Instability, intermittency, and multiscaling in discrete growth models of kinetic roughening

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhangequation and the Lai-Das Sarma-Villain equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such ''controlled instability'' models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the ''turbulent'' behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth.

Age and size composition, growth rate, reproductive biology, and habitats of the West Australian dhufish (Glaucosoma hebraicum) and their relevance to the management of this species

Samples of the commercially and recreationally important West Australian dhufish (Glaucosoma hebraicum) were obtained from the lower west coast of Australia by a variety of methods. Fish <300 mm TL were caught over flat, hard substrata and low-lying limestone reefs, whereas larger fish were caught over larger limestone and coral reef formations. Maximum total lengths, weights, and ages were 981 mm, 15.3 kg, and 39 years, respectively, for females and 1120 mm, 23.2 kg, and 41 years, respectively, for males. The von Bertalanffy growth curves for females and males were significantly different. The values for L∞, k, and t0 in the von Bertalanffy growth equations were 929 mm, 0.111/year, and –0.141 years, respectively, for females, and 1025 mm, 0.111/year, and –0.052 years, respectively, for males. Preliminary estimates of total mortality indicated that G. hebraicum is now subjected to a level of fishing pressure that must be of concern to fishery managers. Glaucosoma hebraicum, which spawns between November and April and predominantly between December and March, breeds at a wide range of depths and is a multiple spawner. The L50’s for females and males at first maturity, i.e. 301 and 320 mm, respectively, were attained by about the end of the third year of life and are well below the minimum legal length (MLL) of 500 mm. Because females and males did not reach the MLL until the end of their seventh and sixth years of life, respectively, they would have had, on average, the opportunity of spawning during four and three spawning seasons, respectively, before they reached the MLL. However, because G. hebraicum caught in water depths >40 m typically die upon release, a MLL is of limited use for conserving this species. Alternative approaches, such as restricting fishing activity in highly fished areas, reducing daily bag limits for recreational fishermen, introducing quotas or revising specific details of certain commercial hand-line licences (or doing both) are more likely to provide effective conservation measures.

Hybrid numerical methods for exponential models of growth

A series of novel numerical methods for the exponential models of growth are proposed. Based on these methods, hybrid predictor-corrector methods are constructed. The hybrid numerical methods can increase the accuracy and the computing speed obviously, as well as enlarge the stability domain greatly. (c) 2005 Published by Elsevier Inc.

Fundamental insights into ontogenetic growth from theory and fish

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as m_∞^(-0.23). This supports our first hypothesis that growth rate scales as m_∞^(-0.25) as predicted by metabolic scaling theory; it implies that species which grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as m_∞^(-0.35). This supports our second hypothesis which predicts that growth rate scales as m_∞^(-0.33) when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to m_∞^(-0.33) scaling, but as species diverge over evolutionary time they evolve the near-optimal m_∞^(-0.25) scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.

Parameter estimation and sensitivity analysis of fat deposition models in beef steers using acslXtreme.

The Davis Growth Model (a dynamic steer growth model encompassing 4 fat deposition models) is currently being used by the phenotypic prediction program of the Cooperative Research Centre (CRC) for Beef Genetic Technologies to predict P8 fat (mm) in beef cattle to assist beef producers meet market specifications. The concepts of cellular hyperplasia and hypertrophy are integral components of the Davis Growth Model. The net synthesis of total body fat (kg) is calculated from the net energy available after accounting tor energy needs for maintenance and protein synthesis. Total body fat (kg) is then partitioned into 4 fat depots (intermuscular, intramuscular, subcutaneous, and visceral). This paper reports on the parameter estimation and sensitivity analysis of the DNA (deoxyribonucleic acid) logistic growth equations and the fat deposition first-order differential equations in the Davis Growth Model using acslXtreme (Hunstville, AL, USA, Xcellon). The DNA and fat deposition parameter coefficients were found to be important determinants of model function; the DNA parameter coefficients with days on feed >100 days and the fat deposition parameter coefficients for all days on feed. The generalized NL2SOL optimization algorithm had the fastest processing time and the minimum number of objective function evaluations when estimating the 4 fat deposition parameter coefficients with 2 observed values (initial and final fat). The subcutaneous fat parameter coefficient did indicate a metabolic difference for frame sizes. The results look promising and the prototype Davis Growth Model has the potential to assist the beef industry meet market specifications.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

Calibration study of bivalve shells : implications for paleoenvironmental reconstruction

The accretionary shells of bivalve mollusks can provide environmental information, such as water temperature, precipitation, freshwater fluxes, primary productivity and anthropogenic activities in the form of variable growth rates and variable geochemical properties, such as stable oxygen and carbon isotopes. However, paleoenvironmental reconstructions are constrained by uncertainties about isotopic equilibrium fractionation during shell formation, which is generally acknowledged as a reasonable assumption for bivalves, but it has been disputed in several species. Furthermore, the variation in shell growth rates is accepted to rely on multiple environmental variables, such as temperature, food availability and salinity, but can differ from species to species. Therefore, it is necessary to perform species-specific calibration studies for both isotope proxies and shell growth rates before they can be used with confidence for environmental interpretations of the past. Accordingly, the principal objective of this Ph.D research is to examine the reliability of selected bivalve species, the long-lived Eurhomalea exalbida (Dillwyn), the short-lived and fast growing species Paphia undulata (Born 1778), and the freshwater mussel Margaritifera falcata (Gould 1850), as paleoenvironmental proxy archives.rnThe first part is focused on δ18Oshell and shell growth history of live-collected E. exalbida from the Falkland Islands. The most remarkable finding, however, is that E. exalbida formed its shell with an offset of -0.48‰ to -1.91‰ from the expected oxygen isotopic equilibrium with the ambient water. If this remained unnoticed, paleotemperature estimates would overestimate actual water temperatures by 2.1-8.3°C. With increasing ontogenetic age, the discrepancy between measured and reconstructed temperatures increased exponentially, irrespective of the seasonally varying shell growth rates. This study clearly demonstrates that, when the disequilibrium fractionation effect is taken into account, E. exalbida can serve as a high-resolution paleoclimate archive for the southern South America. The species therefore provides quantifiable temperature estimates, which yields new insights into long-term paleoclimate dynamics for mid to high latitudes on the southern hemisphere.rnThe stable carbon isotope of biogenic carbonates is generally considered to be useful for reconstruction of seawater dissolved inorganic carbon. The δ13Cshell composition of E. exalbida was therefore, investigated in the second part of this study. This chapter focuses on inter-annual and intra-annual variations in δ13Cshell. Environmental records in δ13Cshell are found to be strongly obscured by changes in shell growth rates, even if removing the ontogenetic decreasing trend. This suggests that δ13Cshell in E. exalbida may not be useful as an environmental proxy, but a potential tool for ecological investigations. rnIn addition to long-lived bivalve species, short-lived species that secrete their shells extremely fast, can also be useful for environmental reconstructions, especially as a high-resolution recorder. Therefore, P. undulata from Daya Bay, South China Sea was utilized in Chapter 4 to evaluate and establish a potential proxy archive for past variations of the East Asian monsoon on shorter time-scales. The δ18Oshell can provide qualitative estimates of the amount of monsoonal rain and terrestrial runoff and the δ13Cshell likely reflect the relative amount of isotopically light terrestrial carbon that reaches the ocean during the summer monsoon season. Therefore, shells of P. undulata can provide serviceable proxy archives to reconstruct the frequency of exceptional summer monsoons in the past. The relative strength of monsoon-related precipitation and associated changes in ocean salinity and the δ13C ratios of the dissolved inorganic carbon signature (δ13CDIC) can be estimated from the δ18Oshell and δ13Cshell values as well as shell growth patterns. rnIn the final part, the freshwater pearl shell M. falcata from four rivers in British Columbia, Canada was preliminarily studied concerning the lifespans and the shell growth rates. Two groups separated by the Georgia Strait can be clearly distinguished. Specimens from the western group exhibit a shorter lifespan, while the eastern group live longer. Moreover, the average lifespan seems to decrease from south to north. The computed growth equations from the eastern and western groups differ as well. The western group exhibits a lower growth rate, while bivalves from the eastern group grow faster. The land use history seems to be responsible for the differences in lifespans of the specimens from the two groups. Differences in growth rate may be induced by differences in water temperature or nutrient input also related to the land use activities.

Effect of Frame Size and Hormone Implant on Performance and Carcass Characteristics of Finishing Yearling Heifers: Returns to a Value-Based Market

Four groups of yearling heifers representing different frame sizes—small, medium, and large Angus and medium Simmental—were fed high-grain finishing diets to average Low Choice quality grade. Half the heifers were implanted with estrogen and trenbolone acetate. Backfat and ribeye area were measured by ultrasound four times during the study to assess growth of muscle and fat. Increasing frame size resulted in increased feed intake, greater rates of gain, and a trend towards reduced feed conversion. Greater returns would have been realized from each of the four groups had they been sold in a premium market based on yield grade rather than the conventional grade and yield market. Increasing frame size resulted in greater returns to the value-based market. Implants increased rate of gain and improved feed conversion but did not result in significantly greater returns to the value-based market compared with the grade and yield market. Ribeye area and backfat increased with body weight and time on feed. Increase in ribeye area was linear with time, whereas accumulation of backfat was exponential. Rate of increase in area of ribeye tended to increase and backfat tended to decrease as frame size increased. Implants increased rate of increase in ribeye area but had no effect on rate of deposition of subcutaneous fat. Equations describing growth of ribeye area and backfat for each group predicted average growth for the heifers but did not predict growth of individual heifers. Final carcass yield grade was related to initial thickness of backfat but not to initial ribeye area. These results indicate that the type of cattle selected to be fed for a premium market based on yield grade is important to the success of the program. More work is needed to develop growth equations from ultrasound measurements, but ultrasound will likely be a useful tool in selecting feeder cattle for a value-based market.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.