Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors

The most promising concept for low frequency (millihertz to hertz) gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal readout. For this to be true, a careful balance of mission parameters is crucial to keep all other parasitic disturbances below shot noise. We developed a web application that uses over 30 input parameters and considers many important technical noise sources and noise suppression techniques to derive a realistic position noise budget. It optimizes free parameters automatically and generates a detailed report on all individual noise contributions. Thus one can easily explore the entire parameter space and design a realistic gravitational wave observatory. In this document we describe the different parameters, present all underlying calculations, and compare the final observatory's sensitivity with astrophysical sources of gravitational waves. We use as an example parameters currently assumed to be likely applied to a space mission proposed to be launched in 2034 by the European Space Agency. The web application itself is publicly available on the Internet at http://spacegravity.org/designer. Future versions of the web application will incorporate the frequency dependence of different noise sources and include a more detailed model of the observatory's residual acceleration noise.

High-temperature superconductivity in the two-dimensional t-J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t-J model with the hopping electron amplitudes t (and t') between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the method's results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed 'grand-canonical Gutzwiller approximation' (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a d(x2-y2) wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the

Predicting Pollicipes pollicipes (Crustacea: Cirripedia) abundance on intertidal rocky shores of SW Portugal: a multi-scale approach based on a simple fetch-based wave exposure index

Understanding and predicting patterns of distribution and abundance of marine resources is important for con- servation and management purposes in small-scale artisanal fisheries and industrial fisheries worldwide. The goose barnacle (Pollicipes pollicipes) is an important shellfish resource and its distribution is closely related to wave exposure at different spatial scales. We modelled the abundance (percent coverage) of P. pollicipes as a function of a simple wave exposure index based on fetch estimates from digitized coastlines at different spatial scales. The model accounted for 47.5% of the explained deviance and indicated that barnacle abundance increases non-linearly with wave exposure at both the smallest (metres) and largest (kilometres) spatial scales considered in this study. Distribution maps were predicted for the study region in SW Portugal. Our study suggests that the relationship between fetch-based exposure indices and P. pollicipes percent cover may be used as a simple tool for providing stakeholders with information on barnacle distribution patterns. This information may improve assessment of harvesting grounds and the dimension of exploitable areas, aiding management plans and support- ing decision making on conservation, harvesting pressure and surveillance strategies for this highly appreciated and socio- economically important marine resource.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Savani: A variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets

International audience

Design and construction of a two dimensional duct equipped with a wave generator and a variable coastal slope and an ocean wave energy conversion system (OWC)

The aims of this thesis were evaluation the type of wave channel, wave current, and effect of some parameters on them and identification and comparison between types of wave maker in laboratory situations. In this study, designing and making of two dimension channels (flume) and wave maker for experiment son the marine buoy, marine building and energy conversion systems were also investigated. In current research, the physical relation between pump and pumpage and the designing of current making in flume were evaluated. The related calculation for steel building, channels beside glasses and also equations of wave maker plate movement, power of motor and absorb wave(co astal slope) were calculated. In continue of this study, the servo motor was designed and applied for moving of wave maker’s plate. One Ball Screw Leaner was used for having better movement mechanisms of equipment and convert of the around movement to linear movement. The Programmable Logic Controller (PLC) was also used for control of wave maker system. The studies were explained type of ocean energies and energy conversion systems. In another part of this research, the systems of energy resistance in special way of Oscillating Water Column (OWC) were explained and one sample model was designed and applied in hydrolic channel at the Sheikh Bahaii building in Azad University, Science and Research Branch. The dimensions of designed flume was considered at 16 1.98 0. 57 m which had ability to provide regular waves as well as irregular waves with little changing on the control system. The ability of making waves was evaluated in our designed channel and the results were showed that all of the calculation in designed flume was correct. The mean of error between our results and theory calculation was conducted 7%, which was showed the well result in this situation. With evaluating of designed OWC model and considering of changes in the some part of system, one bigger sample of this model can be used for designing the energy conversion system model. The obtained results showed that the best form for chamber in exit position of system, were zero degree (0) in angle for moving below part, forty and five (45) degree in front wall of system and the moving forward of front wall keep in two times of height of wave.

Understanding the tsunami with a simple model

In this paper, we use the approximation of shallow water waves (Margaritondo G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth. A short explanation about how the tsunami hit the west coast of India is given based on the refraction phenomenon. Our procedure also includes a simple numerical calculation suitable for undergraduate students in physics and engineering.

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.

Wave climate in the Arctic 1992-2014: seasonality and trends

Over the past decade, the diminishing Arctic sea ice has impacted the wave field, which depends on the ice-free ocean and wind. This study characterizes the wave climate in the Arctic spanning 1992–2014 from a merged altimeter data set and a wave hindcast that uses CFSR winds and ice concentrations from satellites as input. The model performs well, verified by the altimeters, and is relatively consistent for climate studies. The wave seasonality and extremes are linked to the ice coverage, wind strength, and wind direction, creating distinct features in the wind seas and swells. The altimeters and model show that the reduction of sea ice coverage causes increasing wave heights instead of the wind. However, trends are convoluted by interannual climate oscillations like the North Atlantic Oscillation (NAO) and Pacific Decadal Oscillation. In the Nordic Greenland Sea the NAO influences the decreasing wind speeds and wave heights. Swells are becoming more prevalent and wind-sea steepness is declining. The satellite data show the sea ice minimum occurs later in fall when the wind speeds increase. This creates more favorable conditions for wave development. Therefore we expect the ice freeze-up in fall to be the most critical season in the Arctic and small changes in ice cover, wind speeds, and wave heights can have large impacts to the evolution of the sea ice throughout the year. It is inconclusive how important wave–ice processes are within the climate system, but selected events suggest the importance of waves within the marginal ice zone.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

A Model for Continuous Measurement of Drilled Shaft Diameter During Construction

Non-Destructive Testing (NDT) of deep foundations has become an integral part of the industry’s standard manufacturing processes. It is not unusual for the evaluation of the integrity of the concrete to include the measurement of ultrasonic wave speeds. Numerous methods have been proposed that use the propagation speed of ultrasonic waves to check the integrity of concrete for drilled shaft foundations. All such methods evaluate the integrity of the concrete inside the cage and between the access tubes. The integrity of the concrete outside the cage remains to be considered to determine the location of the border between the concrete and the soil in order to obtain the diameter of the drilled shaft. It is also economic to devise a methodology to obtain the diameter of the drilled shaft using the Cross-Hole Sonic Logging system (CSL). Performing such a methodology using the CSL and following the CSL tests is performed and used to check the integrity of the inside concrete, thus allowing the determination of the drilled shaft diameter without having to set up another NDT device. This proposed new method is based on the installation of galvanized tubes outside the shaft across from each inside tube, and performing the CSL test between the inside and outside tubes. From the performed experimental work a model is developed to evaluate the relationship between the thickness of concrete and the ultrasonic wave properties using signal processing. The experimental results show that there is a direct correlation between concrete thicknesses outside the cage and maximum amplitude of the received signal obtained from frequency domain data. This study demonstrates how this new method to measuring the diameter of drilled shafts during construction using a NDT method overcomes the limitations of currently-used methods. In the other part of study, a new method is proposed to visualize and quantify the extent and location of the defects. It is based on a color change in the frequency amplitude of the signal recorded by the receiver probe in the location of defects and it is called Frequency Tomography Analysis (FTA). Time-domain data is transferred to frequency-domain data of the signals propagated between tubes using Fast Fourier Transform (FFT). Then, distribution of the FTA will be evaluated. This method is employed after CSL has determined the high probability of an anomaly in a given area and is applied to improve location accuracy and to further characterize the feature. The technique has a very good resolution and clarifies the exact depth location of any void or defect through the length of the drilled shaft for the voids inside the cage. The last part of study also evaluates the effect of voids inside and outside the reinforcement cage and corrosion in the longitudinal bars on the strength and axial load capacity of drilled shafts. The objective is to quantify the extent of loss in axial strength and stiffness of drilled shafts due to presence of different types of symmetric voids and corrosion throughout their lengths.

Ranganathan’s Layers of Classification Theory and the FASDA Model of Classification

Describes four waves of Ranganathan’s dynamic theory of classification. Outlines components that distinguish each wave, and porposes ways in which this understanding can inform systems design in the contemporary environment, particularly with regard to interoperability and scheme versioning. Ends with an appeal to better understanding the relationship between structure and semantics in faceted classification schemes and similar indexing languages.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.