Hydrodynamic Pressure on a Dam During Earthquakes

A straightforward analysis involving Fourier cosine transforms and the theory of Fourier seies is presented for the approximate calculation of the hydrodynamic pressure exerted on the vertical upstream face of a dam due to constant earthquake ground acceleration. The analysis uses the “Parseval relation” on the Fourier coefficients of square integrable functions, and directly brings out the mathematical nature of the approximate theory involved.

Rapid distortion of axisymmetric turbulence

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Prediction of breakout noise from an elliptical duct of finite length

This paper describes a predictive model for breakout noise from an elliptical duct or shell of finite length. The transmission mechanism is essentially that of ``mode coupling'', whereby higher structural modes in the duct walls get excited because of non-circularity of the wall. Effect of geometry has been taken care of by evaluating Fourier coefficients of the radius of curvature. The noise radiated from the duct walls is represented by that from a finite vibrating length of a semi infinite cylinder in a free field. Emphasis is on understanding the physics of the problem as well as analytical modeling. The analytical model is validated with 3-D FEM. Effects of the ovality, curvature, and axial terminations of the duct have been demonstrated. (C) 2010 Institute of Noise Control Engineering.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

On quasimodular eigenforms

We derive a multiplicity one result for quasimodular eigenforms on SL2(Z) by completing the description of all quasimodular eigenforms. As applications of our results, we complete the answer to the question of finding all quasimodular eigenforms arising as a product of two eigenforms and also give an estimate for the size of the maximum gap in the sequence of the Fourier coefficients of a quasimodular form.

Wave Sensor Technologies, St Petersburg, Florida, March 7-9, 2007: workshop proceedings

The Alliance for Coastal Technologies (ACT) convened a workshop on "Wave Sensor Technologies" in St. Petersburg, Florida on March 7-9, 2007, hosted by the University of South Florida (USF) College of Marine Science, an ACT partner institution. The primary objectives of this workshop were to: 1) define the present state of wave measurement technologies, 2) identify the major impediments to their advancement, and 3) make strategic recommendations for future development and on the necessary steps to integrate wave measurement sensors into operational coastal ocean observing systems. The participants were from various sectors, including research scientists, technology developers and industry providers, and technology users, such as operational coastal managers and coastal decision makers. Waves consistently are ranked as a critical variable for numerous coastal issues, from maritime transportation to beach erosion to habitat restoration. For the purposes of this workshop, the participants focused on measuring "wind waves" (i.e., waves on the water surface, generated by the wind, restored by gravity and existing between approximately 3 and 30-second periods), although it was recognized that a wide range of both forced and free waves exist on and in the oceans. Also, whereas the workshop put emphasis on the nearshore coastal component of wave measurements, the participants also stressed the importance of open ocean surface waves measurement. Wave sensor technologies that are presently available for both environments include bottom-mounted pressure gauges, surface following buoys, wave staffs, acoustic Doppler current profilers, and shore-based remote sensing radar instruments. One of the recurring themes of workshop discussions was the dichotomous nature of wave data users. The two separate groups, open ocean wave data users and the nearshore/coastal wave data users, have different requirements. Generally, the user requirements increase both in spatial/temporal resolution and precision as one moves closer to shore. Most ocean going mariners are adequately satisfied with measurements of wave period and height and a wave general direction. However, most coastal and nearshore users require at least the first five Fourier parameters ("First 5"): wave energy and the first four directional Fourier coefficients. Furthermore, wave research scientists would like sensors capable of providing measurements beyond the first four Fourier coefficients. It was debated whether or not high precision wave observations in one location can take the place of a less precise measurement at a different location. This could be accomplished by advancing wave models and using wave models to extend data to nearby areas. However, the consensus was that models are no substitution for in situ wave data.[PDF contains 26 pages]

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

Eigenmodes of lined flow ducts with rigid splices

This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure eigenmodes is given in terms of an azimuthal Fourier sum, with the Fourier coefficients given by a recurrence relation. Since this expression is derived using a Greens function method, the completeness of the expansion is guaranteed. A numerical procedure is described for solving this recurrence relation, which is found to converge exponentially with respect to number of Fourier terms used and is in practice quick to compute; this is then used to give several numerical examples for both uniform and sheared mean flow. An asymptotic expression is derived to directly calculate the pressure eigenmodes for thin splices. This asymptotic expression is shown to be quantitatively accurate for ducts with very thin splices of less than 1 % unlined area and qualitatively helpful for thicker splices of the order of 6 % unlined area. A thin splice is in some cases shown to increase the damping of certain acoustic modes. The influences of thin splices and thin boundary layers are compared and found to be of comparable magnitude for the parameters considered. Trapped modes at the splices are also identified and investigated. © 2011 Cambridge University Press.

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL_3 über Funktionenkörpern

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL(3) über Funktionenkörpern lassen sich als ein Analogon zu den auf der oberen Halbebene definierten klassischen Spitzenformen verstehen. An die Stelle des starken Abklingens der Spitzenformen tritt hier die Endlichkeit des Trägers modulo einer gewissen Untergruppe. Der erste Teil der vorliegenden Arbeit befaßt sich mit der Untersuchung und Charakterisierung dieses Trägers. Im weiteren Verlauf werden gewisse Konzepte der klassischen Theorie auf harmonische Funktionen übertragen. So wird gezeigt, daß diese sich ebenfalls als Fourierreihe darstellen lassen und es werden explizite Formeln für die Fourierkoeffizienten hergeleitet. Es stellt sich heraus, daß sich die Harmonizität in gewissen Relationen zwischen den Fourierkoeffizienten widerspiegelt und sich umgekehrt aus einem Satz passender Koeffizienten eine harmonische Funktion erzeugen läßt. Dies wird zur expliziten Konstruktion zweier quasi-harmonischer Funktionen genutzt, die ein Pendant zu klassischen Poincaré-Reihen darstellen. Abschließend werden Hecke-Operatoren definiert und Formeln für die Fourierkoeffizienten der Hecke-Transformierten einer harmonischen Funktion hergeleitet.

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at √sNN = 2.76 TeV are shown using a dataset of approximately 7μb−1 collected at the LHC in 2010. The measurements are performed for charged particles with transversemomenta 0.5 < pT < 20 GeV and in the pseudorapidity range |η| < 2.5. The anisotropy is characterized by the Fourier coefficients, vn, of the charged-particle azimuthal angle distribution for n = 2–4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the vn coefficients are presented. The elliptic flow, v2, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, v3 and v4, are determined with two- and four-particle cumulants. Flow harmonics vn measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to vn measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Morphometrics data on Holocene Melanopsidae of Lake Petea

The dataset includes measurements of Microcolpia parreyssii parreyssii (Philippi, 1847) and Microcolpia parreyssii sikorai (Brusina, 1903) from Holocene deposits of Lake Petea near Oradea, Romania. Additionally, the tps-files generated with the program TpsDig2 and containing pairwise x,y-coordinates describing the outlines of the digitized images are supplied. Finally, the matrix of Fourier coefficients resulting from the Fast Fourier Transform is provided.

Observations on the propagation of internal tidal waves on the continental slope off Sierra Leone

During R/V Meteor-cruise no. 30 4 moorings with 17 current meters were placed on the continental slope of Sierra Leone at depths between 81 and 1058 meters. The observation period started on March 8, 1973, 16.55 hours GMT and lasted 19 days for moorings M30_068MOOR, M30_069MOOR, M30_070MOOR on the slope and 9 days for M30_067MOOR on the shelf. One current meter recorded at location M30_067MOOR for 22 days. Hydrographic data were collected at 32 stations by means of the "Kieler Multi-Meeressonde". Harmonic analysis is applied to the first 15 days of the time series to determine the M2 and S2 tides. By vertically averaging of the Fourier coefficients the field of motion is separated into its barotropic and its baroclinic component. The expected error generated by white Gaussian noise is estimated. To estimate the influence of the particular vertical distribution of the current meters, the barotropic M2 tide is calculated by ommitting and interchanging time series of different moorings. It is shown that only the data of moorings M30_069MOOR, M30_070MOOR and M30_067MOOR can be used. The results for the barotropic M2 tide agree well with the previous publications of other authors. On the slope at a depth of 1000 m there is a free barotropic wave under the influence of the Coriolis-force propagating along the slope with an amplitude of 3.4 cm S**-1. On the shelf, the maximum current is substantially greater (5.8 cm s**-1) and the direction of propagation is perpendicular to the slope. As for the continental slope a separation into different baroclinic modes using vertical eigenmodes is not reasonable, an interpretation of the total baroclinic wave field is tried by means of the method of characteristis. Assuming the continental slope to generate several linear waves, which superpose, baroclinic tidal ellipses are calculated. The scattering of the direction of the major axes M30_069MOOR is in contrast to M30_070MOOR, where they are bundled within an angle of 60°. This is presumably caused by the different character of the bottom topography in the vicinity of the two moorings. A detailed discussion of M30_069MOOR is renounced since the accuracy of the bathymetric chart is not sufficient to prove any relation between waves and topography. The bundeling of the major axes at M30_070MOOR can be explained by the longslope changes of the slope, which cause an energy transfer from the longslope barotropic component to the downslope baroclinic component. The maximum amplitude is found at a depth of 245 m where it is expected from the characteristics originating at the shelf edge. Because of the dominating barotropic tide high coherence is found between most of the current meters. To show the influence of the baroclinic tidal waves, the effect of the mean current is considered. There are two periods nearly opposite longshore mean current. For 128 hours during each of these periods, starting on March 11, 05.00, and March 21, 08.30, the coherences and energy spectra are calculated. The changes in the slope of the characteristics are found in agreement with the changes of energy and coherence. Because of the short periods of nearly constant mean current, some of the calculated differences of energy and coherence are not statistically significant. For the M2 tide a calculation of the ratios of vertically integrated total baroclinic energy and vertically integrated barotropic kinetic energy is carried out. Taking into account both components (along and perpendicular to the slope) the obtained values are 0.75 and 0.98 at the slope and 0.38 at the shelf. If each component is considered separately, the ratios are 0.39 and 1.16 parallel to the slope and 5.1 and 15.85 for the component perpendicular to it. Taking the energy transfer from the longslope component to the doenslope component into account, a simple model yields an energy-ratio of 2.6. Considering the limited application of the theory to the real conditions, the obtained are in agreement with the values calculated by Sandstroem.