Changes In Mesh Size Research Articles

Trawl gear selectivity and the effect of mesh size on the deep-water rose shrimp ( Parapenaeus longirostris, Lucas, 1846) fishery off the gulf of Cádiz (SW Spain)

The deep-water rose shrimp ( Parapenaeus longirostris, Lucas, 1846) is a typical shrimp which is one of the main target species in the demersal fishery in the Spanish south Atlantic region. In this paper, the selectivity parameters of this species have been studied in two different selectivity survey designs (research vessels and in commercial fishing vessels). We have found 2 mm difference between both methods in the 50% retention length ( L 50). The selection factors obtained from the oceanographic vessels range from 0.37 to 0.49, while those from the commercial vessels are lower, from 0.32 to 0.39. The effects of mesh size changes in the present exploitation pattern are also considered. The present exploitation pattern is far from to optimal due to an overexploitation of the smaller sizes. The different simulations of changes in mesh size do not show great differences in maximum sustainable yields, but important market variations occur above 30% and 50% over the present obtained values. In reference to the immediate effects which could produce an increase of the mesh size, losses of 36%, 51% and 62% for the referred mesh sizes (50, 55 and 60) using the selectivity parameters obtained from the surveys of research vessels are estimated. If obtained from the surveys of the commercial vessels, these values correspond, respectively, to 27%, 42% and 73%.

Finite Difference Schemes for [formula omitted] That Inherit Energy Conservation or Dissipation Property

We propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations, such as the Korteweg–de Vries (KdV) equation and the Cahn–Hilliard equation. The most important feature of our procedure is a rigorous discretization of variational derivatives using summation by parts, which implies that the inherited properties are satisfied exactly. Since the inherited properties are kept even if the time mesh size changes in the time-evolution process, we can use some appropriate time mesh adaptive methods to obtain numerical solutions through the derived schemes. Because of these properties the derived schemes are expected to be numerically stable and yield solutions converging to PDE solutions and sufficiently flexible to treat. The inheritance of the energy conservation and dissipation properties are verified numerically for the KdV equation and the Cahn–Hilliard equation

Hydrogels and drug delivery

Recent developments include the use of water-swollen, crosslinked biomedical polymers as carriers for the delivery of drugs, peptides and proteins, as targeting agents for site-specific delivery, or as components for preparation of protein or enzyme conjugates. The network structure and the thermodynamic nature of the components of these networks play a key role in their diffusional behavior, molecular mesh size changes (especially in environmentally responsive hydrogels), and the associated molecular stability of the incorporated bioactive agents.

Optimum mesh size of the numerical analysis for structural vibration and noise prediction

An engineering goal in vibration and noise professionals is to develope quiet machines at the preliminary design stage, and various numerical techniques such as FEM, SEA or BEM are one of the schemes toward the goal. In this paper, the research has been focused on the sensitivity effect of mesh sizes for FEM application so that the optimum size of the mesh that leads to engineering solution within acceptable computing time could be generated. In order to evaluate the mesh size effect, three important parameters have been examined : natural frequencies, number of modes and driving point mobility. First, several lower modes including the fundamental frequency of a 2-D plate structure have been calculated as mesh size changes. Since theoretical values of natural frequencies for a simple structure are known, the deviation between the numerical and theoretical values is obtained as a function of mesh size. The result shows that the error is no longer decreased if the mesh size becomes a quarter wavelength or smaller than that. Second, the mesh size effect is also investigated for the number of modes. For the frequency band up to 1.4 kHz, the structure should have 38 modes in total. As the mesh size reaches to the quarter wavelength, the total count in modes approaches to the same values. Third, a mobility function at the driving point is compared between SEA and FEM result. In SEA application, the mobility function is determined by the modal density and the mass of the structure. It is independent of excitation frequencies. When the mobility function is calculated from a wavelength to one-tenth of it, the mobility becomes constant if the mesh becomes a quarter wavelength or smaller. We can conclude that dynamic parameters, such as eigenvalues, mode count, and mobility function, can be correctly estimated, while saving the computing burden, if a quarter wavelength (.lambda./4) mesh is used. Therefore, (.lambda./4) mesh is recommended in structural vibration analysis.

Spurious numerical refraction

AbstractThe purpose of this paper is to investigate the effect of a non‐uniform mesh in two dimensions (2D). A change in mesh size will, in general, result in spurious refraction (and reflection) which is entirely numerical (rather than physical) in origin. To facilitate the analysis, the mesh geometry has been highly simplified in that only a single change in mesh size is considered. The analysis is based on a finite element wave model.The domain consists of two conterminous regions discernible only by their different nodal spacings in the x‐direction. The interface between the two regions is internal to the mesh and is a straight line. The model is based upon the Crank‐Nicolson linear finite element scheme applied to the second order wave equation. The results of the analysis are confirmed by numerical experiments. It is shown that under particular numerical conditions total internal reflection may occur and when this is the case, the transmitted wave is evanescent. An analysis of the energy flux associated with the incident, reflected and trasmitted waves shows that energy is conserved across the interface between the two regions.

Design features of the orb web of the spider, Araneus diadematus

Analysis of orb webs of the garden cross spider (Araneus diadematus) showed that these vertical webs have a significant up/down asymmetry. Experiments demonstrated that the spider runs down faster than up, and thus confers a relatively higher foraging value to sections below the hub. Simulations suggested that the density of capture spiral spacing, prey size, and the density of prey should all affect the capture efficiency of a web. Webs lose effective capture area because of overlap of the capture zone around each thread; the smaller the prey, the finer the mesh can be without losing effective area. Lower sectors of the web have a particular mesh size (height and length of capture spiral segments) throughout, whereas in the upper sectors the mesh size changes, widening from the hub towards the periphery.

Assessment of multispecies cichlid fisheries of the Southeast Arm of Lake Malawi, Africa

The multispecies cichlid fisheries of southern Lake Malawi have been managed by control of fishing effort, based on Gulland's (1961; Fishery Invest., Lond., Ser. 2, 23: 1—52) modification of the Schaefer (1954; Bull. inter-Am, trop. Tuna Commn, 1: 27-56) stock assessment model, together with continual monitoring and adaptation to changes in the fisheries as they occur. Schaefer yield estimates are updated in this paper. For the demersal trawl fishery, which exploits 160+ species, maximum sustainable yield (MSY) is estimated to be 1355 tonnes/year at an effort level of 620 boat days, and effort is controlled at a level of approximately 500 boat days. MSY for the Chambo (three Oreochromis spp.) ringnet fishery is estimated to be 2190 tonnes/year at an effort level of 11 360 ringnet pulls. Walter's (1986) equilibrium yield model has also been applied to the Chambo fishery and indicates maximum yields of between 1800 and 2500 tonnes at approximately 10000 ringnet pulls. Catch rates in both fisheries are influenced by a number of factors apart from fishing effort. In the demersal trawl fishery the effects of changes in species composition, variability in recruitment, a change in mesh size, and a decline in efficiency of certain fishing units can all be detected in catch and effort data. In the Chambo fishery, catches are related to changes in annual mean lake level three years previously. A hypothesis is proposed here which links wind-induced mixing of nutrientrich deep water with improved survival of planktivorous juvenile fish. The use of simple stock-assessment models combined with close observation and monitoring is effective in managing fisheries for tropical, short-lived species.

Effects of a change in mesh size on Nephrops stocks in Portuguese waters

An assessment of the effects of a change in mesh size on the Alentejo and Algarve Nephrops norvegicus L. stocks, based on the method of length-cohort analysis is presented in this work. Since Nephrops cannot be aged, this model is suitable because it uses length rather than age classes; analytically it is based on a procedure similar to age-cohort analysis. The analysis shows that provided instantaneous natural loss ( M) is less than 0.42, an increase in mesh size to 80 mm should lead to long-term gains in yield per recruit and biomass per recruit in both stocks. Overall the magnitudes of these gains are about 90% in the case of biomass and 27% in the case of yield per recruit for females and males combined.

Supra-Convergent Schemes on Irregular Grids

As Tikhonov and Samarskil showed for k = 2, it is not essential that k th-order compact difference schemes be centered at the arithmetic mean of the stencil's points to yield second-order convergence (although it does suffice). For stable schemes and even k, the main point is seen when the k th difference quotient is set equal to the value of the k th derivative at the middle point of the stencil; the proof is particularly transparent for k = 2. For any k, in fact, there is a ( k/2J -parameter family of symmetric averages of the values of the k th derivative at the points of the stencil which, when similarly used, yield second-order convergence. The result extends to stable compact schemes for equations with lower-order terms under general boundary conditions. Although the extension of Numerov's tridiagonal scheme (approximating D2y = f with third-order truncation error) yields fourth-order con- vergence on meshes consisting of a bounded number of pieces in which the mesh size changes monotonically, it yields only third-order convergence to quintic polynomials on any three- periodic mesh with unequal adjacent mesh sizes and fixed adjacent mesh ratios. A result of some independent interest is appended (and applied): it characterizes, simply, those functions of k variables which possess the property that their average value, as one translates over one period of an arbitrary periodic sequence of arguments, is zero; i.e., those bounded functions whose average value, as one translates over arbitrary finite sequences of arguments, goes to zero as the length of the sequences increases.

Supra-convergent schemes on irregular grids

As Tikhonov and Samarskiĭ showed for k = 2 k = 2 , it is not essential that kth-order compact difference schemes be centered at the arithmetic mean of the stencil’s points to yield second-order convergence (although it does suffice). For stable schemes and even k, the main point is seen when the kth difference quotient is set equal to the value of the kth derivative at the middle point of the stencil; the proof is particularly transparent for k = 2 k = 2 . For any k, in fact, there is a ⌊ k / 2 ⌋ \left \lfloor {k/2} \right \rfloor -parameter family of symmetric averages of the values of the kth derivative at the points of the stencil which, when similarly used, yield second-order convergence. The result extends to stable compact schemes for equations with lower-order terms under general boundary conditions. Although the extension of Numerov’s tridiagonal scheme (approximating D 2 y = f {D^2}y = f with third-order truncation error) yields fourth-order convergence on meshes consisting of a bounded number of pieces in which the mesh size changes monotonically, it yields only third-order convergence to quintic polynomials on any three-periodic mesh with unequal adjacent mesh sizes and fixed adjacent mesh ratios. A result of some independent interest is appended (and applied): it characterizes, simply, those functions of k variables which possess the property that their average value, as one translates over one period of an arbitrary periodic sequence of arguments, is zero; i.e., those bounded functions whose average value, as one translates over arbitrary finite sequences of arguments, goes to zero as the length of the sequences increases.

Flux-corrected transport and diffusion on a non-uniform mesh

The flux corrected transport (FCT) algorithm of Boris and Book [ J. Comput. Phys. 11 (1973) , 38–69] is used to solve the continuity equations for electrons and ions on a nonuniform mesh, to facilitate the study of plasma structure near electrodes. It is shown that extreme (even abrupt) mesh size changes can be accommodated with negligible distortion of a density pulse advecting with a constant velocity. The advection of a pulse by a spatially nonuniform velocity field across a non-uniform mesh also gives results comparable with those for a uniform mesh. A treatment of diffusion on a variable mesh is also developed and is shown to agree well with the analytic solution.

A parallel algorithm for high subsonic compressible flow over a circular cylinder

The development of superfast computers, which operate on data other than on the purely sequential principle, calls for new computational algorithms which make full use of the machine capabilities. Using the inviscid compressible supercritical flow over a circular cylinder as an example, a computational algorithm is developed for a parallel processing computer. All boundary conditions are satisfied explicitly and boundary points are computed in parallel with interior points, thereby greatly increasing the “machine utilization.” Treatment of mesh size changes with the parallel algorithm has been accomplished in a novel way. The influence of various finite difference formulations of the wall boundary condition on the computed results is studied and the results compared with those obtained by other authors. The importance of correlating the formulation of the physical problem with the numerical technique and the computational procedure to secure a high machine utilization in parallel computation is demonstrated.

Remarks on the Order of Convergence of Discrete Analogs for Second-Order Elliptic Partial Differential Equations

IN SOLVING partial differential equations numerically by the method of finite differences, the solution u of the differential equation is replaced by the solution v of a finite set of analogous equations li(v) = si. The difference u v is expected to become smaller with successive mesh refinements. Order of refers to the maximum value of u v I as related to the fineness of the mesh. This paper is concerned with estimating the order of convergence for various discrete analogs of boundary value problems associated with certain elliptic partial differential equations. In particular we examine the effect of interfaces and mesh size changes on the order of convergence for the Dirichlet problem connected with Poisson's equation in two dimensions. The methods used here are based on those used by Gerschgorin [1] and also by Batschelet [11]. These methods give bounds on the error committed by using the discrete analog of the boundary value problem in terms of the derivatives through the fourth order of the true solution, provided they exist and are bounded in the domain. Boundedness of the fourth derivatives is a requirement often not satisfied in even the simplest practical problems, and therefore must be recognized as a heavy limitation on Gerschgorin's method. However, this limitation has been made easier to bear by recent results concerning regularity properties in the closed region of solutions to strongly elliptic equations, for example in [6], [7], [8]. A conclusion is that if the coefficients in equation (1.1) below are in C3, 0 < A < 1, and the Dirichlet data and boundary are in C4, then the solution is in CA4 on the closed region, i.e., the fourth order derivatives of the solution are uniformly Holder continuous with exponent ,u on the closed region. However, a second difficulty is that the magnitude of the bounds on the derivatives is usually unknown even though the existence of such bounds is guaranteed. In the recent works of Walsh, Young, Wasow, and others, these difficulties have been overcome for special equations or special geometry, as in [5]. Nonetheless, Gerschgorin's bounds are useful in that they afford some information concerning the improvement one can expect for a given mesh refinement, as well as an indication of the magnitude of the problem. For most cases of practical interest, it is desirable that the discrete analogs have convergence of order h2, where h is the mesh spacing. Generally such problems may be solved satisfactorily with the order of 103 mesh points, a reasonable number on modern computers. When the order of convergence is only h, many