Small Variations In Initial Conditions Research Articles

Alignment Parameters: Quantifying Dense Core Alignment in Star-forming Regions

Abstract Recent high-resolution observations at millimeter (mm) and submillimeter wavelengths reveal a diverse spatial distribution for subparsec-scale dense cores within star-forming regions, ranging from clustered to aligned arrangements. To address the increasing volume of observational and simulation data, we introduce “alignment parameters” as a quantitative and reproducible method to automatically assess core alignment. We first demonstrate the effectiveness of these parameters by applying them to artificial test clumps and comparing the results with labels from visual inspection. A threshold value is then proposed to differentiate between “clustered” and “aligned” categories. Subsequently, we apply these parameters to dense cores identified from a sample of Atacama Large Millimeter/submillimeter Array 1.3 mm dust continuum images in high-mass star-forming regions. Analysis exploring correlations between alignment parameters and clump properties rules out the presence of a moderate or strong correlation, indicating that clump properties do not appear to strongly influence the outcome of fragmentation. One possible explanation for this is that the fragmentation process is chaotic, meaning that small variations in initial conditions can lead to significant differences in fragmentation outcomes, thus obscuring any direct link between clump properties and core alignment/distribution.

The effects of boundary proximity on Kelvin–Helmholtz instability and turbulence

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial flow as an isolated shear layer. In geophysical cases, however, the instability often occurs near boundaries and may therefore be influenced by boundary proximity effects. Ensembles of direct numerical simulations are conducted to understand the effect of boundary proximity on the evolution of the instability and the resulting turbulence. Ensemble averages are used to reduce sensitivity to small variations in initial conditions. Both the transition to turbulence and the resulting turbulent mixing are modified when the shear layer is near a boundary: the time scales for the onset of instability and turbulence are longer, and the height of the KH billow is reduced. Subharmonic instability is suppressed by the boundary because phase lock is prevented due to the diverging phase speeds of the KH and subharmonic modes. In addition, the disruptive influence of three-dimensional secondary instabilities on pairing is more profound as the two events coincide more closely. When the shear layer is far from the boundary, the shear-aligned convective instability is dominant; however, secondary central-core instability takes over when the shear layer is close to the boundary, providing an alternate route for the transition to turbulence. Both the efficiency of the resulting mixing and the turbulent diffusivity are dramatically reduced by boundary proximity effects.

The Effect of Agents' Psychology and Social Environment on the Opinion Formation: C/PA Relative Agreement Model in SW and SF Societies

Opinion dynamics in relative agreement models seen as an extension of bounded confidence ones, involve a new agents’ variable usually called opinion uncertainty and have higher level of complexity than that of bounded confidence models. After revising the meaning of the opinion uncertainty variable we conclude that it has to be interpreted as the agent’s opinion toleration, that changes the type of the variable from the social to the psychological one. Since the convergence rates to the stationary states in dynamics of sociological and psychological variables are in general different, we study the effect of agents’ psychology and social environment interaction on the opinion dynamics, using concord and partial antagonism relative agreement model in small-world and scale-free societies. The model considers agents of two psychological types, concord and partial antagonism, that differs it from other relative agreement models. The analysis of opinion dynamics in particular scenarios was used in this work. Simulation results show the importance of this approach, in particular, the effect of small variations in initial conditions on the final state. We found significant mutual influence of opinion and toleration resulting in a variety of statistically stationary states such as quasi consensus, polarization and fragmentation of society into opinion and toleration groups of different configurations. Consensus was found to be rather rare state in a wide range of model parameters, especially in scale-free societies. The model demonstrates different opinion and toleration dynamics in small-world and scale-free societies.

Second-Order Trajectory Sensitivity Analysis of Hybrid Systems

Hybrid dynamical systems are characterized by intrinsic coupling between continuous dynamics and discrete events. This paper has adopted a differential-algebraic impulsive switched (DAIS) model to capture such dynamic behavior. For such systems, trajectory sensitivity analysis provides a valuable approach for describing perturbations of system trajectories resulting from small variations in initial conditions and/or uncertain parameters. The first-order sensitivities have been fully described for hybrid system and used in a variety of applications. This paper formulates the differential-algebraic equations (DAE) that govern second-order sensitivities over regions where dynamics are smooth, i.e., away from events. It also establishes the jump conditions that describe the step change in second-order sensitivities at discrete (switching and state reset) events. These results together fully characterize second-order sensitivities for general hybrid dynamical system.

Instability Resistance Training Decreases Motor Noise During Challenging Walking Tasks in Older Adults: A 10-Week Double-Blinded RCT.

Locomotor stability is challenged by internal perturbations, e.g., motor noise, and external perturbations, e.g., changes in surface compliance. One means to compensate for such perturbations is to employ motor synergies, defined here as co-variation among a set of elements that acts to stabilize, or provide similar trial-to-trial (or step-to-step) output, even in the presence of small variations in initial conditions. Whereas evidence exists that synergies related to the upper extremities can be trained, the extent to which lower limb synergies, such as those which may be needed to successfully locomote in complex environments, remains unknown. The purpose of this study was to evaluate if resistance training (RT) in unstable environments could promote coordination patterns associated with stronger synergies during gait. Sixty-eight participants between the age of 65 and 80 were randomly assigned to one of three different RT modalities: stable whole-limb machine-based RT (S-MRT), instability free-weight RT (I-FRT), and stable machine-based adductor/abductor RT (S-MRTHIP). Before and after RT, participants walked across an even lab floor and a more challenging uneven surface with and without holding a weighted bag. The uncontrolled manifold control analysis (UCM) was used to calculate the synergy index (i.e., strength of the kinematic synergy) related to stabilization of our performance variable, the mediolateral trajectory of the swing foot, under each condition. Regardless of RT group, there was no effect of RT on the synergy index when walking across the even lab floor. However, the synergy index during the two uneven surface conditions was stronger after I-FRT but was not affected by the other RT modalities. The stronger synergy index for the I-FRT group was due to improved coordination as quantified by an overall increase in variability in elemental variable space but a decrease in the variability that negatively affects performance. The unstable environment offered by I-FRT allows for exploration of motor solutions in a manner that appears to transfer to challenging locomotor tasks. Introducing tasks that promote, rather than limit, exploration of motor solutions seems to be a valuable exercise modality to strengthen kinematic synergies that cannot be achieved with traditional strengthening paradigms (e.g., S-MRT).Clinical Trial Registration: www.ClinicalTrials.gov, identifier NCT03017365.

The Impact of Educational Interventions on Real & Stylized Cities

Abstract : Different cities and different populations react differently to various types of educational interventions due to small differences in population, socio-demographic traits, intervention media type, and a variety of other factors. The social simulation tool Construct was used to evaluate the effectiveness of several educational interventions on one stylized and four real cities to examine the types of behavior that could be observed given these small variations in initial conditions. This technical report describes the experimental design, parameters, and setup for the Construct educational intervention virtual experiments, then reports the results obtained when the experiments were run. The results from the stylized city and real cities are compared, and general similarities and conclusions are discussed.

Image Authentication using RSA and Chaotic Map

Authentication is basically a way by which sender and recipient must prove their identities to each other. Image authentication verifies the originality of an image by detecting malicious manipulations. Reliable image authentication technology must be able to protect an image from time it was first produced until the final stage of use. In this paper we describe an effective technique for image authentication which can prevent malicious manipulations by using RSA and Baker’s map. Chaos refers to a type of complex dynamical behavior that possesses some special features such as being extremely sensitive to small variations in initial conditions. Moreover this is certificateless-based scheme and allows people to verify the signature without the certificate. For this reason, we do not need the certificate authority to store and manage user’s certificates. In 2014, Chin-Chen Chang, Chin-Yu Sun, and Shih-Chang Chang has given a similar designed certificateless-based signature scheme based on RSA operations; however, their scheme is modified and improved by using it on image rather than text [2]. General Terms Chaotic map, RSA, Digital Signature, Random number, MD5. SHA-1.

High predictability of spring phytoplankton biomass in mesocosms at the species, functional group and community level

Summary1. Models aim to predict phytoplankton dynamics based on observed initial conditions and a set of equations and parameters. However, our knowledge about initial conditions in nature is never perfect. Thus, if phytoplankton dynamics are sensitive to small variations in initial conditions, they are difficult to predict.2. We used time‐series data from indoor mesocosm experiments with natural phyto‐ and zooplankton communities to quantify the extent to which small initial differences in the species, functional group and community biomass in parallel treatments were amplified or buffered over time. We compared the differences in dynamics between replicates and among all mesocosms of 1 year.3. Temperature‐sensitive grazing during the exponential growth phase of phytoplankton caused divergence. In contrast, negative density dependence caused convergence.4. Mean differences in biomass between replicates were similar for all hierarchical levels. This indicates that differences in their initial conditions were amplified to the same extent. Even though large differences in biomass occasionally occurred between replicates for a short time, dynamics returned to the same path at all hierarchical levels. This suggests that internal feedback mechanisms make the spring development of phytoplankton highly predictable.

Chaos: A Very Short Introduction

This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2.' Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book is also getting a bit too intricate for the complete layman, and experts may not agree on all details of the more conceptual discussions. Altogether I thoroughly enjoyed reading this book. It was a happy companion while travelling and a nice bedtime literature. It is furthermore an excellent reminder of the `big picture' underlying nonlinear science as it applies to the real world. I will gladly recommend this book as background literature for students in my introductory course on dynamical systems. However, the book will be of interest to anyone who is looking for a very short account on fundamental problems and principles in modern nonlinear science.

Entanglement, fidelity and quantum chaos in cavity QED

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom–field system as a quantum–classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Chaos manifests itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with prominent fractal-like behavior and in the quantum atom–field degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom–field resonance correlate strongly. It is shown that the Jaynes–Cummings dynamics can be unstable in the regime of chaotic walking of an atom in the quantized field of a standing wave in the absence of any other interaction with environment. Quantum instability manifests itself in strong variations of quantum purity and entropy and in exponential sensitivity of fidelity of quantum states to small variations in the atom–field detuning. It is quantified in terms of the respective classical maximal Lyapunov exponent that can be estimated in appropriate in–out experiments. This result provides a quantum–classical correspondence in a closed physical system.

A systems approach to self‐organization in the dreaming brain

This systems model of dreaming consciousness examines the self‐organizing properties of the sleeping brain, offering a step towards reconciling brain‐based and content‐based attempts to understand the nature of dreaming. The brain can be understood as a complex self‐organizing system that, in dreaming, responds to subtle influences such as residual feelings and memories. The hyper‐responsiveness of the brain during dreaming is viewed in terms of the tendency of complex chaotic‐like systems to respond to small variations in initial conditions and to the amplification of subtle emotional and cognitive signals through the mechanism of stochastic resonance, all in combination with psychophysiological changes in the brain during both slow wave and rapid eye movement (REM) dreaming. These changes include the active inhibition of extroceptive stimulation and, especially in REM sleep, alterations in the brain's dominant neuromodulatory systems, bombardment of the visual cortex with bursts of PGO activity, increases in limbic system activity, and a reduction of activity in the prefrontal regions.

Building the B-29 by Jacob Vander Meulen, and: Courage and Air Warfare: The Allied Aircrew Experience in the Second World War by Mark K. Wells

788 Book Reviews TECHNOLOGY AND CULTURE renz and others demonstrated in the 1970s that the atmosphere is a chaotic system whose behavior is all too sensitive to small variations in initial conditions. Once again, Nebeker points out, the refractory nature of meteorology stimulated mathematical innovation. Except for a few pages showing the results of archival research in the papers of von Neumann and Charney, Nebeker exploits only published sources. There is ample material among these, however, including numerous retrospective and review articles by meteorolo­ gists, for a first survey of an uncharted area. The author takes care to explain most technical concepts, though occasionally he falters: readers outside of meteorology would appreciate, for example, an explanation of the significance of the 500 mb surface. Otherwise the book reads well and offers convincing suggestions of the ways in which institutional and military factors directed meteorology to­ ward computational approaches. Calculating the Weather is a wel­ come addition to a field still largely neglected by historians of sci­ ence. Theodore S. Feldman Dr. Feldman studies the history of meteorology in the early modern period and is currently preparing a book on the idea of climate in the Enlightenment. BuildingtheB-29. Byjacob Vander Meulen. Washington, D.C.: Smith­ sonian Institution Press, 1995. Pp. 128; illustrations, figures, bibli­ ography. $18.95 (cloth). Courage and Air Warfare: TheAlliedAircrewExperience in the Second World War. By Mark K. Wells. London: Frank Cass, 1995. Pp. xv+240; illustrations, notes, bibliography, index. $40.00 (cloth) $22.50 (paper). Human factors are often the key to successful deployment of mili­ tary technology in wartime. These two titles take a look at such fac­ tors from two different perspectives. Mark Wells’s Courage and Air Warfare analyzes operational functions; Jacob Vander Meulen’s Building the B-29 considers the manufacturing process. Mark Wells, a United States Air Force colonel, amassed some 2,400 flight hours and acquired a Ph.D. in War Studies from King’s Col­ lege, University of London; he currently teaches history at the Air Force Academy. He uses a comparative method to assess the experi­ ence of the U.S. Eighth Air Force and the RAF’s Bomber Command over Europe in World War II. Both air arms had a common goal, but applied different approaches in terms of crew selection, combat assignments, and responses to wartime stress. In the RAF, aircrew who experienced severe combat fatigue and were unable to fly on combat missions were declared to have “Lack of Moral Fiber” TECHNOLOGY AND CULTURE Book Reviews 789 (LMF) and assigned to a variety of nonflying tasks. Such reassign­ ments were clearly seen as punitive, and the stigma of LMF stamped on one’s personnel file often contributed to a lifetime of guilt and resentment. Using obscure medical records and impressive research techniques, Wells effectively compares the British practice with the American approach, which was more inclined to psychological treat­ ment and rehabilitation. Still, both services experienced roughly the same number of emotional casualties. This is a sensitive, informative study. Jacob Vander Meulen, professor of history at Dalhousie Univer­ sity, has written on the politics of aircraft production and various aspects of labor relations. In this brief but engrossing book, he fo­ cuses on the remarkable story of the Boeing B-29 Superfortress. This was one of the first airplane production efforts to effectively employ a style later tagged as “concurrency,” in which construction offacto­ ries and specialized tooling began as the plane progressed through preliminary design and early test phases. By the time the B-29 was cleared for production, an elaborate system of subcontractors and new fabrication facilities was already in place. Vander Meulen also describes the incredibly diverse work force recruited for B-29 pro­ duction lines, employing seamstresses, filling station attendants, cocktail waitresses, farmhands, and others. All had to be trained in esoteric production tasks for hydraulic lines, fuel gauges, electronic gun sights, and huge slabs of aluminum skin—the myriad compo­ nents for one ofthe most sophisticated military machines of the war. Many components were designed so as to be more producible by the masses of unskilled workers on B-29 assembly lines. Enhanced by dozens of rare photos, this is...

Inelastic collapse of three particles.

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.

Estimation of skill and uncertainty in regional numerical models

AbstractThe results from 72‐hour simulations and forecasts from the Penn State/NCAR limited‐area model, in which a number of numerical and physical factors are varied, are analysed to understand the contribution to model error or uncertainty introduced by these factors. The factors include the initial conditions, horizontal resolution (80 km and 160 km) and domain size, lateral boundary conditions, and physical parametrizations. The results are compared with those of a global forecast model (the NCAR Community Climate Model). The simulations and forecasts are verified both for 12 individual cases and for the ensemble average of the 12 cases, using several objective measures of skill. The differences in these skill scores between different models are tested for their statistical significance.The use of observed lateral boundary conditions (LBC) exerts a strong control on the growth of errors over a domain size 3600 × 4800 km2. Objective measures of error show little growth beyond about 36 hours, so that 72‐hour errors are nearly as low as the 36‐hour errors. On these time and space scales, the quality of the LBC is more important than any other factor tested in the temporal evolution of the model errors. These results show that the large‐scale atmospheric motions have a major effect on the evolution of small‐scale features in the model.Small variations in initial conditions have little effect on the model skill beyond 12–24 hours. Of all the factors examined, small uncertainties or errors in the initial conditions have the least effect on model skill beyond 12 hours.Latent heating effects associated with condensation and precipitation, and sensible and latent heat fluxes from the surface have a statistically significant effect on model skill. However, relatively simple parametrizations of these effects produce nearly the same skill as do more complex schemes for the cases studied here.There is a large variation in model skill from case to case; some cases are easier to forecast than others. Also, there is much greater variation in different model performances for a single case than when averaged over all 12 cases.The concept of climatological use and verification of regional models is introduced. The climatological skill of the control model version which includes all physical processes appears to be quite good. The skill scores of the ensemble average simulation are considerably better than the average scores for individual cases, the model has small bias errors, and the horizontal structure of the model‐simulated atmosphere is similar to the observed structure for scales of motion resolved by the upper‐air observational network over the United States.

How well does Turing's theory of morphogenesis work?

In 1952 Turing published a paper which showed how under restricted conditions a class of chemical reactions could give biological patterns in diffusion-coupled cells. Although this theory has been much discussed, little has been learnt about the range and type of pattern it can generate. In order to do this and to see how stable the patterns are, we have examined the system in detail and written a computer program to simulate Turing's kinetics for two morphogens over various assemblies of cells. We find that on one-dimensional lines of cells, patterns can indeed be produced and that the chemical wavelengths follow all of Turing's predictions. The results show that stable repeating peaks of chemical concentration of periodicity 2–20 cells can be obtained in embryos in periods of time of less than an hour. We do find however that these patterns are not reliable: small variations in initial conditions give small but significant changes in the number and positions of observed peaks. Similar results are observed in two-dimensional assemblies of cells. On rectangles, random blotches are observed whose position cannot be reliably predicted. On cylinders whose circumference is less than the chemical wavelength, annular stripes are produced. For larger cylinders, blotches that lie very approximately on helices are generated; again sharp prediction of the detailed pattern is impossible. The significance of these results for the developing embryo is discussed. We conclude that Turing kinetics, at least in the simple cases that we have studied, are too unreliable to serve as the generating mechanism for features such as digits which are characterized by a consistent number of units. The theory is however more than adequate by these criteria to specify less well-defined developing patterns such as those of hair follicles or leaf organization. It is emphasized however that the Turing theory is quite unable to generate regulative systems, only mosaicpatterns can be produced.