Second-order electromagnetic eigenfrequencies of a triaxial ellipsoid II

Experimental fishing with bottom-set gill nets of different mesh sizes was carried out in Parakrama Samudra, a man-made reservoir in Sri Lanka, May to September 1983. The optimum retention length of Oreochromis mossambicus, the dominant fish species in the reservoir fishery, was estimated for each mesh size using the Baranov-Holt method. The optimal length of 0. mossambicus is a function of mesh size and is described by the equation: Y = 3.4763 + 2.0237X (r = 0.992; p < 0.01) where Y = optimal total length in cm and X = stretched mesh size in cm. The desirable mesh size corresponding to the acceptable size of 0. mossambicus to the consumer (20-28 cm) is 10.2cm. Natural mortality (M) was estimated to be 1.10 using Loo = 31.3 cm and K = 0.48 year-1 estimated from length-frequency data of the catches. The long-term biological effects of the increase in mesh size in the gill-net·fishery on the harvests and catch rates are discussed using length-structured yield-per-recruit and biomass-per-recruit analyses based on ko and M/K for different levels of exploitation rates and different sizes of first capture corresponding to various mesh sizes.

Implicit geometry neural network for mesh generation

The numerical studies of magnetization dynamics in micromagnetic systems with spatially distributed magnetization crucially rely on the computation of magnetostatic fields generated by the ferromagnet. The solution of the magnetostatic problem can be written as convolution of an appropriate Green’s function with the magnetization vector field. Since the Green’s function is long-range, after discretization of the problem in N cells, the direct numerical computation of the convolution integral has a computational cost scaling as N2.In this work, we use, as it is often done in micromagnetics, the Fast Fourier Transform (FFT) method to reduce the computational cost scaling to N logN. We consider micromagnetic systems with thin-film geometry where the magnetization can be considered constant across the thickness of the magnet. In these situations, only the field averaged across the thickness is relevant to the magnetostatic interactions and both the magnetization and the averaged field inside the magnet depend only on two spatial variables. The usual approach to deal with this type of problem is to use FFT to compute the discretized version of the convolution integral relating the field and the magnetization [1]. The dual approach to the usual one, is based on the discretization of the integral relation between the field (averaged across the thickness) and the magnetization in the reciprocal space (k-space). The connection in the k-space is given by the Fourier transform of Green function of the magnetostatic problem which, in case of infinite thin-films, can be written in a special form taking into account the thin-film geometry [2]. The analysis in the k-space has been extensively used in connection with linear spin wave dynamics in thin films working as magnonic waveguide, where all the relation of practical use (e.g dispersion relations), are easily obtained by algebraic manipulations. When the dimensions of the thin film are finite, the reconstruction of the magnetostatic field with the infinite film Green's function, is altered by the presence of replicas of the thin film in the ordinary space due to the sampling operation in the k-space. This effect is usually smoothed by using zero-padding, which increases the distance between two interacting replicas weakening their coupling.In this work, a fast convolution algorithm in the k-space able to remove the influence of replicas in the reconstruction of the magnetostatic field in thin films of finite size, is proposed and applied to study linear spin wave dynamics. It is based on the use of the Fourier transform of truncated Green function, which has been recently used to compute volume potentials defined on free-space in a finite (truncated) domain [3]. Such method, guarantees a regularization of the Green function by cutting off the interaction in physical space beyond the domain of interest and this in turn produces spectral accuracy [5] for the Fourier transform evaluation by FFT algorithm. The accuracy of the proposed method is studied by comparing the results with analytical calculations and with those obtained by fast convolution with the infinite thin film Green's function as a function of mesh size. For example, in the figure, the computation of the demagnetizing factor along the x direction for a thin film of dimensions Lx = 300nm, Ly = 100nm and Lz = 3nm as a function of the mesh dimension (kxmax = kymax = kmax) and discretization step-size (Δkx = Δky = Δk) in the k-space is considered. With solid lines, the curves in the infinite film approximation (infin.) are indicated, while curves with symbols results from the proposed approach (trunc.). The horizontal dotted line, represents the analytical value of the demagnetizing factor evaluated with Newell’s formula [6]. Computation with Δk< π/300 nm-1, for the duality property of the Fourier transform, are equivalent to use zero padding in the ordinary space. This produces a substantial improving of estimation accuracy with respect to the analytical value, in case of infinite film approximation. As a benchmark of the proposed approach, it results that the curves computed with the truncated Green function, show a weak dependence from Δk for Δk>π/R and collapse into the same one for Δk<π/R, where R is the radius of a disk region which defines the compact support of the truncated Green function. This, as a confirmation of the fact, that when the region that exceeds the support of the truncated Green's function is zero padded, there is no effect on the computation of the magnetostatic field. Moreover, for sufficient value of kmax the asymptotic value tends towards analytical one, since when Δk<π/R the influence of replicas on the magnetostatic field computation is removed. **

The problems associated to the optimization of the systems of a future fusion reactor require new developments due to the limits of existing models, which are unable to describe the experimental behaviour of diagnostics with the required accuracy. This is also true for the study of the coupling antenna-plasma or the computations of the deposits of power for the plasma heating. Simulations on wave propagation on full ITER size is a key issue properly to take into account all the possible effects arising during the wave propagation. These effects should be the scattering processes, back- and forward- scattering, absorption, multi-reflections, diffraction, interference, depolarisation, and mode conversion. Each phenomenon requires an adapted description having its own numerical conditions, which are functions of mesh size, density of modes associated to given plasma fluctuations to name a few. The numerical requirements to fulfil the theoretical modelling cannot always be reached especially when all the space dimensions are needed to have a realistic description of the wave propagation in fluctuating plasmas. A rapid review of each model with its limitations and the specific tools associated to the different kinds of reflectometry diagnostics is detailed. A discussion on the problems and the works underway in the plasma reflectometry community concludes this review.

Extensive research has been conducted to investigate the characteristics of blast load due to single charge explosion, including numerical simulations and experimental blast tests in both unconfined and confined environments. Further, available guidelines for blast resistant design such as UFC-3-340-02 (2008) and ASCE 59-11 (2011) provide details to predict blast loads on a structure subjected to single charge explosion. However, blast load characteristics due to multiple charge explosions are poorly discussed in available literature. In this paper, commercially available Hydrocode, AUTODYN is calibrated for single charge explosions. Based on a comparison between numerical simulation and UFC prediction, correction factors for peak reflected pressure and positive reflected impulse as a function of charge weight, scaled distance and mesh size of the numerical model are proposed to minimize the errors in simulations. The calibrated AUTODYN model is then used to conduct parametric studies to investigate the effects of charge weight, scaled distance, number of charges and distance between the charges on the characteristics of free air blast load due to simultaneous detonated multiple charges. Numerical simulation results are used to derive analytical formulas for predictions of peak reflected pressure ratio and positive reflected impulse ratio between single and multiple explosions. The discussion is made on characteristics of free air blast load due to simultaneous detonated multiple charges.

Mass transfer studies were conducted in a stable liquid foam reactor under various operating conditions to evaluate gas holdup, effective interfacial area, liquid‐phase mass transfer coefficient and a modified interfacial mass transfer coefficient to include the surface‐active agents employed. Gas holdup and effective interfacial area were evaluated experimentally. The interfacial mass transfer coefficient was evaluated semitheoretically, by considering the interfacial region as a separate phase and using the experimental data developed for mass transfer accompanied by a fast first‐order chemical reaction. The liquid‐phase mass transfer coefficient was also evaluated semitheoretically, using Danckwert's theory for the liquid phase and the experimental data on mass transfer accompanied by a slow pseudofirst‐order chemical reaction.An experimental unit was set up to provide a stable flowing foam column, simulating the foam reactor. Mass transfer rates were studied for superfacial gas velocities in the range from 1.5 × 10−2 m/s to 5 × 10−2 m/s, giving gas residence times in the range from 20 to 55 seconds. A cationic and nonionic surface‐active agent and three different wire mesh sizes, giving bubble size distributions in the range from 2.2 to 5.4 mm Sauter mean diameters, were employed.It is observed that gas holdup is insensitive to the type of surface‐active agent; it is however, dependent on wire mesh size and gas velocity. The bubble diameter and, hence, the interfacial area are found to be insensitive to gas velocity in the range studied; they are, however, strong functions of wire mesh size. The liquid‐phase mass transfer coefficient increases with increase in gas velocity. The surface‐active agent introduces additional resistance to mass transfer in both reaction cases, this being the controlling one in the case of the fast reaction. A comparison with conventional packed bed contactors indicates the mass transfer rates to be about 8 times lower for the foam reactor, for the fast reaction case; for slow reactions, the foam reactor has mass transfer rates approximately 2‐4 times higher than those for conventional packed bed contactors.

Small-angle neutron scattering (SANS) experiments were performed to determine the conformational behavior of unattached deuterated linear poly(dimethylsiloxane) (PDMS) chains of Mn ) 51 000 g mol-1 in uncompressed and compressed end-linked protonated PDMS networks with a mini- mal amount of defects. The networks were prepared from low-polydispersity precursor chains with Mn ) 9900 g mol-1, 34 800 g mol-1, and 71 500 g mol-1. The samples are hereafter labeled 10K, 35K, and 70K. The mixtures of the 10K network with the linear chains were prepared by cross-linking around the linear chains, while the 35K and 70K network systems were swollen with the linear chains after the network was formed. No significant variation of the radius of gyration of the linear chains was observed as a function of network mesh size, in agreement with recent Monte Carlo simulations. The results from the compressed 35K and 70K networks exhibited excess scattering at small wave vectors, indicating phase segregation, and they could not be quantitatively analyzed. The scattering data from the trapped chains in the compressed 10K networks were fitted well with a Kratky-Porod wormlike chain model, indicating segment alignment consistent with Monte Carlo simulations and deuterium NMR results.

The methods by which fossils are extracted from sediments can alter their observed size-frequency distributions, which can in turn alter observed paleoecologic patterns. Building on previous work, this study uses virtual sieving (i.e., replicated via subsampling on a computer) to test the effects of size filtering on the apparent ecologic composition of a database of Miocene mollusks in which the size of every specimen was measured. When simulated mesh sizes varied by nearly an order of magnitude (2–10 mm), the apparent relative abundances of tiering, motility, and feeding categories varied substantially in some individual bulk samples. Not surprisingly, the extent to which variations in mesh size affected the ecologic proportions of a sample depended in part on its size-frequency distribution. If the goal is to characterize the ecology of adult assemblages, the chosen mesh size should not be so small that juveniles dominate the results or so large that a majority of specimens are excluded. For many molluscan assemblages, 2–4 mm should often be appropriate. For preexisting data sets composed of heterogeneously collected data, there is a positive result: averaging samples together to produce a mean view of ecologic composition tends to remove the more egregious effects of the size-filtering bias. Thus, comparisons of the ecologic composition of single samples may be sensitive to mesh-size effects, but comparisons of regional or global faunas are likely more robust, and variations in size filtering may not be an obstacle to large-scale, secular comparisons of ecospace use. Measuring ecologic importance using biomass instead of abundance also reduced the effects of the mesh-size bias by reducing the influence of small-bodied individuals on ecologic proportions.

Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework

A new family of iterative methods for solving systems of nonlinear equations is introduced, extending and unifying several existing approaches within a general framework. In the single-variable case, Newton’s method was accelerated using Padé approximations. This strategy is then extended to systems of nonlinear equations, leading to the construction of higher-order iteration functions with convergence orders ranging from two to four. By varying the order (p, q) of the Padé approximation, several known methods and their modifications emerge as special cases of this generalized approach. Theoretical convergence rates are established, and numerical experiments, conducted using high-precision arithmetic, confirm both the predicted behavior and improved computational efficiency across a variety of test problems.

Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depth-from-motion, including navigation and manipulation, require algorithms that can estimate depth in an on-line, incremental fashion. This requires a representation that records the uncertainty in depth estimates and a mechanism that integrates new measurements with existing depth estimates to reduce the uncertainty over time. Kalman filtering provides this mechanism. Previous applications of Kalman filtering to depth-from-motion have been limited to estimating depth at the location of a sparse set of features. In this paper, we introduce a new, pixel-based (iconic) algorithm that estimates depth and depth uncertainty at each pixel and incrementally refines these estimates over time. We describe the algorithm and contrast its formulation and performance to that of a feature-based Kalman filtering algorithm. We compare the performance of the two approaches by analyzing their theoretical convergence rates, by conducting quantitative experiments with images of a flat poster, and by conducting qualitative experiments with images of a realistic outdoor-scene model. The results show that the new method is an effective way to extract depth from lateral camera translations. This approach can be extended to incorporate general motion and to integrate other sources of information, such as stereo. The algorithms we have developed, which combine Kalman filtering with iconic descriptions of depth, therefore can serve as a useful and general framework for low-level dynamic vision.

The Multiscale Spectral Generalized Finite Element Method (MS-GFEM) was developed in recent work by Babuska and Lipton. The method uses optimal local shape functions, optimal in the sense of the Kolmogorov n-width, to approximate solutions to a second order linear elliptic partial differential equation with L-infinity coefficients. In this dissertation an implementation of MS-GFEM over a two subdomain partition of unity is outlined and several numerical experiments are presented. The method is applied to compute local fields inside high contrast particle suspensions. The method's performance is evaluated for various examples with different contrasts between reinforcement particles and matrix material. The numerical experiments are shown to agree with a new theoretical estimate that shows the convergence rate is independent of the elastic properties of particles and matrix materials. A new domain decomposition method based on MS-GFEM is presented. Numerical computations using this iterative method are discussed and the theoretical convergence rate is provided. It is shown that the convergence rate is given by the same near-exponential bound given for MS-GFEM. A systematic method for identifying the worst case load amongst all boundary loads of a fixed energy is introduced. Here the worst case load delivers the largest fraction of input energy into a prescribed subdomain of interest. This leads to an eigenvalue problem, for which the largest eigenvalue is the maximum fraction of energy which concentrates in the subdomain. The associated eigenfunctions are the worst case solutions. These eigenfunctions are related back to the MS-GFEM shape functions and numerical results are presented for several different geometries.

In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the solution with respect to the random variables. This justifies the application of sparse grids for the computation of statistical measures. Convergence rates are derived and are shown to be subexponential or algebraic with respect to the number of realizations of random perturbations. Due the accuracy of the method, sparse grids are well suited for computing low probability events with high confidence. We apply our method to the power flow problem. Numerical experiments on the non-trivial 39 bus New England power system model with large stochastic loads are consistent with the theoretical convergence rates. Moreover, compared to the Monte Carlo method our approach is at least 1011 times faster for the same accuracy.

The fractional Fokker-Planck equation is often used to characterize anomalous diffusion. In this paper, a fully discrete approximation for the nonlinear spatial fractional Fokker-Planck equation is given, where the discontinuous Galerkin finite element approach is utilized in time domain and the Galerkin finite element approach is utilized in spatial domain. The priori error estimate is derived in detail. Numerical examples are presented which are inline with the theoretical convergence rate.

A new class of implicit–explicit BDF[formula omitted] SAV schemes for general dissipative systems and their error analysis