Asymptotic Width Research Articles

Inference for ARMA time series with mildly varying trend

Statistical inference is studied for ARMA time series with a mildly varying smooth trend. Following properly calibrated B-spline estimation of the trend, approximates of the unobserved ARMA series are used instead to estimate ARMA parameters by maximum likelihood. The parameter estimates are shown to be oracally efficient in the sense that they are asymptotically as efficient as if the true trend function was known and removed to obtain the true ARMA series. The mildly varying trend function is estimated by Nadaraya–Watson method with asymptotically correct simultaneous confidence band (SCB). The SCB sprawls over an interval that eventually covers the half real line, instead of a bounded interval in the existing literature, with asymptotic width of the SCB dependent on ARMA coefficients. Simulation experiments corroborate the theoretical findings.

Population parameters of the orange mud crab Scylla olivacea (Herbst, 1796) from the Sundarban mangrove forest in Bangladesh

Population parameters of orange mud crab (Scylla olivacea) were estimated, aiming to determine sex ratios, carapace width-body weight (CW-BW) relationships, asymptotic width (CW∝), growth coefficient (K), mortality (Z, M, and F), recruitment and level of exploitation (E) in the Sundarban mangrove forest, located in the south-western part of Bangladesh. Year-round samples were collected using hook-lines and baited traps, the population parameters were measured from CW frequency data using FiSAT-II analyzer. The study showed that the overall male and female sex ratio was 1:0.66, revealing a male domination in the study area. The CW-BW relationship indicated that the increment rate in the BW of the male crabs (b = 3.06, R2 = 0.98) were higher than that of female (b = 2.62; R2 = 0.98) S. olivacea. The b value differed significantly (P < 0.006) from isometric growth (b = 3) where males exhibited positive and females exhibited negative growth allometry. Estimated CW∝ for male and female were 164 mm and 152 mm along with K values 0.90 yr−1 and 0.76 yr−1, respectively. Total mortality (Z) was 2.67 yr−1 and 1.57 yr−1, natural mortality (M) was 0.98 yr−1 and 0.90 yr−1 and fishing mortality (F) was 1.69 yr−1 and 0.67 yr−1 for male and female, accordingly. Recruitment of both sexes exhibited a bimodal recruitment pattern where young population occurs continuously throughout the year and a major peak of recruitment for males was observed from November to January and for female it was from February to April. The estimated exploitation rate (E) for male (0.63) was higher than the female (0.43) where the E for male exceeded the maximum permissible limit (E = 0.50). A remarkable range of fishing pressure at lower size classes was revealed in this study and thus framing minimum legal size is crucial for effective management of the population.

Growth and longevity of the spider crab Libinia ferreirae (Majoidea, Epialtidae)

Abstract We estimated the growth parameters of the spider crab, Libinia ferreirae (age, asymptotic size and growth rate) using the von Bertalanffy growth equation model. We obtained nine cohorts for female carapace asymptotic width (CW∞) = 64.32 mm, growth coefficient (day-1) (k) = 0.0027 e t0= 0.77 days) and seven for males (CW∞ = 81.93 mm, k= 0.0021 e t0= 0.49 days). The longevity for males was higher than that for females, estimated 2,156 days (5.91 years) and 1,706 days (4.68 years), respectively. The growth curves for males and females differed (F = 34.67 e p < 0.001). Males reached gonadal maturity before morphometric maturity and occurred at 8.8 and 16.6 months of life, respectively. Females reach gonad and morphometric maturity synchronously and this was estimated to occur at about 11.42 months of life. These crabs invest a great amount of energy in growth during a brief period of their development until reaching the terminal moult. This growth strategy would bring less wear to the organism and consequently a greater longevity.

New axisymmetric containers for isochronous sloshing: a tribute to B. Andreas Troesch

Two new families of axisymmetric isochronous containers for first-mode sloshing about nodal circles are found using the inverse method of solution. These containers support standing waves in annular geometries which separate naturally into even ( and ) and odd () series with increasing radius. It is convenient to present results by fixing , where is the isochronous frequency and g is gravity. In this formulation, the maximum asymptotic widths of the containers monotonically decrease from to . For , both the even and odd containers take the shape of the planar isochronous container. A simple analysis reveals that mass is conserved for first-mode sloshing about the respective nodal circles.

Redundancy-Optimal FF Codes for a General Source and Its Relationships to the Rate-Optimal FF Codes

SUMMARY In this paper we consider fixed-to-fixed length (FF) coding of a general source X with vanishing error probability and define two kinds of optimalities with respect to the coding rate and the redundancy, where the redundancy is defined as the difference between the coding rate and the symbolwise ideal codeword length. We first show that the infimum achievable redundancy coincides with the asymptotic width W(X )o f the entropy spectrum. Next, we consider the two sets C H (X )a ndCW (X )a nd investigate relationships between them, where CH(X )a ndCW (X) denote the sets of all the optimal FF codes with respect to the coding rate and the redundancy, respectively. We give two necessary and sufficient conditions corresponding to C H (X) ⊆C W (X )a ndCW (X) ⊆C H (X), respectively. We can also show the existence of an FF code that is optimal with respect to

Global theory of steady deep-cellular growth in directional solidification

The present paper is concerned with the global asymptotic theory of steady deep-cellular growth in directional solidification of binary mixtures. We consider the two-dimensional model with nonzero isotropic surface tension and obtain the global uniformly valid asymptotic solutions for the steady state of the system in the limit of the Péclet number ε→0; ε is defined as the ratio of the radius of the cell's tip and mass diffussion length. The whole physical space is divided into the outer region and root region; the solutions in each subregion are solved, respectively, and matched with each other in the intermediate region. The results show that given growth conditions and material properties, the global solutions for steady state of the system contain two free parameters: the Péclet number and asymptotic width parameter λ(0), which are related to the geometry of cellular structure: the cell tip radius and primary spacing. One of the most important conclusions drawn from this analysis is that the steady-state solutions of cellular growth have a complicated structure with three internal layers in the root region; for given (ε,λ(0)), there exists a discrete set of the global steady-state solutions subject to the quantization condition that are profoundly affected by the surface tension. Each eigenvalue calculated from this quantization condition determines the total length of the finger described by the corresponding global steady-state solution.

Crescimento de Callinectes sapidus (Crustacea, Decapoda, Portunidae) no estuário da laguna dos Patos, RS, Brasil

Utilizando o método de deslocamento modal para a identificação das idades, estimou-se o crescimento do siri-azul Callinectes sapidus Rathbun, 1896 em duas áreas de pesca no estuário da Lagoa dos Patos. Os indivíduos foram coletados entre fevereiro de 2005 e março de 2006 no Saco da Mangueira e Saco do Arraial por meio de arrasto de rede de portas da pesca artesanal. Coletou-se um total de 2.609 animais, sendo 1.193 machos e 1.416 fêmeas. Para obtenção das curvas de crescimento utilizou-se o modelo de von Bertalanffy. As curvas foram validadas pela sua adequação ao ciclo de vida e aspectos biológicos da espécie. O tamanho máximo de largura de carapaça (LCmáx) utilizado foi mantido fixo em todas as análises (LCmáx=162,71mm; ± d.p.=3,10 para machos e LCmáx=157,78mm; ± d.p.=5,45 para fêmeas), sendo esses valores médios das maiores medidas obtidas em mais de 20 anos de coletas no estuário. Os parâmetros de crescimento e longevidade foram estimados para machos (Saco da Mangueira, K=0,0039/dia; t o=-6.07; 1.195 dias; Saco do Arraial, K=0,0041/dia; t o=-5,84; 1.102 dias) e fêmeas (Saco da Mangueira, K=0,0040/dia; t o=-6,22; 1.153 dias; Saco do Arraial, K=0,0039/dia; t o=-5.91; 1.181 dias). As curvas de crescimento estimadas nesse trabalho denotam que a espécie atinge o tamanho mínimo de captura praticamente no primeiro ano de vida (120mm).

Universal wake structures of Kármán vortex streets in two-dimensional flows

Formation of Kármán vortex streets by circular rods is studied in a flowing soap film channel. The two-dimensional fluid flow in the film allows stable vortex streets to be generated and studied over a broad range of Reynolds numbers, 10&amp;lt;Re&amp;lt;2000. There have been many studies of the Kármán vortex streets. The current study focuses on the universal feature of the near-wake structures generated by circular cylinders in a uniform two-dimensional (2D) flow. The new approach in the investigation is to decompose the street into a series of vortex couples, which defines the outer envelope of the wake, and to study the expansion rate of these couples. Our experiment shows that motion of vortex couples are powered by bursts of transverse jets, and the jet intensity determines the asymptotic width and the expansion rate of the wake. A simple model is constructed that not only allows us to extract the kinetic energy encapsulated in the vortices but also explains the universal appearance of the 2D laminar wakes generated by large and small rods. To the best of our knowledge, this is the first time that the efficiency of energy injected into vortices is estimated and this efficiency turns out to be ∼5%.

Morphology and growth kinetics of organic thin films deposited by hot wall epitaxy

In this work we have used atomic force microscopy and X-ray diffraction by synchrotron radiation to investigate the growth kinetics and morphology of para-sexiphenyl layers. The results of our investigations can be summarized as follows: (a) para-sexiphenyl grows on mica epitaxialy; (b) a rearrangement from randomly distributed small para-sexiphenyl islands with compact shape to elongated islands occurs during the growth if the critical island density is reached; (c) with further increase of the growth time the islands become elongated, quickly reaching a fixed asymptotic width while their height remains much smaller than their length and width.

Morphology and growth kinetics of organic thin films deposited by hot wall epitaxy

In this work we have used atomic force microscopy and X-ray diffraction by synchrotron radiation to investigate the growth kinetics and morphology of para-sexiphenyl layers. The results of our investigations can be summarized as follows: (a) para-sexiphenyl grows on mica epitaxialy; (b) a rearrangement from randomly distributed small para-sexiphenyl islands with compact shape to elongated islands occurs during the growth if the critical island density is reached; (c) with further increase of the growth time the islands become elongated, quickly reaching a fixed asymptotic width while their height remains much smaller than their length and width.

Asymptotic Particle Size Distributions Attained during Coagulation Processes

The effects of the collision kernel on the self-preserving size distribution and on the gelation phenomenon of aerosol coagulation were investigated. An analytical solution for the asymptotic width of log-normally preserving size distribution during coagulation was obtained as a function of the degree of homogeneity using arbitrary shape of homogeneous collision kernels. From the solution obtained, it was shown that when the degree of homogeneity is larger than 1, self-preserving size distribution does not exist, and gelation occurs. A very accurate numerical coagulation simulation method, the sectional method, was also used for calculating the self-preserving particle size distribution for some specific classes of coagulation kernels and the results were compared with the analytical solution obtained by the log-normal method.

New method for field studies on the parapatric distribution of sibling species

Spatial segregation (parapatry) often occurs between closely related species. The distributions of the two species are sometimes defined with a small overlapping zone (called a `sympatric area') which generally shifts. Exclusion is necessary to explain the persistence and shift of such a spatial pattern. Field studies are carried out to identify the type of interaction that leads to the required exclusion. This is usually achieved by estimating competition and predation parameters to define the type of interaction strong enough to imply exclusion. But interaction parameters are estimated by quantitative methods which require prolonged observation (5–10 years). These estimations are thus difficult to obtain and are open to criticism because of the spatial and temporal variations in the biotic context. Now the study of these variations requires estimation of several other interaction parameters (for different times and sites); therefore, we are unable to discuss these criticisms from a study of realistic duration. We have, therefore, developed a faster study method using the spatial properties of the sympatric area (width and velocity). We used a between-species competition and a predation model, spatially extended with coupled map lattice formalism (CML), to generate substitution waves corresponding to the `moving sympatric area' and to study their spatial properties (asymptotic width and velocity). The relationships between the asymptotic width and the interaction level had different shapes with competition and predation parameters. We used this difference to define a rapid study method that does not use quantitative estimations of the interaction parameters. This method is more reliable than the usual method with respect to the above criticisms. These findings may have considerable consequences for field studies of parapatry.

Asymptotic widths of size distributions resulting from collisional growth assuming log-normally distributed fractal aggregates

Asymptotic widths of size distributions resulting from collisional growth assuming log-normally distributed fractal aggregates

On the influence of coastline orientation on the steady state width of a latent heat polynya

This paper investigates under what conditions the steady state shape of a coastal latent heat polynya is influenced by (1) the direction of flow of free‐drifting frazil ice and the consolidated offshore ice sheet and (2) coastline orientation. Analytical solutions are obtained for coastal polynyas when the coastline is straight and when a coastline has a single step. From the solutions it is shown that the asymptotic polynya width is given by the generalized Pease (1987) width, L cos θ, where L is the “classical Pease width” and θ is the angle between the consolidated ice sheet velocity and the normal to the coastline. An expression is also obtained for the alongshore length scale LC, over which the polynya adjusts toward its asymptotic width, and it is shown that LC depends upon the directions of travel of the frazil ice and the consolidated ice sheet. When the frazil ice and the consolidated ice sheet both drift offshore, normal to the coast, LC = 0, in agreement with the classical Pease theory. Variations in the coastline which occur on a length scale much smaller than LC are not reproduced in the polynya shape. Two numerical simulations are presented for Terra Nova Bay, Antarctica, and the St. Lawrence Island Polynya in the Bering Sea. Both examples employ realistic coastline geometry and information about the direction of drift of the consolidated ice sheet. In each example a realistic polynya shape is obtained. The examples highlight the versatility of the model because in the former case the ice sheet drifts almost parallel to the coast, while in the latter it drifts offshore.

Distribution-Free Confidence Intervals for Conditional Probabilities and Ratios of Expectations

Many simulation experiments are concerned with the estimation of a ratio of two unknown means, the estimation of a conditional probability being an example. We propose confidence intervals for the case in which the ratio is estimated by using independent, identically distributed random pairs with bounded and ordered components. Emphasis is given to the case in which each component can be expressed as the product of a Bernoulli and a bounded random variable. The proposed intervals result from distribution-free bounds on error probabilities, are valid for every sample size, and their asymptotic width decreases at the same rate as that of confidence intervals based on the central limit theorem. We evaluate their performance by means of two experiments. The first considers the estimation of the probability that a path in a directed a network is shortest while the second considers the estimation of the distribution of the inventory level in a stationary inventory system with periodic review. The experiments show that the intervals are conservative with superior coverage for small sample sizes (≤50).

Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors

When buoyant fluid is released into the base of a crack in an elastic medjura the crack will propagate upwards, driven by the buoyancy of the fluid. Viscous fluid flow in such a fissure is described by the equations of lubrication theory with the pressure given by the sum of the hydrostatic pressure of the fluid and the elastic pressures exerted by the walls of the crack. The elastic pressure and the width of the crack are further coupled by an integro-differential equation derived from the theory of infinitesimal dislocations in an elastic medium. The steady buoyancy-driven propagation of a two-dimensional fluid-filled crack through an elastic medium is analysed and the governing equations for the pressure distribution and the shape of the crack are solved numerically using a collocation technique. The fluid pressure in the tip of an opening crack is shown to be very low. Accordingly, a region of relatively inviscid vapour or exsolved volatiles in the crack tip is predicted and allowed for in the formulation of the problem. The solutions show that the asymptotic width of the crack, its rate of ascent and the general features of the flow are determined primarily by the fluid mechanics; the strength of the medium and the vapour pressure in the crack tip affect only the local structure near the advancing tip of the crack. When applied to the transport of molten rock through the Earth's lithosphere by magma-fracture, this conclusion is of fundamental importance and challenges the geophysicist's usual emphasis on the controlling influence of fracture mechanics rather than that of fluid mechanics.

Penetration of fluid into a Hele–Shaw cell: the Saffman–Taylor experiment

A theoretical account is given of experiments performed by Saffman &amp; Taylor (1958) in which a fluid drives a liquid out of a long straight channel of very small thickness formed between two parallel sheets sealed at the edges. The penetrating fluid forms a long finger, whose sides are parallel to the edges of the channel, and which has a rounded tip, which advances with unaltered shape at a constant speed U. The theory correctly predicts the shape of the finger as a function of the ratio λ = (asymptotic width of finger)/(width of channel) and gives the relation between λ and U, which is in good agreement with experiment. In particular it shows that, as U increases from zero to infinity, λ steadily decreases from 1 to 0·5.