Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

Want to get experience? Want to get any ideas to create new things in your life? Read methods of numerical integration now! By reading this book as soon as possible, you can renew the situation to get the inspirations. Yeah, this way will lead you to always think more and more. In this case, this book will be always right for you. When you can observe more about the book, you will know why you need this.

Methods of Numerical Integration

Wind speeds over the world’s oceans have increased over the past two decades, as have wave heights. Studies of climate change typically consider measurements or predictions of temperature over extended periods of time. Climate, however, is much more than temperature. Over the oceans, changes in wind speed and the surface gravity waves generated by such winds play an important role. We used a 23-year database of calibrated and validated satellite altimeter measurements to investigate global changes in oceanic wind speed and wave height over this period. We find a general global trend of increasing values of wind speed and, to a lesser degree, wave height, over this period. The rate of increase is greater for extreme events as compared to the mean condition.

https://researchbank.swinburne.edu.au/file/bca43746-6f16-4ad2-a4b7-27f8d8d60fed/1/PDF (Published version).pdf

Global trends in wind speed and wave height over the past 25 years

This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.

/pdf/the-interaction-of-ocean-waves-and-wind-28iwun4lpm.pdf

The Interaction of Ocean Waves and Wind

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to one-dimensional Fredholm integral equations of the second kind. If the plate is heaving, the problem becomes axisymmetric, and the resulting integral equation has a very simple structure; it is a generalization of Love's integral equation for the electrostatic field of a parallel-plate capacitor. Numerical solutions of the new integral equation are presented. It is found that the added-mass coefficient becomes negative for a range of frequencies when the disc is sufficiently close to the free surface.

/pdf/radiation-of-water-waves-by-a-heaving-submerged-horizontal-508jgbtnxl.pdf

Radiation of water waves by a heaving submerged horizontal disc

Numerical simulation of extreme wave runup during storm events in Tramandaí Beach, Rio Grande do Sul, Brazil

Scattering of water waves by a submerged disc using a hypersingular integral equation

. Using the wave model SWAN (simulating waves nearshore), high waves on the southwestern Atlantic generated by extra-tropical cyclones are simulated from 2000 to 2010, and their impact on the Rio Grande do Sul (RS) coast is studied. The modeled waves are compared with buoy data and good agreement is found. The six extreme events in the period that presented significant wave heights above 5 m, on a particular point of interest, are investigated in detail. It is found that the cyclogenetic pattern between the latitudes 31.5 and 34° S is the most favorable for developing high waves. Hovmoller diagrams for deep water show that the region between the south of Rio Grande do Sul up to a latitude of 31.5° S is the most energetic during a cyclone's passage, although the event of May 2008 indicates that the location of this region can vary, depending on the cyclone's displacement. On the other hand, the Hovmoller diagrams for shallow water show that the different shoreface morphologies were responsible for focusing or dissipating the waves' energy; the regions found are in agreement with the observations of erosion and progradation regions. It can be concluded that some of the urban areas of the beaches of Hermenegildo, Cidreira, Pinhal, Tramandai, Imbe and Torres have been more exposed during the extreme wave events on the Rio Grande do Sul coast, and are more vulnerable to this natural hazard.

/pdf/analysis-of-extreme-wave-events-on-the-southern-coast-of-53n67h8vme.pdf

Analysis of extreme wave events on the southern coast of Brazil

The problem of optimization of analytical and numerical approximations of Hasselmann's nonlinear kinetic integral is discussed in general form. Considering the general expression for the kinetic integral, a principle to obtain the optimal approximation is formulated. From this consideration it follows that the most well-accepted approximations, such as Discrete Interaction Approximation (DIA) (Hasselmann et al., 1985), Reduced Integration Approximation (RIA) (Lin and Perry, 1999), and the Diffusion Approximation proposed recently in Zakharov and Pushkarev (1999) (ZPA), have the same roots. The only difference among them is, essentially, the choice of the 4-wave configuration for the interacting waves. To evaluate a quality of any approximation for the 2-D nonlinear energy transfer, a mathematical measure of relative error is constructed and the meaning of approximation efficiency is postulated. By the use of these features it is shown that DIA has better accuracy and efficiency than ZPA. Following to the general idea of optimal approximation and by using the measures introduced, more efficient and faster versions of DIA are proposed.

/pdf/on-the-problem-of-optimal-approximation-of-the-four-wave-2h9oba99mt.pdf

Leandro Farina

Papers

Radiation of water waves by a heaving submerged horizontal disc

Numerical simulation of extreme wave runup during storm events in Tramandaí Beach, Rio Grande do Sul, Brazil

Scattering of water waves by a submerged disc using a hypersingular integral equation

Analysis of extreme wave events on the southern coast of Brazil

On the problem of optimal approximation of the four-wave kinetic integral