in viscid and homogeneous
International Nuclear Information System (INIS)
Devaure, Bernard.
1982-01-01
This invention concerns a device for simulating earth tremors. This device includes a seismic wave generator formed of a cylinder, one end of which is closed by one of the walls of a cell containing a soil, the other end being closed by a wall on which are fixed pyrotechnic devices generating shock waves inside the cylinder. These waves are transmitted from the cylinder to the cell through openings made in the cell wall. This device also includes a mechanical device acting as low-pass filter, located inside the cylinder and close to the cell wall [fr
DEFF Research Database (Denmark)
Margheritini, Lucia; Vicinanza, Diego; Frigaard, Peter
2008-01-01
The SSG (Sea Slot-cone Generator) is a wave energy converter of the overtopping type. The structure consists of a number of reservoirs one on the top of each others above the mean water level, in which the water of incoming waves is stored temporary. In each reservoir, expressively designed low...... head hydroturbines are converting the potential energy of the stored water into power. A key to success for the SSG will be the low cost of the structure and its robustness. The construction of the pilot plant is scheduled and this paper aims to describe the concept of the SSG wave energy converter...
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Kaliski, S
2013-01-01
This book gives a comprehensive overview of wave phenomena in different media with interacting mechanical, electromagnetic and other fields. Equations describing wave propagation in linear and non-linear elastic media are followed by equations of rheological models, models with internal rotational degrees of freedom and non-local interactions. Equations for coupled fields: thermal, elastic, electromagnetic, piezoelectric, and magneto-spin with adequate boundary conditions are also included. Together with its companion volume Vibrations and Waves. Part A: Vibrations this work provides a wealth
Andrei, B. Utkin
2011-10-01
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.
International Nuclear Information System (INIS)
Utkin, Andrei B.
2011-01-01
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
McCormick, Michael E
2007-01-01
This volume will prove of vital interest to those studying the use of renewable resources. Scientists, engineers, and inventors will find it a valuable review of ocean wave mechanics as well as an introduction to wave energy conversion. It presents physical and mathematical descriptions of the nine generic wave energy conversion techniques, along with their uses and performance characteristics.Author Michael E. McCormick is the Corbin A. McNeill Professor of Naval Engineering at the U.S. Naval Academy. In addition to his timely and significant coverage of possible environmental effects associa
Lattice Waves, Spin Waves, and Neutron Scattering
Brockhouse, Bertram N.
1962-03-01
Use of neutron inelastic scattering to study the forces between atoms in solids is treated. One-phonon processes and lattice vibrations are discussed, and experiments that verified the existence of the quantum of lattice vibrations, the phonon, are reviewed. Dispersion curves, phonon frequencies and absorption, and models for dispersion calculations are discussed. Experiments on the crystal dynamics of metals are examined. Dispersion curves are presented and analyzed; theory of lattice dynamics is considered; effects of Fermi surfaces on dispersion curves; electron-phonon interactions, electronic structure influence on lattice vibrations, and phonon lifetimes are explored. The dispersion relation of spin waves in crystals and experiments in which dispersion curves for spin waves in Co-Fe alloy and magnons in magnetite were obtained and the reality of the magnon was demonstrated are discussed. (D.C.W)
Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.
2018-01-01
High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.
National Oceanic and Atmospheric Administration, Department of Commerce — The NOAA NDBC SOS server is part of the IOOS DIF SOS Project. The stations in this dataset have waves data. Because of the nature of SOS requests, requests for data...
National Research Council Canada - National Science Library
Reynolds, Stephen A; Levine, Murray D
2005-01-01
.... A processing module is developed that takes profile estimates as input and uses numerically simulated linear internal wave displacements to create two-dimensional range-dependent sound speed fields...
Instantaneous wave emission model
International Nuclear Information System (INIS)
Kruer, W.L.
1970-12-01
A useful treatment of electrostatic wave emission by fast particles in a plasma is given. First, the potential due to a fast particle is expressed as a simple integration over the particle orbit; several interesting results readily follow. The potential in the wake of an accelerating particle is shown to be essentially that produced through local excitation of the plasma by the particle free-streaming about its instantaneous orbit. Application is made to one dimension, and it is shown that the wave emission and adsorption synchronize to the instantaneous velocity distribution function. Guided by these calculations, we then formulate a test particle model for computing the instantaneous wave emission by fast particles in a Vlasov plasma. This model lends itself to physical interpretation and provides a direct approach to many problems. By adopting a Fokker-Planck description for the particle dynamics, we calculate the broadening of the wave-particle resonance due to velocity diffusion and drag
Sound wave transmission (image)
When sounds waves reach the ear, they are translated into nerve impulses. These impulses then travel to the brain where they are interpreted by the brain as sound. The hearing mechanisms within the inner ear, can ...
Acoustics waves and oscillations
Sen, S.N.
2013-01-01
Parameters of acoustics presented in a logical and lucid style Physical principles discussed with mathematical formulations Importance of ultrasonic waves highlighted Dispersion of ultrasonic waves in viscous liquids explained This book presents the theory of waves and oscillations and various applications of acoustics in a logical and simple form. The physical principles have been explained with necessary mathematical formulation and supported by experimental layout wherever possible. Incorporating the classical view point all aspects of acoustic waves and oscillations have been discussed together with detailed elaboration of modern technological applications of sound. A separate chapter on ultrasonics emphasizes the importance of this branch of science in fundamental and applied research. In this edition a new chapter ''Hypersonic Velocity in Viscous Liquids as revealed from Brillouin Spectra'' has been added. The book is expected to present to its readers a comprehensive presentation of the subject matter...
International Nuclear Information System (INIS)
Yemm, Richard
2000-01-01
It is claimed that important developments over the past five years mean that there will be a range of competing pre-commercial wave-energy systems by 2002. The generation costs should be on a par with biomass schemes and offshore wind systems. The environmental advantages of wave energy are extolled. Ocean Power Delivery (OPD) have produced a set of criteria to be satisfied for a successful wave power scheme and these are listed. OPD is responsible for the snake-like Pelamis device which is a semi-submerged articulated series of cylindrical sections connected through hinged joints. How the wave-induced movement of the hinges is used to generate electricity is explained. The system is easily installed and can be completely removed at the end of its life
Gravitational Waves and Neutrinos
Sturani, Riccardo
2018-01-01
We give an overview about the recent detection of gravitational waves by the Advanced LIGO first and second observing runs and by Advanced Virgo, with emphasis on the prospects for multi-messenger astronomy involving neutrinos detections.
Hietala, V.M.; Vawter, G.A.
1993-12-14
The traveling-wave photodetector of the present invention combines an absorptive optical waveguide and an electrical transmission line, in which optical absorption in the waveguide results in a photocurrent at the electrodes of the electrical transmission line. The optical waveguide and electrical transmission line of the electrically distributed traveling-wave photodetector are designed to achieve matched velocities between the light in the optical waveguide and electrical signal generated on the transmission line. This velocity synchronization provides the traveling-wave photodetector with a large electrical bandwidth and a high quantum efficiency, because of the effective extended volume for optical absorption. The traveling-wave photodetector also provides large power dissipation, because of its large physical size. 4 figures.
Turbulence generation by waves
Energy Technology Data Exchange (ETDEWEB)
Kaftori, D.; Nan, X.S.; Banerjee, S. [Univ. of California, Santa Barbara, CA (United States)
1995-12-31
The interaction between two-dimensional mechanically generated waves, and a turbulent stream was investigated experimentally in a horizontal channel, using a 3-D LDA synchronized with a surface position measuring device and a micro-bubble tracers flow visualization with high speed video. Results show that although the wave induced orbital motion reached all the way to the wall, the characteristics of the turbulence wall structures and the turbulence intensity close to the wall were not altered. Nor was the streaky nature of the wall layer. On the other hand, the mean velocity profile became more uniform and the mean friction velocity was increased. Close to the free surface, the turbulence intensity was substantially increased as well. Even in predominantly laminar flows, the introduction of 2-D waves causes three dimensional turbulence. The turbulence enhancement is found to be proportional to the wave strength.
Magnetoresistive waves in plasmas
International Nuclear Information System (INIS)
Felber, F.S.; Hunter, R.O. Jr.; Pereira, N.R.; Tajima, T.
1982-01-01
The self-generated magnetic field of a current diffusing into a plasma between conductors can magnetically insulate the plasma. Propagation of magnetoresistive waves in plasmas is analyzed. Applications to plasma opening switches are discussed
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Parametric decay of lower hybrid wave into drift waves
International Nuclear Information System (INIS)
Sanuki, Heiji.
1976-12-01
A dispersion relation describing the parametric decay of a lower hybrid wave into an electrostatic drift wave and a drift Alfven wave is derived for an inhomogeneous magnetized plasma. Particularly the stimulated scattering of a drift Alfven wave in such a plasma was investigated in detail. The resonance backscattering instability is found to yield the minimum threshold. (auth.)
Generating gravity waves with matter and electromagnetic waves
International Nuclear Information System (INIS)
Barrabes, C.; Hogan, P A.
2008-01-01
If a homogeneous plane lightlike shell collides head on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision
International Nuclear Information System (INIS)
Perera, Judith
1999-01-01
The advantages of using wave power as a renewable energy source are discussed. Various methods of harnessing wave power are also discussed, together with investment requirements and the relative costs of producing electricity by other means. Island communities who currently rely on imported diesel are interested. The provision of power for reverse osmosis plants producing drinking water is an attractive application. There are many potential devices but the best way forward has yet to be identified. (UK)
International Nuclear Information System (INIS)
Belblidia, L.A.; Bratianu, C.
1979-01-01
Boiling flow in a steam generator, a water-cooled reactor, and other multiphase processes can be subject to instabilities. It appears that the most predominant instabilities are the so-called density-wave oscillations. They can cause difficulties for three main reasons; they may induce burnout; they may cause mechanical vibrations of components; and they create system control problems. A comprehensive review is presented of experimental and theoretical studies concerning density-wave oscillations. (author)
International Nuclear Information System (INIS)
Benoit, M.; Marcos, F.; Teisson, Ch.
1999-01-01
Nuclear power stations located on the coast take the water they use to cool their circuits from the sea. The water intake and discharge devices must be able to operate in all weathers, notably during extreme storms, with waves 10 m high and over. To predict the impact of the waves on the equipment, they are modeled digitally from the moment they form in the middle of the ocean right up to the moment they break on the shore. (authors)
The wave of the future - Searching for gravity waves
International Nuclear Information System (INIS)
Goldsmith, D.
1991-01-01
Research on gravity waves conducted by such scientists as Gamov, Wheeler, Weber and Zel'dovich is discussed. Particular attention is given to current trends in the theoretical analysis of gravity waves carried out by theorists Kip Thorne and Leonid Grishchuk. The problems discussed include the search for gravity waves; calculation of the types of gravity waves; the possibility of detecting gravity waves from localized sources, e.g., from the collision of two black holes in a distant galaxy or the collapse of a star, through the Laser Interferometer Gravitational Wave Observatory; and detection primordial gravity waves from the big bang
Wave Equation Inversion of Skeletonized SurfaceWaves
Zhang, Zhendong
2015-08-19
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.
Grimshaw, RHJ
2007-01-01
After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid 1960's with the seminal paper of Zabusky and Kruskal describing the discovery of the soliton. This was followed by the rapid development of the theory of solitons and integrable systems. At the same time came the realization that solitary waves occur naturally in many physical systems, and play a fundamental role in many circumstances. The aim of this text is to describe the role that soliton theory plays in fluids in several contexts. After an historical introduction, the book is divided five chapters covering the basic theory of the Korteweg-de Vries equation, and the subsequent application to free-surface solitary waves in water to internal solitary waves in the coastal ocean and the atmospheric boundary layer, solitary waves in rotating flows, ...
Numerical investigation of freak waves
Chalikov, D.
2009-04-01
Paper describes the results of more than 4,000 long-term (up to thousands of peak-wave periods) numerical simulations of nonlinear gravity surface waves performed for investigation of properties and estimation of statistics of extreme (‘freak') waves. The method of solution of 2-D potential wave's equations based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by JONSWAP and Pierson-Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in appearance of very big waves. The shape of freak waves varies within a wide range: some of them are sharp-crested, others are asymmetric, with a strong forward inclination. Some of them can be very big, but not steep enough to create dangerous conditions for vessels (but not for fixed objects). Initial generation of extreme waves can occur merely as a result of group effects, but in some cases the largest wave suddenly starts to grow. The growth is followed sometimes by strong concentration of wave energy around a peak vertical. It is taking place in the course of a few peak wave periods. The process starts with an individual wave in a physical space without significant exchange of energy with surrounding waves. Sometimes, a crest-to-trough wave height can be as large as nearly three significant wave heights. On the average, only one third of all freak waves come to breaking, creating extreme conditions, however, if a wave height approaches the value of three significant wave heights, all of the freak waves break. The most surprising result was discovery that probability of non-dimensional freak waves (normalized by significant wave height) is actually independent of density of wave energy. It does not mean that statistics of extreme waves does not depend on wave energy. It just proves that normalization of wave heights by significant wave height is so effective, that statistics of non-dimensional extreme waves tends to be independent
Fast wave current drive above the slow wave density limit
International Nuclear Information System (INIS)
McWilliams, R.; Sheehan, D.P.; Wolf, N.S.; Edrich, D.
1989-01-01
Fast wave and slow wave current drive near the mean gyrofrequency were compared in the Irvine Torus using distinct phased array antennae of similar principal wavelengths, frequencies, and input powers. The slow wave current drive density limit was measured for 50ω ci ≤ω≤500ω ci and found to agree with trends in tokamaks. Fast wave current drive was observed at densities up to the operating limit of the torus, demonstrably above the slow wave density limit
Partnership for Wave Power - Roadmaps
DEFF Research Database (Denmark)
Nielsen, Kim; Krogh, Jan; Brodersen, Hans Jørgen
This Wave Energy Technology Roadmap is developed by the Partnership for Wave Power including nine Danish wave energy developers. It builds on to the strategy [1] published by the Partnership in 2012, a document that describes the long term vision of the Danish Wave Energy sector: “By 2030...
Some considerations of wave propagation
Verdonk, P. L. F. M.
The meaning of group velocity and its relation to conserved quantities are demonstrated. The origin of wave dispersion in terms of nonlocal and relaxation phenomena are clarified. The character of a wave described by an equation with a general type of nonlinearity and general dispersion terms is explained. The steepening of a wave flank and the occurrence of stationary waves are discussed.
Rogue waves in nonlinear science
International Nuclear Information System (INIS)
Yan Zhenya
2012-01-01
Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.
Periodic waves in nonlinear metamaterials
International Nuclear Information System (INIS)
Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo
2012-01-01
Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.
Revivals of Rydberg wave packets
International Nuclear Information System (INIS)
Bluhm, R.; Kostelecky, V.A.; Tudose, B.
1998-01-01
We examine the revival structure of Rydberg wave packets. These wave packets exhibit initial classical periodic motion followed by a sequence of collapse, fractional (or full) revivals, and fractional (or full) superrevivals. The effects of quantum defects on wave packets in alkali-metal atoms and a squeezed-state description of the initial wave packets are also considered. We then examine the revival structure of Rydberg wave packets in the presence of an external electric field - that is, the revival structure of Stark wave packets. These wave packets have energies that depend on two quantum numbers and exhibit new types of interference behavior
Directory of Open Access Journals (Sweden)
M. Caputo
1998-06-01
Full Text Available Since the dispersion and attenuation properties of dielectric and anelastic media, in the frequency domain, are expressed by similar formulae, as shown experimentally by Cole and Cole (1941 and Bagley and Torvik (1983, 1986 respectively, we note that the same properties may be represented in the time domain by means of an equation of the same form; this is obtained by introducing derivatives of fractional order into the system functions of the media. The Laplace Transforms (LT of such system functions contain fractional powers of the imaginary frequency and are, therefore, multivalued functions defined in the Riemann Sheets (RS of the function. We determine the response of the medium (dielectric o anelastic to a generic signal summing the time domain representation due to the branches of the solutions in the RSs of the LT. It is found that, if the initial conditions are equal in all the RSs, the solution is a sum of two exponentials with complex exponents, if the initial conditions are different in some of the RSs, then a transient for each of those RSs is added to the exponentials. In all cases a monochromatic wave is split into a set of waves with the same frequency and slightly different wavelengths which interfere and disperse. As a consequence a monochromatic electromagnetic wave with frequency around 1 MHz in water has a relevant dispersion and beats generating a tunnel effect. In the atmosphere of the Earth the dispersion of a monochromatic wave with frequency around 1 GHz, like those used in tracking artificial satellites, has a negligible effect on the accuracy of the determination of the position of the satellites and the positioning of the bench marks on the Earth. We also find the split eigenfunctions of the free modes of infinite plates and shells made of dielectric and anelastic media.
Capillary waves in slow motion
International Nuclear Information System (INIS)
Seydel, Tilo; Tolan, Metin; Press, Werner; Madsen, Anders; Gruebel, Gerhard
2001-01-01
Capillary wave dynamics on glycerol surfaces has been investigated by means of x-ray photon correlation spectroscopy performed at grazing angles. The measurements show that thermally activated capillary wave motion is slowed down exponentially when the sample is cooled below 273 K. This finding directly reflects the freezing of the surface waves. The wave-number dependence of the measured time constants is in quantitative agreement with theoretical predictions for overdamped capillary waves
Wave calculus based upon wave logic
International Nuclear Information System (INIS)
Orlov, Y.F.
1978-01-01
A number operator has been introduced based upon the binary (p-nary) presentation of numbers. This operator acts upon a numerical state vector. Generally the numerical state vector describes numbers that are not precise but smeared in a quantum sense. These states are interrupted in wave logic terms, according to which concepts may exist within the inner language of a phenomenon that in principle cannot be translated into the language of the investigator. In particular, states may exist where mean values of a quantity, continuous in classical limits, take only discrete values. Operators for differentiation and integration of operator functions are defined, which take the usual form in the classical limit. (author)
Metamaterials, from electromagnetic waves to water waves, bending waves and beyond
Dupont, G.
2015-08-04
We will review our recent work on metamaterials for different types of waves. Transposition of transform optics to water waves and bending waves on plates will be considered with potential applications of cloaking to water waves protection and anti-vibrating systems.
Soomere, T.
2010-07-01
Most of the processes resulting in the formation of unexpectedly high surface waves in deep water (such as dispersive and geometrical focusing, interactions with currents and internal waves, reflection from caustic areas, etc.) are active also in shallow areas. Only the mechanism of modulational instability is not active in finite depth conditions. Instead, wave amplification along certain coastal profiles and the drastic dependence of the run-up height on the incident wave shape may substantially contribute to the formation of rogue waves in the nearshore. A unique source of long-living rogue waves (that has no analogues in the deep ocean) is the nonlinear interaction of obliquely propagating solitary shallow-water waves and an equivalent mechanism of Mach reflection of waves from the coast. The characteristic features of these processes are (i) extreme amplification of the steepness of the wave fronts, (ii) change in the orientation of the largest wave crests compared with that of the counterparts and (iii) rapid displacement of the location of the extreme wave humps along the crests of the interacting waves. The presence of coasts raises a number of related questions such as the possibility of conversion of rogue waves into sneaker waves with extremely high run-up. Also, the reaction of bottom sediments and the entire coastal zone to the rogue waves may be drastic.
Millimeter wave and terahertz wave transmission characteristics in plasma
International Nuclear Information System (INIS)
Ma Ping; Qin Long; Chen Weijun; Zhao Qing; Shi Anhua; Huang Jie
2013-01-01
An experiment was conducted on the shock tube to explore the transmission characteristics of millimeter wave and terahertz wave in high density plasmas, in order to meet the communication requirement of hypersonic vehicles during blackout. The transmission attenuation curves of millimeter wave and terahertz wave in different electron density and collision frequency were obtained. The experiment was also simulated by auxiliary differential equation finite-difference time-domain (ADE-FDTD) methods. The experimental and numerical results show that the transmission attenuation of terahertz wave in the plasma is smaller than that of millimeter wave under the same conditions. The transmission attenuation of terahertz wave in the plasma is enhanced with the increase of electron density. The terahertz wave is a promising alternative to the electromagnetic wave propagation in high density plasmas. (authors)
Infragravity Waves Produced by Wave Groups on Beaches
Institute of Scientific and Technical Information of China (English)
邹志利; 常梅
2003-01-01
The generation of low frequency waves by a single or double wave groups incident upon two plane beaches with the slope of 1/40 and 1/100 is investigated experimentally and numerically. A new type of wave maker signal is used to generate the groups, allowing the bound long wave (set-down) to be included in the group. The experiments show that the low frequency wave is generated during breaking and propagation to the shoreline of the wave group. This process of generation and propagation of low frequency waves is simulated numerically by solving the short-wave averaged mass and momentum conservation equations. The computed and measured results are in good agreement. The mechanism of generation of low frequency waves in the surf zone is examined and discussed.
Prototype Testing of the Wave Energy Converter Wave Dragon
DEFF Research Database (Denmark)
Kofoed, Jens Peter; Frigaard, Peter; Friis-Madsen, Erik
2006-01-01
The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power. In the period...... from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57!27 m wide and 237 tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world’s first offshore wave energy...... converter. The prototype is fully equipped with hydro turbines and automatic control systems, and is instrumented in order to monitor power production, wave climate, forces in mooring lines, stresses in the structure and movements of the Wave Dragon. In the period May 2003 to January 2005 an extensive...
Prototype Testing of the Wave Energy Converter Wave Dragon
DEFF Research Database (Denmark)
Kofoed, Jens Peter; Frigaard, Peter Bak; Friis-Madsen, Erik
2004-01-01
The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power. In the period...... from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57 x 27 m wide and 237 tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world's first offshore wave energy...... converter. The prototype is fully equipped with hydro turbines and automatic control systems, and is instrumented in order to monitor power production, wave climate, forces in mooring lines, stresses in the structure and movements of the Wave Dragon. During the last months, extensive testing has started...
Rupture, waves and earthquakes.
Uenishi, Koji
2017-01-01
Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but "extraordinary" phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable.
Energy Technology Data Exchange (ETDEWEB)
1983-10-01
The Tapered Channel Wave Power Plant (TAPCHAN) is based on a new method for wave energy conversion. The principle of operation can be explained by dividing the system into the following four sub-systems: Firstly, a collector which is designed to concentrate the water energy and optimize collection efficiency for a range of frequencies and directions. Secondly, the energy converter, in which the energy of the collected waves is transformed into potential energy in an on-shore water reservoir. This is the unique part of the power plant. It consists of a gradually narrowing channel with wall heights equal to the filling level of the reservoir (typical heights 3-7 m). The waves enter the wide end of the channel and as they propagate down the narrowing channel, the wave height is amplified until the wavecrests spill over the walls. Thirdly, a reservoir which provides a stable water supply for the turbines. Finally, the hydroelectric power plant, where well established techniques are used for the generation of electric power. The water turbine driving the electric generator is of a low head type, such as a Kaplan or a tubular turbine. It must be designed for salt water operation and should have good regulation capabilities. Power plants based on the principle described, are now offered on a commercial basis.
Micrononcasual Euclidean wave functions
International Nuclear Information System (INIS)
Enatsu, H.; Takenaka, A.; Okazaki, M.
1978-01-01
A theory which describes the internal attributes of hadrons in terms of space-time wave functions is presented. In order to develop the theory on the basis of a rather realistic model, covariant wave equations are first derived for the deuteron, in which the co-ordinates of the centre of mass of two nucleons can be defined unambiguously. Then the micro-noncasual behaviour of virtual mesons mediating between the two nucleons is expressed by means of wave functions depending only on the relative Euclidean co-ordinates with respect to the centre of mass of the two nucleons; the wave functions are assumed to obey the 0 4 and SU 2 x SU 2 groups. The properties of the wave functions under space inversion, time reversal and particle-antiparticle conjugation are investigated. It is found that the internal attributes of the mesons, such as spin, isospin, strangeness, intrinsic parity, charge parity and G-parity are explained consistently. The theory is applicable also to the case of baryons
Magnetostatic wave tunable resonators
Castera, J.-P.; Hartemann, P.
1983-06-01
Theoretical principles and techniques for the implementation of magnetostatic surface wave and volume wave resonators in high frequency oscillators are discussed. Magnetostatic waves are magnetic waves that propagate in materials exposed to a polarized magnetic field. The propagation speed ranges from 3-300 km/sec for wavelengths between 1 micron and 10 mm, in the presence of lags from 10-1000 nsec/ cm. Tunable resonators in the 1-20 GHz frequency range have been manufactured with YIG using liquid phase epitaxy for deposition on gadolinium and gallium substrates. Distributed-mirror Fabry-Perot cavity resonators are described and performance tests results are reported, including losses of 8 dB, a quality coefficient under voltage of 450, and frequency rejection outside of resonance better than 10 dB. However, saturation occurs at low power levels at frequencies lower than 4.2 GHz, a feature overcome with forward volume magnetostatic wave generators, which have a quality factor of 500, an insertion loss of 22 dB, and rejection around 15 dB.
Experimental Study on the WavePiston Wave Energy Converter
DEFF Research Database (Denmark)
Pecher, Arthur; Kofoed, Jens Peter; Angelelli, E.
This report presents the results of an experimental study of the power performance of the WavePiston wave energy converter. It focuses mainly on evaluating the power generating capabilities of the device and the effect of the following issues: Scaling ratios PTO loading Wave height and wave period...... dependency Oblique incoming waves Distance between plates During the study, the model supplied by the client, WavePiston, has been rigorously tested as all the anticipated tests have been done thoroughly and during all tests, good quality data has been obtained from all the sensors....
Testing, Analysis and Control of Wave Dragon, Wave Energy Converter
DEFF Research Database (Denmark)
Tedd, James
of the incident waves upon a wave device allows the possibility of accurately tuning the power-take off mechanism (the hydro-turbines for the Wave Dragon) to capture more energy. A digital filter method for performing this prediction in real-time with minimal computational effort is presented. Construction...... of digital filters is well known within signal processing, but their use for this application in Wave Energy is new. The filter must be designed carefully as the frequency components of waves travel at different speeds. Research presented in this thesis has advanced the development of the Wave Dragon device...
Yerganian, Simon Scott
2001-07-17
A piezoelectric motor having a stator in which piezoelectric elements are contained in slots formed in the stator transverse to the desired wave motion. When an electric field is imposed on the elements, deformation of the elements imposes a force perpendicular to the sides of the slot, deforming the stator. Appropriate frequency and phase shifting of the electric field will produce a wave in the stator and motion in a rotor. In a preferred aspect, the piezoelectric elements are configured so that deformation of the elements in direction of an imposed electric field, generally referred to as the d.sub.33 direction, is utilized to produce wave motion in the stator. In a further aspect, the elements are compressed into the slots so as to minimize tensile stresses on the elements in use.
Gurnett, Donald A.
1995-01-01
An overview is given of spacecraft observations of plasma waves in the solar system. In situ measurements of plasma phenomena have now been obtained at all of the planets except Mercury and Pluto, and in the interplanetary medium at heliocentric radial distances ranging from 0.29 to 58 AU. To illustrate the range of phenomena involved, we discuss plasma waves in three regions of physical interest: (1) planetary radiation belts, (2) planetary auroral acceleration regions and (3) the solar wind. In each region we describe examples of plasma waves that are of some importance, either due to the role they play in determining the physical properties of the plasma, or to the unique mechanism involved in their generation.
Electrostatic ion acoustic waves
International Nuclear Information System (INIS)
Hasegawa, A.
1983-01-01
In this paper, certain aspects of plasma physics are illustrated through a study of electrostatic ion acoustic waves. The paper consists of three Sections. Section II deals with linear properties of the ion acoustic wave including derivation of the dispersions relation with the effect of Landau damping and of an ambient magnetic field. The section also introduces the excitation processes of the ion acoustic wave due to an electron drift or to a stimulated Brillouin scattering. The nonlinear properties are introduced in Section III and IV. In Section III, incoherent nonlinear effects such as quasilinear and mode-coupling saturations of the instability are discussed. The coherent nonlinear effects such as the generation of ion acoustic solitons, shocks and weak double layers are presented in Section IV. (Auth.)
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Farkas, I.; Helbing, D.; Vicsek, T.
2003-12-01
Mexican wave first widely broadcasted during the 1986 World Cup held in Mexico, is a human wave moving along the stands of stadiums as one section of spectators stands up, arms lifting, then sits down as the next section does the same. Here we use variants of models originally developed for the description of excitable media to demonstrate that this collective human behaviour can be quantitatively interpreted by methods of statistical physics. Adequate modelling of reactions to triggering attempts provides a deeper insight into the mechanisms by which a crowd can be stimulated to execute a particular pattern of behaviour and represents a possible tool of control during events involving excited groups of people. Interactive simulations, video recordings and further images are available at the webpage dedicated to this work: http://angel.elte.hu/wave.
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
DEFF Research Database (Denmark)
Jensen, Jonas
This PhD project investigates and further develops methods for ultrasound plane wave imaging and blood flow estimation with the objective of overcoming some of the major limitations in conventional ultrasound systems, which are related to low frame rates and only estimation of velocities along...... the ultrasound beam. The first part of the contribution investigates the compromise between frame rate and plane wave image quality including the influence of grating lobes from a λ-pitch transducer. A method for optimizing the image quality is suggested, and it is shown that the frame rate can be increased...... healthy volunteers. Complex flow patterns were measured in an anthropomorphic flow phantom and showed good agreement with the velocity field simulated using computational fluid dynamics. The last part of the contribution investigates two clinical applications. Plane wave imaging was used for slow velocity...
Wave friction factor rediscovered
Le Roux, J. P.
2012-02-01
The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion ( A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by {{U_{{wb}}/T_{{w}}}}{{2π }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549-560, (2010).
Shaarawi, Amr Mohamed
In this work, nondispersive wavepacket solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs' Airy packet, MacKinnon's wave packet and Brittingham's Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in a infinite acoustic waveguide and to the launchability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young's two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet.
Directory of Open Access Journals (Sweden)
A. V. Vikulin
2014-01-01
Full Text Available Gravity phenomena related to the Earth movements in the Solar System and through the Galaxy are reviewed. Such movements are manifested by geological processes on the Earth and correlate with geophysical fields of the Earth. It is concluded that geodynamic processes and the gravity phenomena (including those of cosmic nature are related. The state of the geomedium composed of blocks is determined by stresses with force moment and by slow rotational waves that are considered as a new type of movements [Vikulin, 2008, 2010]. It is shown that the geomedium has typical rheid properties [Carey, 1954], specifically an ability to flow while being in the solid state [Leonov, 2008]. Within the framework of the rotational model with a symmetric stress tensor, which is developed by the authors [Vikulin, Ivanchin, 1998; Vikulin et al., 2012a, 2013], such movement of the geomedium may explain the energy-saturated state of the geomedium and a possibility of its movements in the form of vortex geological structures [Lee, 1928]. The article discusses the gravity wave detection method based on the concept of interactions between gravity waves and crustal blocks [Braginsky et al., 1985]. It is concluded that gravity waves can be recorded by the proposed technique that detects slow rotational waves. It is shown that geo-gravitational movements can be described by both the concept of potential with account of gravitational energy of bodies [Kondratyev, 2003] and the nonlinear physical acoustics [Gurbatov et al., 2008]. Based on the combined description of geophysical and gravitational wave movements, the authors suggest a hypothesis about the nature of spin, i.e. own moment as a demonstration of the space-time ‘vortex’ properties.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
International Nuclear Information System (INIS)
Stix, H.
1981-01-01
The physics of Alfven-wave heating is particularly sensitive to the character of the linear mode conversion which occurs at the Alfven resonance layer. Parameter changes can profoundly affect both the location within the plasma and the mechanism for the power absorption. Under optimal conditions the heating power may be absorbed by electron Landau damping and by electron transit-time magnetic pumping in the plasma interior, or by the same processes acting near the resonance layer on the mode-converted kinetic Alfven wave. The method is outlined for computing the coefficients for reflection, transmission and absorption at the resonance layer and some representative results are offered
Metamaterials and wave control
Lheurette, Eric
2013-01-01
Since the concept was first proposed at the end of the 20th Century, metamaterials have been the subject of much research and discussion throughout the wave community. More than 10 years later, the number of related published articles is increasing significantly. Onthe one hand, this success can be attributed to dreams of new physical objects which are the consequences of the singular properties of metamaterials. Among them, we can consider the examples of perfect lensing and invisibility cloaking. On other hand,metamaterials also provide new tools for the design of well-known wave functions s
DEFF Research Database (Denmark)
Jensen, J.; Houmann, Jens Christian Gylden; Bjerrum Møller, Hans
1975-01-01
with the symmetry, we deduce the dispersion relation for the spin waves in a basal-plane ferromagnet. This phenomenological spin-wave theory accounts for the observed behavior of the magnon energies in Tb. The two q⃗-dependent Bogoliubov components of the magnon energies are derived from the experimental results......, which are corrected for the effect of the direct coupling between the magnons and the phonons, and for the field dependence of the relative magnetization at finite temperatures. A large q⃗-dependent difference between the two energy components is observed, showing that the anisotropy of the two...
International Nuclear Information System (INIS)
Mori, W.; Joshi, C.; Dawson, J.M.
1982-01-01
It was shown that the insertion of a cross magnetic field prevents the particles from getting out of phase with the electric field of the plasma wave in the beat wave accelerator scheme. Thus, using a CO 2 laser, n/sub c//n/sub e/ = (ω 0 /ω/sub p/) 2 approx. 35, and a 300 kG magnetic field, electrons can be (in principle) accelerated to 100 GeV in 2 meters. For comparison without the magnetic field, the same energies may be obtained in a n/sub c//n/sub e/ approx. 10 5 plasma over a distance of 100 meters
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Lominadze, D G
2013-01-01
Cyclotron Waves in Plasma is a four-chapter text that covers the basic physical concepts of the theory of cyclotron waves and cyclotron instabilities, brought about by the existence of steady or alternating plasma currents flowing perpendicular to the magnetic field.This book considers first a wide range of questions associated with the linear theory of cyclotron oscillations in equilibrium plasmas and in electron plasmas in metals and semiconductors. The next chapter deals with the parametric excitation of electron cyclotron oscillations in plasma in an alternating electric field. A chapter f
Mechanics, Waves and Thermodynamics
Ranjan Jain, Sudhir
2016-05-01
Figures; Preface; Acknowledgement; 1. Energy, mass, momentum; 2. Kinematics, Newton's laws of motion; 3. Circular motion; 4. The principle of least action; 5. Work and energy; 6. Mechanics of a system of particles; 7. Friction; 8. Impulse and collisions; 9. Central forces; 10. Dimensional analysis; 11. Oscillations; 12. Waves; 13. Sound of music; 14. Fluid mechanics; 15. Water waves; 16. The kinetic theory of gases; 17. Concepts and laws of thermodynamics; 18. Some applications of thermodynamics; 19. Basic ideas of statistical mechanics; Bibliography; Index.
Wave Tank Studies of Phase Velocities of Short Wind Waves
Ermakov, S.; Sergievskaya, I.; Shchegolkov, Yu.
Wave tank studies of phase velocities of short wind waves have been carried out using Ka-band radar and an Optical Spectrum Analyser. The phase velocities were retrieved from measured radar and optical Doppler shifts, taking into account measurements of surface drift velocities. The dispersion relationship was studied in centimetre (cm)- and millimetre(mm)-scale wavelength ranges at different fetches and wind speeds, both for a clean water surface and for water covered with surfactant films. It is ob- tained that the phase velocities do not follow the dispersion relation of linear capillary- gravity waves, increasing with fetch and, therefore, depending on phase velocities of dominant decimetre (dm)-centimetre-scale wind waves. One thus can conclude that nonlinear cm-mm-scale harmonics bound to the dominant wind waves and propagat- ing with the phase velocities of the decimetric waves are present in the wind wave spectrum. The resulting phase velocities of short wind waves are determined by re- lation between free and bound waves. The relative intensity of the bound waves in the spectrum of short wind waves is estimated. It is shown that this relation depends strongly on the surfactant concentration, because the damping effect due to films is different for free and bound waves; this results to changes of phase velocities of wind waves in the presence of surfactant films. This work was supported by MOD, UK via DERA Winfrith (Project ISTC 1774P) and by RFBR (Project 02-05-65102).
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Interaction between electromagnetic waves and plasma waves in motional plasma
International Nuclear Information System (INIS)
Chen, S. Y.; Gao, M.; Tang, C. J.; Peng, X. D.
2009-01-01
The electromagnetic wave (EM wave) behavior and the electromagnetic instability caused by the interaction between an EM wave and a plasma wave in motional plasma are studied. The dispersion relation of EM waves and the dielectric tensor of motional plasma are derived by magnetohydrodynamics, and the wave phenomenon in motional plasma is displayed. As a result, the electromagnetic instability, which is excited by the interaction between the EM waves and the plasma waves, is revealed. The mechanism of the instability is the coupling between high frequency electromagnetic field and the transverse electron oscillation derived from the deflection of longitudinal electron oscillation due to self-magnetic field. The present research is useful with regard to the new type of plasma radiation source, ion-focusing accelerator, and plasma diagnostic technique.
Skeletonized wave equation of surface wave dispersion inversion
Li, Jing; Schuster, Gerard T.
2016-01-01
We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel
Assimilation of Wave Imaging Radar Observations for Real-Time Wave-by-Wave Forecasting
Haller, M. C.; Simpson, A. J.; Walker, D. T.; Lynett, P. J.; Pittman, R.; Honegger, D.
2016-02-01
It has been shown in various studies that a controls system can dramatically improve Wave Energy Converter (WEC) power production by tuning the device's oscillations to the incoming wave field, as well as protect WEC devices by decoupling them in extreme wave conditions. A requirement of the most efficient controls systems is a phase-resolved, "deterministic" surface elevation profile, alerting the device to what it will experience in the near future. The current study aims to demonstrate a deterministic method of wave forecasting through the pairing of an X-Band marine radar with a predictive Mild Slope Equation (MSE) wave model. Using the radar as a remote sensing technique, the wave field up to 1-4 km surrounding a WEC device can be resolved. Individual waves within the radar scan are imaged through the contrast between high intensity wave faces and low intensity wave troughs. Using a recently developed method, radar images are inverted into the radial component of surface slope, shown in the figure provided using radar data from Newport, Oregon. Then, resolved radial slope images are assimilated into the MSE wave model. This leads to a best-fit model hindcast of the waves within the domain. The hindcast is utilized as an initial condition for wave-by-wave forecasting with a target forecast horizon of 3-5 minutes (tens of wave periods). The methodology is currently being tested with synthetic data and comparisons with field data are imminent.
International Nuclear Information System (INIS)
Verde, Stefano
2008-01-01
The M A wave has involved EU energy companies since late Nineties and is supported by economic, strategic and political rationales. These reasons differ according to the merger product and geographic dimension. Currently, British Energy and Iberdrola are targeted by the main EU energy companies and potential concentrations will be analyzed by national and/or EU competition authorities [it
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2012-04-03
Shock initiation in a plastic-bonded explosives (PBX) is due to hot spots. Current reactive burn models are based, at least heuristically, on the ignition and growth concept. The ignition phase occurs when a small localized region of high temperature (or hot spot) burns on a fast time scale. This is followed by a growth phase in which a reactive front spreads out from the hot spot. Propagating reactive fronts are deflagration waves. A key question is the deflagration speed in a PBX compressed and heated by a shock wave that generated the hot spot. Here, the ODEs for a steady deflagration wave profile in a compressible fluid are derived, along with the needed thermodynamic quantities of realistic equations of state corresponding to the reactants and products of a PBX. The properties of the wave profile equations are analyzed and an algorithm is derived for computing the deflagration speed. As an illustrative example, the algorithm is applied to compute the deflagration speed in shock compressed PBX 9501 as a function of shock pressure. The calculated deflagration speed, even at the CJ pressure, is low compared to the detonation speed. The implication of this are briefly discussed.
DEFF Research Database (Denmark)
Dühring, Maria Bayard
The work of this project is concerned with the simulation of surface acoustic waves (SAW) and topology optimization of SAW devices. SAWs are elastic vibrations that propagate along a material surface and are extensively used in electromechanical filters and resonators in telecommunication. A new...
Westerhof, E.
1994-01-01
The essential elements of the theory of electron cyclotron waves are reviewed, The two main electro-magnetic modes of propagation are identified and their dispersion and absorption properties are discussed. The importance of the use of the relativistic resonance condition is stressed.
Glitches and gravitational waves
Indian Academy of Sciences (India)
A M Srivastava
2017-10-09
Oct 9, 2017 ... We also discuss gravitational wave production due to rapidly changing ... efficient source of energy loss during the cooling of the neutron star. ..... [3] U S Gupta, R K Mohapatra, A M Srivastava and V K. Tiwari, Phys. Rev. D 82 ...
"Hearing" Electromagnetic Waves
Rojo, Marta; Munoz, Juan
2014-01-01
In this work, an educational experience is described in which a microwave communication link is used to make students aware that all electromagnetic waves have the same physical nature and properties. Experimental demonstrations are linked to theoretical concepts to increase comprehension of the physical principles underlying electromagnetic…
Indian Academy of Sciences (India)
Keywords. General relativity; gravitational waves; astrophysics; interferometry. Author Affiliations. P Ajith1 K G Arun2. LIGO Laboratory and Theoretical Astrophysics California Institute of Technology MS 18-34, Pasadena CA 91125, USA. Chennai Mathematical Institute Plot H1, SIPCOT IT Park Siruseri, Padur Post Chennai ...
DEFF Research Database (Denmark)
Frigaard, Peter; Kofoed, Jens Peter; Tedd, James William
2006-01-01
's first offshore wave energy converter. During this period an extensive measuring program has established the background for optimal design of the structure and regulation of the power take off system. Planning for full scale deployment of a 7 MW unit within the next 2 years is in progress. The prototype...
Semiclassical multicomponent wave function
Mostovoy, M.V.
A consistent method for obtaining the semiclassical multicomponent wave function for any value of adiabatic parameter is discussed and illustrated by examining the motion of a neutral particle in a nonuniform magnetic field. The method generalizes the Bohr-Sommerfeld quantization rule to
DEFF Research Database (Denmark)
Bredmose, Henrik; Peregrine, D.H.; Bullock, G.N.
2009-01-01
When an ocean wave breaks against a steep-fronted breakwater, sea wall or a similar marine structure, its impact on the structure can be very violent. This paper describes the theoretical studies that, together with field and laboratory investigations, have been carried out in order to gain a bet...
Bursts of electron waves modulated by oblique ion waves
International Nuclear Information System (INIS)
Boswell, R.W.
1984-01-01
Experimental evidence is presented which shows small packets of electron plasma waves modulated by large amplitude obliquely propagating non-linear ion plasma waves. Very often the whole system is modulated by an oscillation near the ion gyro frequency or its harmonics. The ion waves seem to be similar to those measured in the current carrying auroral plasma. These results suggest that the generation of ion and electron waves in the auroral plasma may be correlated
Abnormal Waves Modelled as Second-order Conditional Waves
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2005-01-01
The paper presents results for the expected second order short-crested wave conditional of a given wave crest at a specific point in time and space. The analysis is based on the second order Sharma and Dean shallow water wave theory. Numerical results showing the importance of the spectral densit...
Seasonal changing sand waves and the effect of surface waves
Sterlini, Fenneke; van Dijk, Thaiënne A.G.P.; IJzer, Steven; Hulscher, Suzanne; Schüttrumpf, Holger; Tomasicchio, Guiseppe Roberto
2012-01-01
Sand waves are wavelike subaqueous sediment structures that exist in large areas in shelf seas. Due to their characteristics sand waves can severely affect human offshore activities, such as navigation. This makes it important to understand the physical processes that shape and change sand waves. In
Skeletonized wave-equation Qs tomography using surface waves
Li, Jing; Dutta, Gaurav; Schuster, Gerard T.
2017-01-01
We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data
Real time wave measurements and wave hindcasting in deep waters
Digital Repository Service at National Institute of Oceanography (India)
Anand, N.M.; Mandal, S.; SanilKumar, V.; Nayak, B.U.
Deep water waves off Karwar (lat. 14~'45.1'N, long. 73~'34.8'E) at 75 m water depth pertaining to peak monsoon period have been measured using a Datawell waverider buoy. Measured wave data show that the significant wave height (Hs) predominantly...
On radio frequency wave induced radial transport and wave helicity
International Nuclear Information System (INIS)
Petrzilka, V.
1992-09-01
Expressions for wave induced radial transport are derived allowing simple estimates. The transport is enhanced due to the presence of poloidal magnetostatic field and in the vicinity of the ion cyclotron resonance. The direction of the wave induced transport depends also on the wave polarization. (author) 19 refs
International Nuclear Information System (INIS)
Robinett, R.W.
2004-01-01
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet ('minipackets' or 'clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities. We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems
Plasma Wave Electronic Terahertz Technology
National Research Council Canada - National Science Library
Shur, Michael
2003-01-01
Plasma waves are oscillations of electron density in time and space. In deep submicron field effect transistors plasma wave frequencies lie in the terahertz range and can be tuned by applied gate bias...
Estimation of directional wave spreading
Digital Repository Service at National Institute of Oceanography (India)
Mandal, S.; Bhat, S.S.; Anand, N.M.; Nayak, B.U.
Directional properties of ocean waves are of great economic interest. The knowledge of wave directionality is important for the design of maritime structures and offshore operations. Two main aspects are considered for this study for the data...
Gravitational Waves: The Evidence Mounts
Wick, Gerald L.
1970-01-01
Reviews the work of Weber and his colleagues in their attempts at detecting extraterrestial gravitational waves. Coincidence events recorded by special detectors provide the evidence for the existence of gravitational waves. Bibliography. (LC)
Fascinating World of Shock Waves
Indian Academy of Sciences (India)
Srimath
travelling at supersonic speeds (more than the sound speed at ... actual earth- quake, travel at supersonic speeds. .... The time scale of the shock wave is also important ..... real lithotripsy where a shock wave is used shatter the kidney stones!
Wave propagation in electromagnetic media
Davis, Julian L
1990-01-01
This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessi...
Greenstadt, E. W.; Le, G.; Strangeway, R. J.
1995-01-01
We review our current knowledge of ULF waves in planetary foreshocks. Most of this knowledge comes from observations taken within a few Earth radii of the terrestrial bow shock. Terrestrial foreshock ULF waves can be divided into three types, large amplitude low frequency waves (approximately 30-s period), upstream propagating whistlers (1-Hz waves), and 3-s waves. The 30-s waves are apparently generated by back-streaming ion beams, while the 1-Hz waves are generated at the bow shock. The source of the 3-s waves has yet to be determined. In addition to issues concerning the source of ULF waves in the foreshock, the waves present a number of challenges, both in terms of data acquisition, and comparison with theory. The various waves have different coherence scales, from approximately 100 km to approximately 1 Earth radius. Thus multi-spacecraft separation strategies must be tailored to the phenomenon of interest. From a theoretical point of view, the ULF waves are observed in a plasma in which the thermal pressure is comparable to the magnetic pressure, and the rest-frame wave frequency can be moderate fraction of the proton gyro-frequency. This requires the use of kinetic plasma wave dispersion relations, rather than multi-fluid MHD. Lastly, and perhaps most significantly, ULF waves are used to probe the ambient plasma, with inferences being drawn concerning the types of energetic ion distributions within the foreshock. However, since most of the data were acquired close to the bow shock, the properties of the more distant foreshock have to be deduced mainly through extrapolation of the near-shock results. A general understanding of the wave and plasma populations within the foreshock, their interrelation, and evolution, requires additional data from the more distant foreshock.
Scattering of internal gravity waves
Leaman Nye, Abigail
2011-01-01
Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves drive vertical transport of heat and mass through the ocean by wave breaking and the mixing subsequently produced. Identifying regions where internal gravity waves contribute to ocean mixing and quantifying this mixing are therefore important for accurate climate ...
Phenomena Associated With EIT Waves
Thompson, B. J.; Biesecker, D. A.; Gopalswamy, N.
2003-01-01
We discuss phenomena associated with "EIT Wave" transients. These phenomena include coronal mass ejections, flares, EUV/SXR dimmings, chromospheric waves, Moreton waves, solar energetic particle events, energetic electron events, and radio signatures. Although the occurrence of many phenomena correlate with the appearance of EIT waves, it is difficult to mfer which associations are causal. The presentation will include a discussion of correlation surveys of these phenomena.
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
Ng, Chiu-king
2010-01-01
When one end of a taut horizontal elastic string is shaken repeatedly up and down, a transverse wave (assume sine waveform) will be produced and travel along it. College students know this type of wave motion well. They know when the wave passes by, each element of the string will perform an oscillating up-down motion, which in mechanics is termed…
Wave Dragon Buoyancy Regulation Study
DEFF Research Database (Denmark)
Jakobsen, Jens; Kofoed, Jens Peter
Wave Dragon is a wave energy converter, which was deployed offshore at Nissum Bredning in Denmark in 2003. The experience gained from operating Wave Dragon during 2003 and 2004 has shown that the buoyancy regulation system can be improved in a number of ways. This study describes the current...
Conceptual Design of Wave Plane
DEFF Research Database (Denmark)
Frigaard, Peter; Trewers, Andrew; Kofoed, Jens Peter
The Wave Plane is a patented Wave Energy device of the overtopping type, designed to capture potential as well as kinetic energy. This is as such different to other overtopping devices, who usually only focus on potential energy. If Wave Plane A/S can deliver the turbine technology to utilize both...
Coherent Wave Measurement Buoy Arrays to Support Wave Energy Extraction
Spada, F.; Chang, G.; Jones, C.; Janssen, T. T.; Barney, P.; Roberts, J.
2016-02-01
Wave energy is the most abundant form of hydrokinetic energy in the United States and wave energy converters (WECs) are being developed to extract the maximum possible power from the prevailing wave climate. However, maximum wave energy capture is currently limited by the narrow banded frequency response of WECs as well as extended protective shutdown requirements during periods of large waves. These limitations must be overcome in order to maximize energy extraction, thus significantly decreasing the cost of wave energy and making it a viable energy source. Techno-economic studies of several WEC devices have shown significant potential to improve wave energy capture efficiency through operational control strategies that incorporate real-time information about local surface wave motions. Integral Consulting Inc., with ARPA-E support, is partnering with Sandia National Laboratories and Spoondrift LLC to develop a coherent array of wave-measuring devices to relay and enable the prediction of wave-resolved surface dynamics at a WEC location ahead of real time. This capability will provide necessary information to optimize power production of WECs through control strategies, thereby allowing for a single WEC design to perform more effectively across a wide range of wave environments. The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000514.
Experiments on the WavePiston, Wave Energy Converter
DEFF Research Database (Denmark)
Angelelli, E.; Zanuttigh, B.; Kofoed, Jens Peter
2011-01-01
This paper analyses the performance of a new Wave Energy Converter (WEC) of the Oscillating Water Column type (OWC), named WavePiston. This near-shore floating device is composed of plates (i.e. energy collectors) sliding around a cylinder, that is placed perpendicular to the shore. Tests...... in the wave basin at Aalborg University allowed to investigate power production in the North Sea typical wave climate, with varying design parameters such as plate dimensions and their mutual distance. The power produced per meter by each collector is about the 5% of the available wave power. Experimental...... results and survivability considerations suggest that the WavePiston would be particularly suited for installations in milder seas. An example application is therefore presented in the Mediterranean Sea, off-shore the island of Sicily. In this case, each collector harvests the 10% of the available wave...
Millimeter wave scattering off a whistler wave in a tokamak
International Nuclear Information System (INIS)
Sawhney, B.K.; Singh, S.V.; Tripathi, V.K.
1994-01-01
Obliquely propagating whistler waves through a plasma cause density perturbations. A high frequency electromagnetic wave sent into such a perturbed region suffers scattering. The process can be used as a diagnostics for whistler. We have developed a theory of electromagnetic wave scattering in a tokamak where density profile is taken a parabolic. Numerical calculations have been carried out to evaluate the ratio of the power of the scattered electromagnetic wave to that of the incident electromagnetic wave. The scattered power decreases with the frequency of the incident electromagnetic wave. For typical parameters, the ratio of the power of the scattered to the incident electromagnetic wave comes out to be of the order of 10 -4 at a scattering angle of 3 which can be detected. (author). 2 refs, 1 fig
Nonlinear wave equation with intrinsic wave particle dualism
International Nuclear Information System (INIS)
Klein, J.J.
1976-01-01
A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)