Perturbation analysis of transient population dynamics using matrix projection models

For the past 15 years zoos and related institutions have increasingly become involved in the captive breeding of endangered animal species. Prerequisites to the success of captive propagation as part of the conservation of biodiversity are optimal achievements at three levels: that of individuals, which should be guaranteed long lives of sufficient quality; that of pairs and groups, which should reproduce sufficiently to guarantee continuity over the generations; and that of populations, which should be kept genetically and demographically healthy. Achievement of these goals requires co-operative management of zoo populations of the species concerned and appropriate population management procedures. Such procedures will depend upon the development of a sound theoretical basis for understanding the genetics and demography of small (and fragmented) populations, of ‘tools’ to bring theory into practice, and of organizational structures to implement management proposals. At each of these three levels considerable progress has been made in recent years. Theoretical knowledge has advanced and continues to be refined. A whole array of ‘tools’ has been developed in the form of computer software for keeping records, compiling studbooks, performing genetic and demographic analyses etc. Such tools enable population managers to formulate master plans for population management. Within the community of zoos and related institutions organizational structures have been set up for co-operative propagation of endangered species, involving a system of regional breeding programmes. Currently 175 such programmes are being conducted in the various regions of the world. In the past five years IUCN/SSC’s Captive Breeding Specialist Group has become increasingly involved in these programmes as a coordinating body. This has led to three important developments.

Animals with only partially known ancestry present a problem for population managers because it can be difficult to determine their relative genetic value to the population. So long as their ancestry is not completely unknown, population management software such as PMx can calculate a mean kinship for these animals, but that mean kinship is calculated such that there is no decrease in relative genetic value or "penalty" for only partially known ancestry. However, there is a longer-term genetic cost to having animals with only partially known ancestry in the population, and thus it is appropriate to "penalize" animals with partially known ancestry to some extent. The challenge is determining the correct "penalty" which will serve to decrease the percent unknown ancestry in subsequent generations while not causing excessive selection against the known ancestry of the animal. A new parameter of relative genetic value is developed which takes into account both an animal's mean kinship as well as its percent known ancestry. The method used in PMx to calculate the mean kinships also in general overestimates the inbreeding coefficients of offspring of animals with partially known ancestry when the known parents share a common ancestor, but can underestimate inbreeding if common ancestors exist within the unknown portion of the pedigree. This may result in population managers selecting less suitable pairs for breeding in an attempt to avoid an apparent higher level of inbreeding. A parameter is developed that adjusts the inbreeding coefficient to more accurately reflect the likely inbreeding coefficient of potential offspring. Zoo Biol. 35:319-325, 2016. © 2016 Wiley Periodicals, Inc.

Short-term, transient population dynamics can differ in important ways from long-term asymptotic dynamics. Just as perturbation analysis (sensitivity and elasticity) of the asymptotic growth rate reveals the effects of the vital rates on long-term growth, the perturbation analysis of transient dynamics can reveal the determinants of short-term patterns. In this article, I present a completely new approach to transient sensitivity and elasticity analysis, using methods from matrix calculus. Unlike previous methods, this approach applies not only to linear time-invariant models but also to time-varying, subsidized, stochastic, nonlinear and spatial models. It is computationally simple, and does not require calculation of eigenvalues or eigenvectors. The method is presented along with applications to plant and animal populations.

Numerical simulation is a powerful tool for the investigation of complex dynamic systems and transient processes on high performance computers. However, the complexity of many realistic problems in transient dynamics requires very large systems with many time steps to get reliable numerical solutions. A fast parallel algorithm for 3-dimensional transient dynamic problems is described. The vectorized program is used for realistic simulations of mechanical waves for crack detection on a SIEMENS S400/40. The numerical results are compared to results from photoelastic investigations. 1 Transient dynamic simulation In computational dynamics the advantages of numerical simulations are: parameter investigations and the visualization of complex time-dependent processes and interactions in dynamic systems with fast interactive on-line graphics for the better understanding of the mechanical behaviour of the physical model. This is of special interest in many fields of application like earthquake engineering, soil dynamics, non-destructive testing and acoustics, where it is not possible or too expensive to obtain all the desired information by measurements: stresses and strain within a continuous system or the energy flow and intensity within a structure. Numerical simulation is a powerful tool for the investigation of complex dynamic systems and transient processes. However, the complexity of many realistic problems in transient dynamics requires very large systems. Nonlinear problems, three-dimensional problems, transient dynamic problems with a broad frequency range and wave propagation problems Transactions on Information and Communications Technologies vol 9, © 1995 WIT Press, www.witpress.com, ISSN 1743-3517

The utility of transient sensitivity for wildlife management and conservation: Bison as a case study

In order to explore the types of ultrasonic rolling tool head used in ultrasonic rolling and finishing processing device, ANSYS Workbench is taken as a tool to simulate the machining process of ultrasonic rolling processing through transient dynamic analysis, and the maximum residual stress distribution and stress concentration of 45 steel workpiece are analyzed. Based on the simulation result, the ball-type ultrasonic rolling tool head is selected in this work. In addition, the transient dynamics module of ANSYS Workbench is also used to simulate the ultrasonic rolling tool head of different structure parameter, in that way, the accurate and reasonable structure parameters of rolling components of ultrasonic rolling tool head can be achieved. The results of this work show that a ball-type ultrasonic rolling tool head of a diameter of 8mm can make the maximum residual stress minimum and stress concentration slightest under the condition of normal processing of the 45 steel workpiece. In other words, it suggests that this ultrasonic rolling tool head can produce the best surface quality of 45 steel workpiece.

While much of theoretical ecology has focused on the study of long-term asymptotic dynamics of populations, a growing realization is that the study of dynamics on more ecologically relevant timescales is of equal or greater importance. Often, dynamics that occur on shorter, ecologically relevant, timescales are referred to as transient dynamics, and include examples such as disease outbreaks and regime shifts. While any perturbation or environmental change that moves a system away from equilibrium will trigger a transient, this article focuses specifically on those “long transients” whose impact persists over a meaningful timescale (very roughly, dozens of generations or longer). Transient dynamics often lead to significant qualitative changes in an ecological system’s state that can occur with little to no warning at all. In the context of management, transients can cloud the manager’s judgment of the stability of a system. It would be easy to assume the system is in a stable state when it may be near a regime shift (long transients), which may result in inaccurate predictions of long-term dynamics based solely on short-term data. Consequently, the study of transient dynamics involves several avenues, including mathematical theory, management implications, and empirical understanding. New literature in these areas has begun to emerge. The notion of transient dynamics was discussed as early as the mid-1900s, where the idea that steady states are the most ecologically relevant quantities was challenged and the exploration of more complex ecological dynamics was sought. In more recent literature, transient dynamics, the underlying theory, empirical evidence, management implications, and ecological implications have all been more explicitly discussed. One major challenge when dealing with transient dynamics is the infancy of the mathematical theory that underpins much of the necessary analysis. Additionally, the implications transient dynamics have on management and ecological applications are still being developed. However, the significance of transients is now appreciated and research in such areas is attracting much attention. Several important avenues for future research have been made apparent in ecology, and new insights continue to be developed.

Demographic models are widely used to produce management recommendations for different species. For invasive plants, current management recommendations to control local population growth are often based on data from a limited number of populations per species, and the assumption of stable population structure (asymptotic dynamics). However, spatial variation in population dynamics and deviation from a stable structure may affect these recommendations, calling into question their generality across populations of an invasive species. Here, I focused on intraspecific variation in population dynamics and investigated management recommendations generated by demographic models across 37 populations of a short-lived, invasive perennial herb (Lupinus polyphyllus). Models that relied on the proportional perturbations of vital rates (asymptotic elasticities) indicated an essential role for plant survival in long-term population dynamics. The rank order of elasticities for different vital rates (survival, growth, retrogression, fecundity) varied little among the 37 study populations regardless of population status (increasing or declining asymptotically). Summed elasticities for fecundity increased, while summed elasticities for survival decreased with increasing long-term population growth rate. Transient dynamics differed from asymptotic dynamics, but were qualitatively similar among populations, that is, depending on the initial size structure, populations tended to either increase or decline in density more rapidly than predicted by asymptotic growth rate. These findings indicate that although populations are likely to exhibit transient dynamics, management recommendations based on asymptotic elasticities for vital rates might be to some extent generalised across established populations of a given short-lived invasive plant species.

Transient landing dynamics analysis for a lunar lander with random and interval fields

For the last 30 years, cooperative management of irreplaceable animal populations in zoos and aquariums has focused primarily on the goal of minimizing genetic decay within defined time frames, and large advances have been made in technologies to optimize genetic management of closed populations. However, recent analyses have shown that most zoo programs are not projected to meet their stated goals. This has been described as a lack of achieving "sustainability" of the populations, yet by definition a goal of managed decay is not a plan for sustainability. True sustainability requires management of the resource in manner that does not deplete its value for the future. Achieving such sustainability for many managed populations may require changing from managing isolated populations to managing populations that are part of a broader metapopulation, with carefully considered exchange between populations across a spectrum of ex situ to in situ. Managing zoo populations as components of comprehensive conservation strategies for the species will require research on determinants of various kinds of genetic, physiological, behavioral, and morphological variation and their roles in population viability, development of an array of management techniques and tools, training of population managers in metapopulation management and integrated conservation planning, and projections of impacts of management strategies on the viability of the captive populations and all populations that are interactively managed or affected. Such a shift in goals and methods would result in zoo population management being an ongoing part of species conservation rather than short-term or isolated from species conservation. Zoo Biol. 32:19-26, 2013. © 2012 Wiley Periodicals, Inc.

We have observed the transient dynamics in nematic electroconvection during a sudden change in the driving voltage. The steady state dynamics of nematic electroconvection during a constant driving voltage are well characterized examples of spatiotemporal chaos, and thus are useful for the study of chaotic transients. For a set of starting conditions, we were able to show that the system can enter a long-lived transient state with a larger power dissipation rate. This transient state decays through the skew varicose instabilities into steady state defect turbulence. We observed the onset of both Eckhaus and skew varicose instabilities, interpret this transition in the framework of dynamical crisis, and quantify the transition through the evolution of the information entropy in the images as well as the power dissipated by the sample. We identify this long-lived but transient state as originating from the structure of the convective rolls in the initial state and hypothesize that the exploitation of transient states such as these may occur in natural systems and could be leveraged for industrial processing.

At present, development of manufacturer’s ultrasonic cleaning tank (UCT) to match the requirements from consumers usually relies on computer simulation based on harmonic response analysis (HRA). However, this technique can only be used with single-frequency UCT. For dual frequency, the manufacturer used information from empirical experiment alongside trial-and-error methods to develop prototypes, resulting in the UCT that may not be fully efficient. Thus, lack of such a proper calculational method to develop the dual frequency UCT was a problem that greatly impacted the manufacturers and consumers. To resolve this problem, we proposed a new model of simulation using transient dynamics analysis (TDA) which was successfully applied to develop the prototype of dual frequency UCT, 400 W, 18 L in capacity, eight horn transducers, 28 and 40 kHz frequencies for manufacturing. The TDA can indicate the acoustic pressure at all positions inside the UCT in transient states from the start to the states ready for proper cleaning. The calculation also reveals the correlation between the positions of acoustic pressure and the placement positions of transducers and frequencies. In comparison with the HRA at 28 kHz UCT, this TDA yielded the results more accurately than the HRA simulation, comparing to the experiments. Furthermore, the TDA can also be applied to the multifrequency UCTs as well. In this article, the step-by-step development of methodology was reported. Finally, this simulation can lead to the successful design of the high-performance dual frequencies UCT for the manufacturers.

In this paper, we study the asymptotic and transient dynamics of a predator–prey model with square root functional responses and random perturbation. Firstly, the mean square stability matrix is obtained from the stability theory of stochastic systems, and three stability indexes (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the ecosystem response to stochastic disturbances are calculated. We find that: (1) no matter which population is disturbed, increasing the intensity of disturbance improves the ability of the system leaves steady state and thus decreases the stability. The root-mean-square amplification envelope rises with increasing disturbance intensity, (2) the system is more sensitive to the disturbance of the predator than disturbance to prey, (3) ρmax and tmax are important indicators, which represent the intensity and time of maximum amplification by disturbance. These findings are helpful for managers to take corresponding management measures to reduce the disturbances, especially for predators, thereby avoiding the possible change of the structure and functions of the ecosystem.

In accordance with the FAA certification requirements, all modern commercial turbofan engines must successfully demonstrate its ability to withstand a fan blade-out (FBO) event through actual test. Possibility of losing a rotating fan blade from a running engine is a flight safety consideration, which must be addressed during the design phase of the engine. A typical fan blade-out event involves very complex nonlinear transient dynamics with large deflection of the release blade and rigid body rotation of the trailing blade as well as progressive failure and fragmentation of various components. Due to the nature of the impact type loading, the solution to the problem should also address dependence of the material behavior such as yield strength as a function of strain rates. In short, the transient dynamic analysis of a fan blade-out event highlights the complexity of the numerical technique, which includes all the nonlinearities of structural dynamics: plastic behavior of the materials, large displacemen...

This study explores the dynamics of pressure wave propagation and cavitation in pressurized pipelines during and after the rapid closure of the pipeline's end ball valve, utilizing a three-dimensional computational fluid dynamics approach with the method of characteristics, validated against Bergant and Simpson's experimental data of three degrees of cavitation. It innovatively examines transient pressure dynamics through both energy transformation and wave propagation perspectives, focusing on the phases of water column separation and coalescence, and the dynamics of flow interruption bubbles. The research delves into the detailed mechanisms of pressure wave propagation and further assesses the effects of physical factors. Key findings include: (1) As initial inlet velocities increase, cavitation starts earlier, extends further, and intensifies, with higher final volume fractions near the valve, indicating that higher velocities exacerbate cavitation. Higher inlet velocities also correlate with more intricate and expansive vortex formations. (2) Secondary pressure surges in water hammer result from the superposition of two-stage positive pressure waves. Initially, positive pressure waves within the conduit reflect twice from air pockets and the upstream boundary, remaining positive. Subsequently, they interact with secondary positive pressure waves reflected by the valve, causing a secondary pressure surge. (3) The fluid flow is laterally symmetry in the pipe cross section, except for minor local asymmetrical spikes in areas with vapor bubbles. Velocity discrepancies are notable near the pipe walls due to vapor accumulation, primarily on the upper wall due to buoyancy. This accumulation may narrow the flow area, possibly accelerating the water passing by. (4) Lower flow velocities, downward inclines, and slower valve closures diminish secondary pressure rise amplitudes in water hammer events, while reduced static heads intensify cavitation despite lessening pulse amplitudes. These findings offer valuable insights for the design and operational guidance of complex hydraulic systems during transient processes in urban water supplies.