Marangoni-driven chemotaxis, chemotactic collapse, and the Keller-Segel equation

NASA Astrophysics Data System (ADS)

Shelley, Michael; Masoud, Hassan

2013-11-01

Almost by definition, chemotaxis involves the biased motion of motile particles along gradients of a chemical concentration field. Perhaps the most famous model for collective chemotaxis in mathematical biology is the Keller-Segel model, conceived to describe collective aggregation of slime mold colonies in response to an intrinsically produced, and diffusing, chemo-attractant. Heavily studied, particularly in 2D where the system is ``super-critical'', it has been proved that the KS model can develop finite-time singularities - so-called chemotactic collapse - of delta-function type. Here, we study the collective dynamics of immotile particles bound to a 2D interface above a 3D fluid. These particles are chemically active and produce a diffusing field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. Remarkably, we show that this system involving 3D diffusion and fluid dynamics, exactly yields the 2D Keller-Segel model for the surface-flow of active particles. We discuss the consequences of collapse on the 3D fluid dynamics, and generalizations of the fluid-dynamical model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rycroft, Chris H.; Bazant, Martin Z.

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape.more » This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.« less

Apparent Strength Conceals Instability in a Model for the Collapse of Historical States

PubMed Central

Lawson, Daniel John; Oak, Neeraj

2014-01-01

An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We examine political disintegration across eras, cultures and geographical scale to form a simple hypothesis that can be expressed verbally yet formulated mathematically. Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion. In lieu of precise data we verify our model using sensitivity analysis. We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree. PMID:24810228

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part II: reactive case

NASA Astrophysics Data System (ADS)

Michael, L.; Nikiforakis, N.

2018-02-01

This work is concerned with the effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The main objective is to understand the origin of localised temperature peaks (hot spots) which play a leading order role at the early stages of ignition. To this end, we perform two- and three-dimensional numerical simulations of shock-induced single gas-cavity collapse in liquid nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. In the first part of this work, we focused on the hydrodynamic effects in the collapse process by switching off the reaction terms in the mathematical formulation. In this part, we reinstate the reactive terms and study the collapse of the cavity in the presence of chemical reactions. By using a multi-phase formulation which overcomes current challenges of cavity collapse modelling in reactive media, we account for the large density difference across the material interface without generating spurious temperature peaks, thus allowing the use of a temperature-based reaction rate law. The mathematical and physical models are validated against experimental and analytic data. In Part I, we demonstrated that, compared to experiments, the generated hot spots have a more complex topological structure and that additional hot spots arise in regions away from the cavity centreline. Here, we extend this by identifying which of the previously determined high-temperature regions in fact lead to ignition and comment on the reactive strength and reaction growth rate in the distinct hot spots. We demonstrate and quantify the sensitisation of nitromethane by the collapse of the isolated cavity by comparing the ignition times of nitromethane due to cavity collapse and the ignition time of the neat material. The ignition in both the centreline hot spots and the hot spots generated by Mach stems occurs in less than half the ignition time of the neat material. We compare two- and three-dimensional simulations to examine the change in topology, temperatures, and reactive strength of the hot spots by the third dimension. It is apparent that belated ignition times can be avoided by the use of three-dimensional simulations. The effect of the chemical reactions on the topology and strength of the hot spots in the timescales considered is also studied, in a comparison between inert and reactive simulations where maximum temperature fields and their growth rates are examined.

Hydrocarbons pipeline transportation risk assessment

NASA Astrophysics Data System (ADS)

Zanin, A. V.; Milke, A. A.; Kvasov, I. N.

2018-04-01

The pipeline transportation applying risks assessment issue in the arctic conditions is addressed in the paper. Pipeline quality characteristics in the given environment has been assessed. To achieve the stated objective, the pipelines mathematical model was designed and visualized by using the software product SOLIDWORKS. When developing the mathematical model the obtained results made possible to define the pipeline optimal characteristics for designing on the Arctic sea bottom. In the course of conducting the research the pipe avalanche collapse risks were examined, internal longitudinal and circular loads acting on the pipeline were analyzed, as well as the water impact hydrodynamic force was taken into consideration. The conducted calculation can contribute to the pipeline transport further development under the harsh climate conditions of the Russian Federation Arctic shelf territory.

Experimental Verification of Steel Pipe Collapse under Vacuum Pressure Conditions

NASA Astrophysics Data System (ADS)

Autrique, R.; Rodal, E.

2016-11-01

Steel pipes are used widely in hydroelectric systems and in pumping systems. Both systems are subject to hydraulic transient effects caused by changes in boundary conditions, such as sudden valve closures, pump failures, or accidents. Water column separation, and its associated vaporization pressure inside the pipe, can cause the collapse of thin walled steel pipes subject to atmospheric pressure, as happened during the well known Oigawa Power Plant accident in Japan, in 1950. The conditions under which thin walled pipes subject to external pressure can collapse have been studied mathematically since the second half of the XIX century, with classical authors Southwell and Von Mises obtaining definitive equations for long and short pipes in the second decade of the XX century, in which the fundamental variables are the diameter to thickness ratio D/t and the length to diameter ratio L/D. In this paper, the predicted critical D/t ratio for steel pipe collapse is verified experimentally, in a physical model able to reproduce hydraulic transients, generating vacuum pressures through rapid upstream valve closures.

All together now: Analogies between chimera state collapses and epileptic seizures

NASA Astrophysics Data System (ADS)

Andrzejak, Ralph G.; Rummel, Christian; Mormann, Florian; Schindler, Kaspar

2016-03-01

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena. A recent and not yet fully understood example is the collapse of coexisting synchronous and asynchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications.

Pore opening dynamics in the exocytosis of serotonin

NASA Astrophysics Data System (ADS)

Ramirez-Santiago, Guillermo; Cercos, Montserrat G.; Martinez-Valencia, Alejandro; Salinas Hernandez, Israel; Rodríguez-Sosa, Leonardo; de-Miguel, Francisco F.

2015-03-01

The current view of the exocytosis of transmitter molecules is that it starts with the formation of a fusion pore that connects the intravesicular and the extracellular spaces, and is completed by the release of the rest of the transmitter contained in the vesicle upon the full fusion and collapse of the vesicle with the plasma membrane. However, under certain circumstances, a rapid closure of the pore before the full vesicle fusion produces only a partial release of the transmitter. Here we show that whole release of the transmitter occurs through fusion pores that remain opened for tens of milliseconds without vesicle collapse. This was demonstrated through amperometric measurements of serotonin release from electrodense vesicles in the axon of leech Retzius neurons and mathematical modelling. By modeling transmitter release with a diffusion equation subjected to boundary conditions that are defined by the experiment, we showed that those pores with a fast half rise time constant remained opened and allowed the full quantum release without vesicle collapse, whereas pores with a slow rise time constant closed rapidly, thus producing partial release. We conclude that a full transmitter release may occur through the fusion pore in the absence of vesicle collapse. This work was founded by a DGAPA-UNAM grants IN200914 and IN118410 CONACYT GRANT 130031, and CONACyT doctoral fellowships.

Survey mirrors and lenses and their required surface accuracy. Volume 2. Concentrator optical performance software (COPS) user's manual. Final report for September 15, 1978-December 1, 1979

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1980-01-01

The mathematical modeling of 11 different concentrating collectors is documented and instructions are given for use of the computer code. The 11 concentrators modeled are: faceted mirror concentration; fixed mirror, two-axis tracking receiver; parabolic trough collector; linear Fresnel; incremental reflector; inflated cylindrical concentrator; CPC-involute reflector with evacuated receiver; CPC-parabolic/involute reflector; V trough collectors, imaging collapsing concentrator; and parabolic dish collector. (MHR)

Behavioral Modulation of Infestation by Varroa destructor in Bee Colonies. Implications for Colony Stability.

PubMed

de Figueiró Santos, Joyce; Coelho, Flávio Codeço; Bliman, Pierre-Alexandre

2016-01-01

Colony Collapse Disorder (CCD) has become a global problem for beekeepers and for the crops that depend on bee pollination. While many factors are known to increase the risk of colony collapse, the ectoparasitic mite Varroa destructor is considered to be the most serious one. Although this mite is unlikely to cause the collapse of hives itself, it is the vector for many viral diseases which are among the likely causes for Colony Collapse Disorder. The effects of V. destructor infestation differ from one part of the world to another, with greater morbidity and higher colony losses in European honey bees (EHB) in Europe, Asia and North America. Although this mite has been present in Brazil for many years, there have been no reports of colony losses amongst Africanized Honey Bees (AHB). Studies carried out in Mexico have highlighted different behavioral responses by the AHB to the presence of the mite, notably as far as grooming and hygienic behavior are concerned. Could these explain why the AHB are less susceptible to Colony Collapse Disorder? In order to answer this question, we have developed a mathematical model of the infestation dynamics to analyze the role of resistance behavior by bees in the overall health of the colony, and as a consequence, its ability to face epidemiological challenges.

Pressure oscillation delivery to the lung: Computer simulation of neonatal breathing parameters.

PubMed

Al-Jumaily, Ahmed M; Reddy, Prasika I; Bold, Geoff T; Pillow, J Jane

2011-10-13

Preterm newborn infants may develop respiratory distress syndrome (RDS) due to functional and structural immaturity. A lack of surfactant promotes collapse of alveolar regions and airways such that newborns with RDS are subject to increased inspiratory effort and non-homogeneous ventilation. Pressure oscillation has been incorporated into one form of RDS treatment; however, how far it reaches various parts of the lung is still questionable. Since in-vivo measurement is very difficult if not impossible, mathematical modeling may be used as one way of assessment. Whereas many models of the respiratory system have been developed for adults, the neonatal lung remains essentially ill-described in mathematical models. A mathematical model is developed, which represents the first few generations of the tracheo-bronchial tree and the 5 lobes that make up the premature ovine lung. The elements of the model are derived using the lumped parameter approach and formulated in Simulink™ within the Matlab™ environment. The respiratory parameters at the airway opening compare well with those measured from experiments. The model demonstrates the ability to predict pressures, flows and volumes in the alveolar regions of a premature ovine lung. Copyright © 2011 Elsevier Ltd. All rights reserved.

Catastrophic desert formation in Daisyworld.

PubMed

Ackland, Graeme J; Clark, Michael A; Lenton, Timothy M

2003-07-07

Feedback between life and its environment is ubiquitous but the strength of coupling and its global implications remain hotly debated. Abrupt changes in the abundance of life for small changes in forcing provide one indicator of regulation, for example, when vegetation-climate feedback collapses in the formation of a desert. Here we use a two-dimensional "Daisyworld" model with curvature to show that catastrophic collapse of life under gradual forcing provides a testable indicator of environmental feedback. When solar luminosity increases to a critical value, a desert forms across a wide band of the planet. The scale of collapse depends on the strength of feedback. The efficiency of temperature regulation is limited by mutation rate in an analogous manner to the limitation of adaptive fitness in evolutionary theories. The final state of the system emerging from single-site rules can be described by two global quantities: optimization of temperature regulation and maximization of diversity, which are mathematically analogous to energy and entropy in thermodynamics.

Numerical modeling of keyhole dynamics in laser welding

NASA Astrophysics Data System (ADS)

Zhang, Wen-Hai; Zhou, Jun; Tsai, Hai-Lung

2003-03-01

Mathematical models and the associated numerical techniques have been developed to study the following cases: (1) the formation and collapse of a keyhole, (2) the formation of porosity and its control strategies, (3) laser welding with filler metals, and (4) the escape of zinc vapor in laser welding of galvanized steel. The simulation results show that the formation of porosity in the weld is caused by two competing mechanisms: one is the solidification rate of the molten metal and the other is the speed that molten metal backfills the keyhole after laser energy is terminated. The models have demonstrated that porosity can be reduced or eliminated by adding filler metals, controlling laser tailing power, or applying an electromagnetic force during keyhole collapse process. It is found that a uniform composition of weld pool is difficult to achieve by filler metals due to very rapid solidification of the weld pool in laser welding, as compared to that in gas metal arc welding.

Newtonian semiclassical gravity in three ontological quantum theories that solve the measurement problem: Formalisms and empirical predictions

NASA Astrophysics Data System (ADS)

Derakhshani, Maaneli

In this thesis, we consider the implications of solving the quantum measurement problem for the Newtonian description of semiclassical gravity. First we review the formalism of the Newtonian description of semiclassical gravity based on standard quantum mechanics---the Schroedinger-Newton theory---and two well-established predictions that come out of it, namely, gravitational 'cat states' and gravitationally-induced wavepacket collapse. Then we review three quantum theories with 'primitive ontologies' that are well-known known to solve the measurement problem---Schroedinger's many worlds theory, the GRW collapse theory with matter density ontology, and Nelson's stochastic mechanics. We extend the formalisms of these three quantum theories to Newtonian models of semiclassical gravity and evaluate their implications for gravitational cat states and gravitational wavepacket collapse. We find that (1) Newtonian semiclassical gravity based on Schroedinger's many worlds theory is mathematically equivalent to the Schroedinger-Newton theory and makes the same predictions; (2) Newtonian semiclassical gravity based on the GRW theory differs from Schroedinger-Newton only in the use of a stochastic collapse law, but this law allows it to suppress gravitational cat states so as not to be in contradiction with experiment, while allowing for gravitational wavepacket collapse to happen as well; (3) Newtonian semiclassical gravity based on Nelson's stochastic mechanics differs significantly from Schroedinger-Newton, and does not predict gravitational cat states nor gravitational wavepacket collapse. Considering that gravitational cat states are experimentally ruled out, but gravitational wavepacket collapse is testable in the near future, this implies that only the latter two are viable theories of Newtonian semiclassical gravity and that they can be experimentally tested against each other in future molecular interferometry experiments that are anticipated to be capable of testing the gravitational wavepacket collapse prediction.

Burrowing activity in channel levees: impact of the invasive red swamp crayfish Procambarus clarkii

NASA Astrophysics Data System (ADS)

Solari, L.; Bendoni, M.; Consumi, L.; Haubrock, P.; Inghilesi, A.; Mazza, G.; Torrini, M.; Tricarico, E.

2016-12-01

The effect of animal burrowing, as an example of bioturbation on the stability of river levees has been recently raised to the scientific community as a consequence of the levee collapses of Secchia and Foenna rivers in Italy (Camici et al., 2010, 2014; Orlandini et al., 2015). Indeed, these authors showed that the presence of animal burrows is crucial in promoting the collapse of the bank. The American red swamp Crayfish Procambarus clarkii is an invasive species in Europe, mostly introduced for commercial purposes related to livestock. It is rapidly spreading throughout the Italian peninsula due to its plasticity, dispersal capability and high reproduction rate (Souty-Grosset et al., 2016). As well as the negative effects on local biodiversity, it damages the levees of the irrigation channel leading to disastrous collapses, relevant repairing and maintenance costs. In this work, we present an experimental activity where specimens of P. clarkii were monitored while burrowing into a small-scale physical model of an earthen levee, coupled with the mathematical modelling of the variations induced by the burrows on the seepage flow patterns through the levee.Preliminary results show the burrowing structure was quite irregular. Generally, crayfish start burrowing under the water level, developing tunnels (diameter ranging 4-7cm) both horizontally and heading upward, also above the water level. Some tunnels showed one or more circular chambers. The highest burrowing activity was observed during the experiments carried out in summer, when the species has a peak of maximum activity due to the higher temperature. Mathematical modelling shows that, for given boundary conditions and experimental duration, the presence of burrows in the levee raises the phreatic line. Critical conditions for levee integrity may be associated either to the internal erosion and stability of the system of tunnels and to the emergence of the phreatic line of the landside of the levee slope. These aspects are currently under investigation.

How Hives Collapse: Allee Effects, Ecological Resilience, and the Honey Bee

PubMed Central

Dennis, Brian; Kemp, William P.

2016-01-01

We construct a mathematical model to quantify the loss of resilience in collapsing honey bee colonies due to the presence of a strong Allee effect. In the model, recruitment and mortality of adult bees have substantial social components, with recruitment enhanced and mortality reduced by additional adult bee numbers. The result is an Allee effect, a net per-individual rate of hive increase that increases as a function of adult bee numbers. The Allee effect creates a critical minimum size in adult bee numbers, below which mortality is greater than recruitment, with ensuing loss of viability of the hive. Under ordinary and favorable environmental circumstances, the critical size is low, and hives remain large, sending off viably-sized swarms (naturally or through beekeeping management) when hive numbers approach an upper stable equilibrium size (carrying capacity). However, both the lower critical size and the upper stable size depend on many parameters related to demographic rates and their enhancement by bee sociality. Any environmental factors that increase mortality, decrease recruitment, or interfere with the social moderation of these rates has the effect of exacerbating the Allee effect by increasing the lower critical size and substantially decreasing the upper stable size. As well, the basin of attraction to the upper stable size, defined by the model potential function, becomes narrower and shallower, indicating the loss of resilience as the hive becomes subjected to increased risk of falling below the critical size. Environmental effects of greater severity can cause the two equilibria to merge and the basin of attraction to the upper stable size to disappear, resulting in collapse of the hive from any initial size. The model suggests that multiple proximate causes, among them pesticides, mites, pathogens, and climate change, working singly or in combinations, could trigger hive collapse. PMID:26910061

Qualitative mathematical models to support ecosystem-based management of Australia's Northern Prawn Fishery.

PubMed

Dambacher, Jeffrey M; Rothlisberg, Peter C; Loneragan, Neil R

2015-01-01

A major decline in the catch of the banana prawn [shrimp], Penaeus (Fenneropenaeus) merguiensis, occurred over a six-year period in the Weipa region of the northeastern Gulf of Carpentaria, Australia. Three main hypotheses have been developed to explain this decline: (1) prawn recruitment collapsed due to overfishing; (2) recruitment collapsed due to a change in the prawn's environment; and (3) adult banana prawns were still present, but fishers could no longer effectively find or catch them. Qualitative mathematical models were used to link population biology, environmental factors, and fishery dynamics to evaluate the alternative hypotheses. This modeling approach provides the means to rapidly integrate knowledge across disciplines and consider alternative hypotheses about how the structure and function of an ecosystem affects its dynamics. Alternative models were constructed to address the different hypotheses and also to encompass a diversity of opinion about the underlying dynamics of the system. Key findings from these analyses are that: instability in the system can arise when discarded fishery bycatch supports relatively high predation pressure; system stability can be enhanced by management of fishing effort or stock catchability; catch per unit effort is not necessarily a reliable indicator of stock abundance; a change in early-season rainfall should affect all stages in the banana prawn's life cycle; and a reduced catch in the Weipa region can create and reinforce a shift in fishing effort away from Weipa. Results from the models informed an approach to test the hypotheses (i.e., an experimental fishing program), and promoted understanding of the system among researchers, management agencies, and industry. The analytical tools developed in this work to address stages of a prawn life cycle and fishery dynamics are generally applicable to any exploited natural. resource.

Axelrod's Metanorm Games on Networks

PubMed Central

Galán, José M.; Łatek, Maciej M.; Rizi, Seyed M. Mussavi

2011-01-01

Metanorms is a mechanism proposed to promote cooperation in social dilemmas. Recent experimental results show that network structures that underlie social interactions influence the emergence of norms that promote cooperation. We generalize Axelrod's analysis of metanorms dynamics to interactions unfolding on networks through simulation and mathematical modeling. Network topology strongly influences the effectiveness of the metanorms mechanism in establishing cooperation. In particular, we find that average degree, clustering coefficient and the average number of triplets per node play key roles in sustaining or collapsing cooperation. PMID:21655211

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect.

PubMed

Hilker, Frank M

2010-01-01

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ℛ(0)≫1.

The role of cavitation in liposome formation.

PubMed

Richardson, Eric S; Pitt, William G; Woodbury, Dixon J

2007-12-15

Liposome size is a vital parameter of many quantitative biophysical studies. Sonication, or exposure to ultrasound, is used widely to manufacture artificial liposomes, yet little is known about the mechanism by which liposomes are affected by ultrasound. Cavitation, or the oscillation of small gas bubbles in a pressure-varying field, has been shown to be responsible for many biophysical effects of ultrasound on cells. In this study, we correlate the presence and type of cavitation with a decrease in liposome size. Aqueous lipid suspensions surrounding a hydrophone were exposed to various intensities of ultrasound and hydrostatic pressures before measuring their size distribution with dynamic light scattering. As expected, increasing ultrasound intensity at atmospheric pressure decreased the average liposome diameter. The presence of collapse cavitation was manifested in the acoustic spectrum at high ultrasonic intensities. Increasing hydrostatic pressure was shown to inhibit the presence of collapse cavitation. Collapse cavitation, however, did not correlate with decreases in liposome size, as changes in size still occurred when collapse cavitation was inhibited either by lowering ultrasound intensity or by increasing static pressure. We propose a mechanism whereby stable cavitation, another type of cavitation present in sound fields, causes fluid shearing of liposomes and reduction of liposome size. A mathematical model was developed based on the Rayleigh-Plesset equation of bubble dynamics and principles of acoustic microstreaming to estimate the shear field magnitude around an oscillating bubble. This model predicts the ultrasound intensities and pressures needed to create shear fields sufficient to cause liposome size change, and correlates well with our experimental data.

A qualitative multiresolution model for counterterrorism

NASA Astrophysics Data System (ADS)

Davis, Paul K.

2006-05-01

This paper describes a prototype model for exploring counterterrorism issues related to the recruiting effectiveness of organizations such as al Qaeda. The prototype demonstrates how a model can be built using qualitative input variables appropriate to representation of social-science knowledge, and how a multiresolution design can allow a user to think and operate at several levels - such as first conducting low-resolution exploratory analysis and then zooming into several layers of detail. The prototype also motivates and introduces a variety of nonlinear mathematical methods for representing how certain influences combine. This has value for, e.g., representing collapse phenomena underlying some theories of victory, and for explanations of historical results. The methodology is believed to be suitable for more extensive system modeling of terrorism and counterterrorism.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. V.; Yerazunis, S. W.

1973-01-01

Problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars are reported. Problem areas include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis, terrain modeling and path selection; and chemical analysis of specimens. These tasks are summarized: vehicle model design, mathematical model of vehicle dynamics, experimental vehicle dynamics, obstacle negotiation, electrochemical controls, remote control, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, and chromatograph model evaluation and improvement.

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case

NASA Astrophysics Data System (ADS)

Michael, L.; Nikiforakis, N.

2018-02-01

This work is concerned with the effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The main objective is to understand the origin of localised temperature peaks (hot spots) which play a leading order role at the early stages of ignition. To this end, we perform two- and three-dimensional numerical simulations of shock-induced single gas-cavity collapse in liquid nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. In order to understand the relative contribution between these two processes, we consider in this first part of the work the evolution of the physical system in the absence of chemical reactions. We employ a multi-phase mathematical formulation which can account for the large density difference across the gas-liquid material interface without generating spurious temperature peaks. The mathematical and physical models are validated against experimental, analytic, and numerical data. Previous inert studies have identified the impact of the upwind (relative to the direction of the incident shock wave) side of the cavity wall to the downwind one as the main reason for the generation of a hot spot outside of the cavity, something which is also observed in this work. However, it is also apparent that the topology of the temperature field is more complex than previously thought and additional hot spot locations exist, which arise from the generation of Mach stems rather than jet impact. To explain the generation mechanisms and topology of the hot spots, we carefully follow the complex wave patterns generated in the collapse process and identify specifically the temperature elevation or reduction generated by each wave. This enables tracking each hot spot back to its origins. It is shown that the highest hot spot temperatures can be more than twice the post-incident shock temperature of the neat material and can thus lead to ignition. By comparing two-dimensional and three-dimensional simulation results in the context of the maximum temperature observed in the domain, it is apparent that three-dimensional calculations are necessary in order to avoid belated ignition times in reactive scenarios.

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Testing collapse models by a thermometer

NASA Astrophysics Data System (ADS)

Bahrami, M.

2018-05-01

Collapse models postulate that space is filled with a collapse noise field, inducing quantum Brownian motions, which are dominant during the measurement, thus causing collapse of the wave function. An important manifestation of the collapse noise field, if any, is thermal energy generation, thus disturbing the temperature profile of a system. The experimental investigation of a collapse-driven heating effect has provided, so far, the most promising test of collapse models against standard quantum theory. In this paper, we calculate the collapse-driven heat generation for a three-dimensional multi-atomic Bravais lattice by solving stochastic Heisenberg equations. We perform our calculation for the mass-proportional continuous spontaneous localization collapse model with nonwhite noise. We obtain the temperature distribution of a sphere under stationary-state and insulated surface conditions. However, the exact quantification of the collapse-driven heat-generation effect highly depends on the actual value of cutoff in the collapse noise spectrum.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exporation

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

The problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars were investigated. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; navigation, terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks were studied: vehicle model design, mathematical modeling of dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement and transport parameter evaluation.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

Investigation of problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars has been undertaken. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks have been under study: vehicle model design, mathematical modeling of a dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer sybsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement.

Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx.

PubMed

Elemans, Coen P H; Muller, Mees; Larsen, Ole Naesbye; van Leeuwen, Johan L

2009-04-01

Birdsong has developed into one of the important models for motor control of learned behaviour and shows many parallels with speech acquisition in humans. However, there are several experimental limitations to studying the vocal organ - the syrinx - in vivo. The multidisciplinary approach of combining experimental data and mathematical modelling has greatly improved the understanding of neural control and peripheral motor dynamics of sound generation in birds. Here, we present a simple mechanical model of the syrinx that facilitates detailed study of vibrations and sound production. Our model resembles the 'starling resistor', a collapsible tube model, and consists of a tube with a single membrane in its casing, suspended in an external pressure chamber and driven by various pressure patterns. With this design, we can separately control 'bronchial' pressure and tension in the oscillating membrane and generate a wide variety of 'syllables' with simple sweeps of the control parameters. We show that the membrane exhibits high frequency, self-sustained oscillations in the audio range (>600 Hz fundamental frequency) using laser Doppler vibrometry, and systematically explore the conditions for sound production of the model in its control space. The fundamental frequency of the sound increases with tension in three membranes with different stiffness and mass. The lower-bound fundamental frequency increases with membrane mass. The membrane vibrations are strongly coupled to the resonance properties of the distal tube, most likely because of its reflective properties to sound waves. Our model is a gross simplification of the complex morphology found in birds, and more closely resembles mathematical models of the syrinx. Our results confirm several assumptions underlying existing mathematical models in a complex geometry.

Natural hazard metaphors for financial crises

NASA Astrophysics Data System (ADS)

Woo, Gordon

2001-02-01

Linguistic metaphors drawn from natural hazards are commonly used at times of financial crisis. A brewing storm, a seismic shock, etc., evoke the abruptness and severity of a market collapse. If the language of windstorms, earthquakes and volcanic eruptions is helpful in illustrating a financial crisis, what about the mathematics of natural catastrophes? Already, earthquake prediction methods have been applied to economic recessions, and volcanic eruption forecasting techniques have been applied to market crashes. The purpose of this contribution is to survey broadly the mathematics of natural catastrophes, so as to convey the range of underlying principles, some of which may serve as mathematical metaphors for financial applications.

Scalar field collapse in gauge theory gravity

NASA Astrophysics Data System (ADS)

Harke, Richard Eugene

A brief introduction to gravitational collapse in General Relativity is given. Then critical phenomena in the collapse of a massless scalar field as discovered by Choptuik are described. My own work in this area is described and some results are presented. Gauge Theory Gravity and its mathematical formalism, geometric algebra are introduced. Because geometric algebra is not widely known, a detailed and rigorous introduction to it is provided. The basic principles of Gauge Theory Gravity (GTG) are described and a derivation of the field equations is presented. An appropriate Lagrangian for the scalar field in GTG is introduced and the energy tensor is derived by the usual variational process. The equations of motion for the scalar field are derived for a spherically symmetric space. Finite difference approximations to these equations are constructed and simulations of gravitational collapse are run on a computer. Graphical results are presented. An unexpected phenomenon is found in which the passage of the scalar field leaves a persistent change in the gravitational gauge field.

Mathematical model reveals role of nucleotide signaling in airway surface liquid homeostasis and its dysregulation in cystic fibrosis

PubMed Central

Sandefur, Conner I.; Boucher, Richard C.; Elston, Timothy C.

2017-01-01

Mucociliary clearance is composed of three components (i.e., mucin secretion, airway surface hydration, and ciliary-activity) which function coordinately to clear inhaled microbes and other foreign particles from airway surfaces. Airway surface hydration is maintained by water fluxes driven predominantly by active chloride and sodium ion transport. The ion channels that mediate electrogenic ion transport are regulated by extracellular purinergic signals that signal through G protein-coupled receptors. These purinoreceptors and the signaling pathways they activate have been identified as possible therapeutic targets for treating lung disease. A systems-level description of airway surface liquid (ASL) homeostasis could accelerate development of such therapies. Accordingly, we developed a mathematical model to describe the dynamic coupling of ion and water transport to extracellular purinergic signaling. We trained our model from steady-state and time-dependent experimental measurements made using normal and cystic fibrosis (CF) cultured human airway epithelium. To reproduce CF conditions, reduced chloride secretion, increased potassium secretion, and increased sodium absorption were required. The model accurately predicted ASL height under basal normal and CF conditions and the collapse of surface hydration due to the accelerated nucleotide metabolism associated with CF exacerbations. Finally, the model predicted a therapeutic strategy to deliver nucleotide receptor agonists to effectively rehydrate the ASL of CF airways. PMID:28808008

Einstein-Langevin and Einstein-Fokker-Planck equations for Oppenheimer-Snyder gravitational collapse in a spacetime with conformal vacuum fluctuations

NASA Astrophysics Data System (ADS)

Miller, Steven David

1999-10-01

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

Postural effects on intracranial pressure: modeling and clinical evaluation.

PubMed

Qvarlander, Sara; Sundström, Nina; Malm, Jan; Eklund, Anders

2013-11-01

The physiological effect of posture on intracranial pressure (ICP) is not well described. This study defined and evaluated three mathematical models describing the postural effects on ICP, designed to predict ICP at different head-up tilt angles from the supine ICP value. Model I was based on a hydrostatic indifference point for the cerebrospinal fluid (CSF) system, i.e., the existence of a point in the system where pressure is independent of body position. Models II and III were based on Davson's equation for CSF absorption, which relates ICP to venous pressure, and postulated that gravitational effects within the venous system are transferred to the CSF system. Model II assumed a fully communicating venous system, and model III assumed that collapse of the jugular veins at higher tilt angles creates two separate hydrostatic compartments. Evaluation of the models was based on ICP measurements at seven tilt angles (0-71°) in 27 normal pressure hydrocephalus patients. ICP decreased with tilt angle (ANOVA: P < 0.01). The reduction was well predicted by model III (ANOVA lack-of-fit: P = 0.65), which showed excellent fit against measured ICP. Neither model I nor II adequately described the reduction in ICP (ANOVA lack-of-fit: P < 0.01). Postural changes in ICP could not be predicted based on the currently accepted theory of a hydrostatic indifference point for the CSF system, but a new model combining Davson's equation for CSF absorption and hydrostatic gradients in a collapsible venous system performed well and can be useful in future research on gravity and CSF physiology.

Consistent resolution of some relativistic quantum paradoxes

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2002-12-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.

Strategic behavior and governance challenges in self-organized coupled natural-human systems

NASA Astrophysics Data System (ADS)

Muneepeerakul, R.; Anderies, J. M.

2017-12-01

Successful and sustainable coupling of human societies and natural systems requires effective governance, which depends on the existence of proper infrastructure (both hard and soft). In recent decades, much attention has been paid to what has allowed many small-scale self-organized coupled natural-human systems around the world to persist for centuries, thanks to a large part to the work by Elinor Ostrom and colleagues. In this work, we mathematically operationalize a conceptual framework that is developed based on this body of work by way of a stylized model. The model captures the interplay between replicator dynamics within the population, dynamics of natural resources, and threshold characteristics of public infrastructure. The model analysis reveals conditions for long-term sustainability and collapse of the coupled systems as well as other tradeoffs and potential pitfalls in governing these systems.

Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications.

PubMed

Martínez-González, Alicia; Calvo, Gabriel F; Pérez Romasanta, Luis A; Pérez-García, Víctor M

2012-12-01

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.

Viscous-enstrophy scaling law for Navier-Stokes reconnection

NASA Astrophysics Data System (ADS)

Kerr, Robert M.

2017-11-01

Simulations of perturbed, helical trefoil vortex knots and anti-parallel vortices find ν-independent collapse of temporally scaled (√{ ν} Z) - 1 / 2, Z enstrophy, between when the loops first touch at tΓ, and when reconnection ends at tx for the viscosity ν varying by 256. Due to mathematical bounds upon higher-order norms, this collapse requires that the domain increase as ν decreases, possibly to allow large-scale negative helicity to grow as compensation for small-scale positive helicity and enstrophy growth. This mechanism could be a step towards explaining how smooth solutions of the Navier-Stokes can generate finite-energy dissipation in a finite time as ν -> 0 .

Collapsing radiating stars with various equations of state

NASA Astrophysics Data System (ADS)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

The electro-structural behaviour of yarn-like carbon nanotube fibres immersed in organic liquids

NASA Astrophysics Data System (ADS)

Terrones, Jeronimo; Windle, Alan H.; Elliott, James A.

2014-10-01

Yarn-like carbon nanotube (CNT) fibres are a hierarchically-structured material with a variety of promising applications such as high performance composites, sensors and actuators, smart textiles, and energy storage and transmission. However, in order to fully realize these possibilities, a more detailed understanding of their interactions with the environment is required. In this work, we describe a simplified representation of the hierarchical structure of the fibres from which several mathematical models are constructed to explain electro-structural interactions of fibres with organic liquids. A balance between the elastic and surface energies of the CNT bundle network in different media allows the determination of the maximum lengths that open junctions can sustain before collapsing to minimize the surface energy. This characteristic length correlates well with the increase of fibre resistance upon immersion in organic liquids. We also study the effect of charge accumulation in open interbundle junctions and derive expressions to describe experimental data on the non-ohmic electrical behaviour of fibres immersed in polar liquids. Our analyses suggest that the non-ohmic behaviour is caused by progressively shorter junctions collapsing as the voltage is increased. Since our models are not based on any property unique to carbon nanotubes, they should also be useful to describe other hierarchical structures.

An assessment on the use of bivariate, multivariate and soft computing techniques for collapse susceptibility in GIS environ

NASA Astrophysics Data System (ADS)

Yilmaz, Işik; Marschalko, Marian; Bednarik, Martin

2013-04-01

The paper presented herein compares and discusses the use of bivariate, multivariate and soft computing techniques for collapse susceptibility modelling. Conditional probability (CP), logistic regression (LR) and artificial neural networks (ANN) models representing the bivariate, multivariate and soft computing techniques were used in GIS based collapse susceptibility mapping in an area from Sivas basin (Turkey). Collapse-related factors, directly or indirectly related to the causes of collapse occurrence, such as distance from faults, slope angle and aspect, topographical elevation, distance from drainage, topographic wetness index (TWI), stream power index (SPI), Normalized Difference Vegetation Index (NDVI) by means of vegetation cover, distance from roads and settlements were used in the collapse susceptibility analyses. In the last stage of the analyses, collapse susceptibility maps were produced from the models, and they were then compared by means of their validations. However, Area Under Curve (AUC) values obtained from all three models showed that the map obtained from soft computing (ANN) model looks like more accurate than the other models, accuracies of all three models can be evaluated relatively similar. The results also showed that the conditional probability is an essential method in preparation of collapse susceptibility map and highly compatible with GIS operating features.

On the stability of lung parenchymal lesions with applications to early pneumothorax diagnosis.

PubMed

Bhandarkar, Archis R; Banerjee, Rohan; Seshaiyer, Padmanabhan

2013-01-01

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems

PubMed Central

Barnett, George; D'Souza, Raissa M.

2015-01-01

An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a new technology platform, collapses in prices and in confidence in financial markets, and protests erupting in multiple countries. A number of mathematical models of these phenomena have multiple equilibria separated by saddle-node bifurcations. We study this behaviour in its normal form as fast–slow ordinary differential equations. In our model, a system consists of multiple subsystems, such as countries in the global economy or patches of an ecosystem. Each subsystem is described by a scalar quantity, such as economic output or population, that undergoes sudden changes via saddle-node bifurcations. The subsystems are coupled via their scalar quantity (e.g. trade couples economic output; diffusion couples populations); that coupling moves the locations of their bifurcations. The model demonstrates two ways in which sudden changes can propagate: they can cascade (one causing the next), or they can hop over subsystems. The latter is absent from classic models of cascades. For an application, we study the Arab Spring protests. After connecting the model to sociological theories that have bistability, we use socioeconomic data to estimate relative proximities to tipping points and Facebook data to estimate couplings among countries. We find that although protests tend to spread locally, they also seem to ‘hop' over countries, like in the stylized model; this result highlights a new class of temporal motifs in longitudinal network datasets. PMID:26559684

Marriages of mathematics and physics: A challenge for biology.

PubMed

Islami, Arezoo; Longo, Giuseppe

2017-12-01

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.

A Mathematical Model of Intra-Colony Spread of American Foulbrood in European Honeybees (Apis mellifera L.).

PubMed

Jatulan, Eduardo O; Rabajante, Jomar F; Banaay, Charina Gracia B; Fajardo, Alejandro C; Jose, Editha C

2015-01-01

American foulbrood (AFB) is one of the severe infectious diseases of European honeybees (Apis mellifera L.) and other Apis species. This disease is caused by a gram-positive, spore-forming bacterium Paenibacillus larvae. In this paper, a compartmental (SI framework) model is constructed to represent the spread of AFB within a colony. The model is analyzed to determine the long-term fate of the colony once exposed to AFB spores. It was found out that without effective and efficient treatment, AFB infection eventually leads to colony collapse. Furthermore, infection thresholds were predicted based on the stability of the equilibrium states. The number of infected cell combs is one of the factors that drive disease spread. Our results can be used to forecast the transmission timeline of AFB infection and to evaluate the control strategies for minimizing a possible epidemic.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Moyer, W. R.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1973-01-01

The following tasks related to the design, construction, and evaluation of a mobile planetary vehicle for unmanned exploration of Mars are discussed: (1) design and construction of a 0.5 scale dynamic vehicle; (2) mathematical modeling of vehicle dynamics; (3) experimental 0.4 scale vehicle dynamics measurements and interpretation; (4) vehicle electro-mechanical control systems; (5) remote control systems; (6) collapsibility and deployment concepts and hardware; (7) design, construction and evaluation of a wheel with increased lateral stiffness, (8) system design optimization; (9) design of an on-board computer; (10) design and construction of a laser range finder; (11) measurement of reflectivity of terrain surfaces; (12) obstacle perception by edge detection; (13) terrain modeling based on gradients; (14) laser scan systems; (15) path selection system simulation and evaluation; (16) gas chromatograph system concepts; (17) experimental chromatograph separation measurements and chromatograph model improvement and evaluation.

Precipitation Processes and their Modulation by Synoptic Conditions and Complex Terrain Observed during the GPM Ground Validation Olympic Mountains Experiment (OLYMPEX)

NASA Astrophysics Data System (ADS)

McMurdie, L. A.; Houze, R.; Zagrodnik, J.; Rowe, A.; DeHart, J.; Barnes, H.

2016-12-01

Successful and sustainable coupling of human societies and natural systems requires effective governance, which depends on the existence of proper infrastructure (both hard and soft). In recent decades, much attention has been paid to what has allowed many small-scale self-organized coupled natural-human systems around the world to persist for centuries, thanks to a large part to the work by Elinor Ostrom and colleagues. In this work, we mathematically operationalize a conceptual framework that is developed based on this body of work by way of a stylized model. The model captures the interplay between replicator dynamics within the population, dynamics of natural resources, and threshold characteristics of public infrastructure. The model analysis reveals conditions for long-term sustainability and collapse of the coupled systems as well as other tradeoffs and potential pitfalls in governing these systems.

Collapse susceptibility mapping in karstified gypsum terrain (Sivas basin - Turkey) by conditional probability, logistic regression, artificial neural network models

NASA Astrophysics Data System (ADS)

Yilmaz, Isik; Keskin, Inan; Marschalko, Marian; Bednarik, Martin

2010-05-01

This study compares the GIS based collapse susceptibility mapping methods such as; conditional probability (CP), logistic regression (LR) and artificial neural networks (ANN) applied in gypsum rock masses in Sivas basin (Turkey). Digital Elevation Model (DEM) was first constructed using GIS software. Collapse-related factors, directly or indirectly related to the causes of collapse occurrence, such as distance from faults, slope angle and aspect, topographical elevation, distance from drainage, topographic wetness index- TWI, stream power index- SPI, Normalized Difference Vegetation Index (NDVI) by means of vegetation cover, distance from roads and settlements were used in the collapse susceptibility analyses. In the last stage of the analyses, collapse susceptibility maps were produced from CP, LR and ANN models, and they were then compared by means of their validations. Area Under Curve (AUC) values obtained from all three methodologies showed that the map obtained from ANN model looks like more accurate than the other models, and the results also showed that the artificial neural networks is a usefull tool in preparation of collapse susceptibility map and highly compatible with GIS operating features. Key words: Collapse; doline; susceptibility map; gypsum; GIS; conditional probability; logistic regression; artificial neural networks.

Method to compute the stress-energy tensor for a quantum field outside a black hole that forms from collapse

NASA Astrophysics Data System (ADS)

Anderson, Paul; Evans, Charles

2017-01-01

A method to compute the stress-energy tensor for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill

Model for quantum effects in stellar collapse

NASA Astrophysics Data System (ADS)

Arderucio-Costa, Bruno; Unruh, William G.

2018-01-01

We present a simple model for stellar collapse and evaluate the quantum mechanical stress-energy tensor to argue that quantum effects do not play an important role for the collapse of astrophysical objects.

A Simple Model for Human and Nature Interaction

NASA Astrophysics Data System (ADS)

Motesharrei, S.; Rivas, J.; Kalnay, E.

2012-12-01

There are widespread concerns that current trends in population and resource-use are unsustainable, but the possibilities of an overshoot and collapse remain unclear and controversial. Collapses of civilizations have occurred many times in the past 5000 years, often followed by centuries of economic, intellectual, and population decline. Many different natural and social phenomena have been invoked to explain specific collapses, but a general explanation remains elusive. Two important features seem to appear across societies that have collapsed: Ecological Strain and Economic Stratification. Our new model (Human And Nature DYnamics, HANDY) has just four equations that describe the evolution of Elites, Commoners, Nature, and Wealth. Mechanisms leading to collapse are discussed and the measure "Carrying Capacity" is developed and defined. The model shows that societal collapse can happen due to either one of two independent factors: (1) over-consumption of natural resources, and/or (2) deep inequity between Elites and Commoners. The model also portrays two distinct types of collapse: (i) collapse followed by recovery of nature, and (ii) full collapse. The model suggests that the estimation of Carrying Capacity is a practical means for early detection of a collapse. Collapse can be avoided, and population can reach a sustainable equilibrium, if the rate of depletion of nature is reduced to a sustainable level, and if resources are distributed in a reasonably equitable fashion.; A type-ii (full) collapse is shown in this figure. With high inequality and high depletion, societies are doomed to collapse. Wealth starts to decrease when population rises above the carrying capacity. The large gap between carrying capacity and its maximum is a result of depletion factor being much larger than the sustainable limit. ; It is possible to overshoot, oscillate, and eventually converge to an equilibrium, even in an inequitable society. However, it requires policies that control birth rates and inequality. Additionally, depletion (production) must be kept within a reasonable range.

Atomistic modeling of shock-induced void collapse in copper

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davila, L P; Erhart, P; Bringa, E M

2005-03-09

Nonequilibrium molecular dynamics (MD) simulations show that shock-induced void collapse in copper occurs by emission of shear loops. These loops carry away the vacancies which comprise the void. The growth of the loops continues even after they collide and form sessile junctions, creating a hardened region around the collapsing void. The scenario seen in our simulations differs from current models that assume that prismatic loop emission is responsible for void collapse. We propose a new dislocation-based model that gives excellent agreement with the stress threshold found in the MD simulations for void collapse as a function of void radius.

An information theory model for dissipation in open quantum systems

NASA Astrophysics Data System (ADS)

Rogers, David M.

2017-08-01

This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.

Assessing Between-School Variation in Educational Resources and Mathematics and Science Achievement in Bulgaria

ERIC Educational Resources Information Center

Bankov, Kiril; Mikova, Dilyana; Smith, Thomas M.

2006-01-01

Following the collapse of the Soviet Union, Bulgaria, along with other Central and Eastern European countries, began a transition towards a democratic political system and market-oriented economy. Socio-economic and political changes associated with this transition have created a growing need for a new kind of citizenry, one equipped with flexible…

Modelling shoal margin collapses and their morphodynamic effect on channels and shoals in a sandy estuary

NASA Astrophysics Data System (ADS)

van Dijk, W. M.; Mastbergen, D. R.; Van der Werf, J. J.; Leuven, J.; Kleinhans, M. G.

2017-12-01

Channel bank failure and collapses of shoal margins due to flow slides have been recorded in Dutch estuaries for the past 200 years. The effects of these collapses on the morphodynamics of estuaries are unknown, but could potentially increase the dynamics of channel-shoal interactions by causing perturbations of up to a million cubic meters per event, which could impact habitats and navigability. The processes of shoal margin collapses are currently not included in numerical morphodynamic models. The objectives of this study are to investigate where shoal margins collapses typically occur, what their dimensions are, and to model how shoal margin collapses affect the morphodynamics at the channel-shoal scale. We identified 300 shoal margin collapses from bathymetry data of the Western Scheldt estuary for the period 1959-2015, and found that the shape of a shoal margin collapse is well represented by 1/3 of an ellipsoid, and that its volume has a log-normal distribution with an average of 100,000 m3. We implemented a parameterization for shoal margin collapses and tested their effects on morphodynamics in a Delft3D numerical model schematization of the Western Scheldt estuary. Three sets of scenarios were analyzed for near-field morphodynamics and far-field effects on flow pattern and channel-bar morphology: 1) an observed single shoal margin collapse of 2014, 2) collapses on various locations that are susceptible to collapses, and 3) our novel stochastic model producing collapses over a time span of a decade. Results show that single shoal margin collapses only affect the local dynamics in longitudinal direction and dampen out within a year when the collapse is small. When larger disturbances reach the seaward or landward sill at tidal channel junctions over a longer time span, the bed elevation at the sill increases on average and decrease the hydraulic geometry of the channel junctions. The extent of far-field effects is sensitive to the grain-size of the deposit, where finer sediments are transported further away. The location of the deposit across the channel matters for disturbing the region around the collapse, where sediment transport is highest for the strongest residual current. These results imply that disturbances caused by dredging and dumping may likewise affect the dynamics of channel junctions.

The role of bank collapse on tidal creek ontogeny: A novel process-based model for bank retreat

NASA Astrophysics Data System (ADS)

Gong, Zheng; Zhao, Kun; Zhang, Changkuan; Dai, Weiqi; Coco, Giovanni; Zhou, Zeng

2018-06-01

Bank retreat in coastal tidal flats plays a primary role on the planimetric shape of tidal creeks and is commonly driven by both flow-induced bank erosion and gravity-induced bank collapse. However, existing modelling studies largely focus on bank erosion and overlook bank collapse. We build a bank retreat model coupling hydrodynamics, bank erosion and bank collapse. To simulate the process of bank collapse, a stress-deformation model is utilized to calculate the stress variation of bank soil after bank erosion, and the Mohr-Coulomb failure criterion is then applied to evaluate the stability of the tidal creek bank. Results show that the bank failure process can be categorized into three stages, i.e., shear failure at the bank toe (stage I), tensile failure on the bank top (stage II), and sectional cracking from the bank top to the toe (stage III). With only bank erosion, the planimetric shapes of tidal creeks are funneled due to the gradually seaward increasing discharge. In contrast to bank erosion, bank collapse is discontinuous, and the contribution of bank collapse to bank retreat can reach 85%, highlighting that the expansion of tidal creeks can be dominated by bank collapse process. The planimetric shapes of tidal creeks are funneled with a much faster expansion rate when bank collapse is considered. Overall, this study makes a further step toward more physical and realistic simulation of bank retreat in estuarine and coastal settings and the developed bank collapse module can be readily included in other morphodynamic models.

Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

NASA Astrophysics Data System (ADS)

Okon, Elias; Sudarsky, Daniel

2014-02-01

We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal, which relates the spontaneous collapse events of objective collapse models to microscopic virtual black holes.

Early warning signals of Atlantic Meridional Overturning Circulation collapse in a fully coupled climate model

NASA Astrophysics Data System (ADS)

Boulton, Chris A.; Allison, Lesley C.; Lenton, Timothy M.

2014-12-01

The Atlantic Meridional Overturning Circulation (AMOC) exhibits two stable states in models of varying complexity. Shifts between alternative AMOC states are thought to have played a role in past abrupt climate changes, but the proximity of the climate system to a threshold for future AMOC collapse is unknown. Generic early warning signals of critical slowing down before AMOC collapse have been found in climate models of low and intermediate complexity. Here we show that early warning signals of AMOC collapse are present in a fully coupled atmosphere-ocean general circulation model, subject to a freshwater hosing experiment. The statistical significance of signals of increasing lag-1 autocorrelation and variance vary with latitude. They give up to 250 years warning before AMOC collapse, after ~550 years of monitoring. Future work is needed to clarify suggested dynamical mechanisms driving critical slowing down as the AMOC collapse is approached.

Early warning signals of Atlantic Meridional Overturning Circulation collapse in a fully coupled climate model

PubMed Central

Boulton, Chris A.; Allison, Lesley C.; Lenton, Timothy M.

2014-01-01

The Atlantic Meridional Overturning Circulation (AMOC) exhibits two stable states in models of varying complexity. Shifts between alternative AMOC states are thought to have played a role in past abrupt climate changes, but the proximity of the climate system to a threshold for future AMOC collapse is unknown. Generic early warning signals of critical slowing down before AMOC collapse have been found in climate models of low and intermediate complexity. Here we show that early warning signals of AMOC collapse are present in a fully coupled atmosphere-ocean general circulation model, subject to a freshwater hosing experiment. The statistical significance of signals of increasing lag-1 autocorrelation and variance vary with latitude. They give up to 250 years warning before AMOC collapse, after ~550 years of monitoring. Future work is needed to clarify suggested dynamical mechanisms driving critical slowing down as the AMOC collapse is approached. PMID:25482065

Early warning signals of Atlantic Meridional Overturning Circulation collapse in a fully coupled climate model.

PubMed

Boulton, Chris A; Allison, Lesley C; Lenton, Timothy M

2014-12-08

The Atlantic Meridional Overturning Circulation (AMOC) exhibits two stable states in models of varying complexity. Shifts between alternative AMOC states are thought to have played a role in past abrupt climate changes, but the proximity of the climate system to a threshold for future AMOC collapse is unknown. Generic early warning signals of critical slowing down before AMOC collapse have been found in climate models of low and intermediate complexity. Here we show that early warning signals of AMOC collapse are present in a fully coupled atmosphere-ocean general circulation model, subject to a freshwater hosing experiment. The statistical significance of signals of increasing lag-1 autocorrelation and variance vary with latitude. They give up to 250 years warning before AMOC collapse, after ~550 years of monitoring. Future work is needed to clarify suggested dynamical mechanisms driving critical slowing down as the AMOC collapse is approached.

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Mitigation of commutation failures in LCC-HVDC systems based on superconducting fault current limiters

NASA Astrophysics Data System (ADS)

Lee, Jong-Geon; Khan, Umer Amir; Lee, Ho-Yun; Lim, Sung-Woo; Lee, Bang-Wook

2016-11-01

Commutation failure in line commutated converter based HVDC systems cause severe damages on the entire power grid system. For LCC-HVDC, thyristor valves are turned on by a firing signal but turn off control is governed by the external applied AC voltage from surrounding network. When the fault occurs in AC system, turn-off control of thyristor valves is unavailable due to the voltage collapse of point of common coupling (PCC), which causes the commutation failure in LCC-HVDC link. Due to the commutation failure, the power transfer interruption, dc voltage drop and severe voltage fluctuation in the AC system could be occurred. In a severe situation, it might cause the protection system to block the valves. In this paper, as a solution to prevent the voltage collapse on PCC and to limit the fault current, the application study of resistive superconducting fault current limiter (SFCL) on LCC-HVDC grid system was performed with mathematical and simulation analyses. The simulation model was designed by Matlab/Simulink considering Haenam-Jeju HVDC power grid in Korea which includes conventional AC system and onshore wind farm and resistive SFCL model. From the result, it was observed that the application of SFCL on LCC-HVDC system is an effective solution to mitigate the commutation failure. And then the process to determine optimum quench resistance of SFCL which enables the recovery of commutation failure was deeply investigated.

Collapse Causes Analysis and Numerical Simulation for a Rigid Frame Multiple Arch Bridge

NASA Astrophysics Data System (ADS)

Zuo, XinDai

2018-03-01

Following the collapse accident of Baihe Bridge, the author built a plane model of the whole bridge firstly and analyzed the carrying capacity of the structure for a 170-tons lorry load. Then the author built a spatial finite element model which can accurately simulate the bridge collapse course. The collapse course was simulated and the accident scene was reproduced. Spatial analysis showed rotational stiffness of the pier bottom had a large influence on the collapse from of the superstructures. The conclusion was that the170 tons lorry load and multiple arch bridge design were the important factors leading to collapse.

A mixed helium-oxygen shell in some core-collapse supernova progenitors

NASA Astrophysics Data System (ADS)

Gofman, Roni Anna; Gilkis, Avishai; Soker, Noam

2018-04-01

We evolve models of rotating massive stars up to the stage of iron core collapse using the MESA code and find a shell with a mixed composition of primarily helium and oxygen in some cases. In the parameter space of initial masses of 13-40M⊙ and initial rotation velocities of 0-450 kms-1 that we investigate, we find a mixed helium-oxygen (He-O) shell with a significant total He-O mass and with a helium to oxygen mass ratio in the range of 0.5-2 only for a small fraction of the models. While the shell formation due to mixing is instigated by rotation, the pre-collapse rotation rate is not very high. The fraction of models with a shell of He-O composition required for an energetic collapse-induced thermonuclear explosion is small, as is the fraction of models with high specific angular momentum, which can aid the thermonuclear explosion by retarding the collapse. Our results suggest that the collapse-induced thermonuclear explosion mechanism that was revisited recently can account for at most a small fraction of core-collapse supernovae. The presence of such a mixed He-O shell still might have some implications for core-collapse supernovae, such as some nucleosynthesis processes when jets are present, or might result in peculiar sub-luminous core-collapse supernovae.

A mixed helium-oxygen shell in some core-collapse supernova progenitors

NASA Astrophysics Data System (ADS)

Gofman, Roni Anna; Gilkis, Avishai; Soker, Noam

2018-07-01

We evolve models of rotating massive stars up to the stage of iron core collapse using the MESA code and find a shell with a mixed composition of primarily helium and oxygen in some cases. In the parameter space of initial masses of 13-40 M⊙ and initial rotation velocities of 0-450 km s-1 that we investigate, we find a mixed helium-oxygen (He-O) shell with a significant total He-O mass and with a helium to oxygen mass ratio in the range of 0.5-2 only for a small fraction of the models. While the shell formation due to mixing is instigated by rotation, the pre-collapse rotation rate is not very high. The fraction of models with a shell of He-O composition required for an energetic collapse-induced thermonuclear explosion is small, as is the fraction of models with high specific angular momentum, which can aid the thermonuclear explosion by retarding the collapse. Our results suggest that the collapse-induced thermonuclear explosion mechanism that was revisited recently can account for at most a small fraction of core-collapse supernovae. The presence of such a mixed He-O shell still might have some implications for core-collapse supernovae, such as some nucleosynthesis processes when jets are present, or might result in peculiar sub-luminous core-collapse supernovae.

Collapse of Corroded Pipelines under Combined Tension and External Pressure

PubMed Central

Ye, Hao; Yan, Sunting; Jin, Zhijiang

2016-01-01

In this work, collapse of corroded pipeline under combined external pressure and tension is investigated through numerical method. Axially uniform corrosion with symmetric imperfections is firstly considered. After verifying with existing experimental results, the finite element model is used to study the effect of tension on collapse pressure. An extensive parametric study is carried out using Python script and FORTRAN subroutine to investigate the influence of geometric parameters on the collapse behavior under combined loads. The results are used to develop an empirical equation for estimating the collapse pressure under tension. In addition, the effects of loading path, initial imperfection length, yielding anisotropy and corrosion defect length on the collapse behavior are also investigated. It is found that tension has a significant influence on collapse pressure of corroded pipelines. Loading path and anisotropic yielding are also important factors affecting the collapse behavior. For pipelines with relatively long corrosion defect, axially uniform corrosion models could be used to estimate the collapse pressure. PMID:27111544

Non-cell-autonomous driving of tumour growth supports sub-clonal heterogeneity.

PubMed

Marusyk, Andriy; Tabassum, Doris P; Altrock, Philipp M; Almendro, Vanessa; Michor, Franziska; Polyak, Kornelia

2014-10-02

Cancers arise through a process of somatic evolution that can result in substantial sub-clonal heterogeneity within tumours. The mechanisms responsible for the coexistence of distinct sub-clones and the biological consequences of this coexistence remain poorly understood. Here we used a mouse xenograft model to investigate the impact of sub-clonal heterogeneity on tumour phenotypes and the competitive expansion of individual clones. We found that tumour growth can be driven by a minor cell subpopulation, which enhances the proliferation of all cells within a tumour by overcoming environmental constraints and yet can be outcompeted by faster proliferating competitors, resulting in tumour collapse. We developed a mathematical modelling framework to identify the rules underlying the generation of intra-tumour clonal heterogeneity. We found that non-cell-autonomous driving of tumour growth, together with clonal interference, stabilizes sub-clonal heterogeneity, thereby enabling inter-clonal interactions that can lead to new phenotypic traits.

Dynamic Compressibility of High-Porosity Dampers of Thermal and Shock Loadings:. Modeling and Experiment

NASA Astrophysics Data System (ADS)

Bragov, Anatoly; Konstantinov, Alexander; Lomunov, Andrey; Sadyrin, Anatoly; Sergeichev, Ivan; Kruszka, Leopold

High-porosity materials, such as chamotte and mullite, possess a heat of fusion. Owing to their properties, these materials can be used with success as damping materials in containers for airplane, automobile, etc. transportation of radioactive or highly toxic materials. Experimental studies of the dynamic properties have been executed with using some original modifications of the Kolsky method. These modified experiments have allowed studying the dynamic compressibility of high-porosity chamotte at deformations up to 80% and amplitudes up to 50 MPa. The equations of the mathematical model describing shock compacting of chamotte as a highly porous, fragile, collapsing material are presented. Deformation of high-porous materials at non-stationary loadings is usually accompanied by fragile destruction of interpore partitions as observed in other porous ceramic materials. Comparison of numerical and experimental results has shown their good conformity.

Preliminary model of fluid and solute distribution and transport during hemorrhage.

PubMed

Gyenge, C C; Bowen, B D; Reed, R K; Bert, J L

2003-01-01

The distribution and transport of fluid, ions, and other solutes (plasma proteins and glucose) are described in a mathematical model of unresuscitated hemorrhage. The model is based on balances of each material in both the circulation and its red blood cells, as well as in a whole-body tissue compartment along with its cells. Exchange between these four compartments occurs by a number of different mechanisms. The hemorrhage model has as its basis a validated model, due to Gyenge et al., of fluid and solute exchange in the whole body of a standard human. Hypothetical but physiologically based features such as glucose and small ion releases along with cell membrane changes are incorporated into the hemorrhage model to describe the system behavior, particularly during larger hemorrhages. Moderate (10%-30% blood volume loss) and large (> 30% blood loss) hemorrhage dynamics are simulated and compared with available data. The model predictions compare well with the available information for both types of hemorrhages and provide a reasonable description of the progression of a large hemorrhage from the compensatory phase through vascular collapse.

Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework

NASA Astrophysics Data System (ADS)

Potirakis, Stelios M.; Zitis, Pavlos I.; Eftaxias, Konstantinos

2013-07-01

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg-Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg-Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares.

Effects of Cascaded Voltage Collapse and Protection of Many Induction Machine Loads upon Load Characteristics Viewed from Bulk Transmission System

NASA Astrophysics Data System (ADS)

Kumano, Teruhisa

As known well, two of the fundamental processes which give rise to voltage collapse in power systems are the on load tap changers of transformers and dynamic characteristics of loads such as induction machines. It has been well established that, comparing among these two, the former makes slower collapse while the latter makes faster. However, in realistic situations, the load level of each induction machine is not uniform and it is well expected that only a part of loads collapses first, followed by collapse process of each load which did not go into instability during the preceding collapses. In such situations the over all equivalent collapse behavior viewed from bulk transmission level becomes somewhat different from the simple collapse driven by one aggregated induction machine. This paper studies the process of cascaded voltage collapse among many induction machines by time simulation, where load distribution on a feeder line is modeled by several hundreds of induction machines and static impedance loads. It is shown that in some cases voltage collapse really cascades among induction machines, where the macroscopic load dynamics viewed from upper voltage level makes slower collapse than expected by the aggregated load model. Also shown is the effects of machine protection of induction machines, which also makes slower collapse.

A validated approach for modeling collapse of steel structures

NASA Astrophysics Data System (ADS)

Saykin, Vitaliy Victorovich

A civil engineering structure is faced with many hazardous conditions such as blasts, earthquakes, hurricanes, tornadoes, floods, and fires during its lifetime. Even though structures are designed for credible events that can happen during a lifetime of the structure, extreme events do happen and cause catastrophic failures. Understanding the causes and effects of structural collapse is now at the core of critical areas of national need. One factor that makes studying structural collapse difficult is the lack of full-scale structural collapse experimental test results against which researchers could validate their proposed collapse modeling approaches. The goal of this work is the creation of an element deletion strategy based on fracture models for use in validated prediction of collapse of steel structures. The current work reviews the state-of-the-art of finite element deletion strategies for use in collapse modeling of structures. It is shown that current approaches to element deletion in collapse modeling do not take into account stress triaxiality in vulnerable areas of the structure, which is important for proper fracture and element deletion modeling. The report then reviews triaxiality and its role in fracture prediction. It is shown that fracture in ductile materials is a function of triaxiality. It is also shown that, depending on the triaxiality range, different fracture mechanisms are active and should be accounted for. An approach using semi-empirical fracture models as a function of triaxiality are employed. The models to determine fracture initiation, softening and subsequent finite element deletion are outlined. This procedure allows for stress-displacement softening at an integration point of a finite element in order to subsequently remove the element. This approach avoids abrupt changes in the stress that would create dynamic instabilities, thus making the results more reliable and accurate. The calibration and validation of these models are shown. The calibration is performed using a particle swarm optimization algorithm to establish accurate parameters when calibrated to circumferentially notched tensile coupons. It is shown that consistent, accurate predictions are attained using the chosen models. The variation of triaxiality in steel material during plastic hardening and softening is reported. The range of triaxiality in steel structures undergoing collapse is investigated in detail and the accuracy of the chosen finite element deletion approaches is discussed. This is done through validation of different structural components and structural frames undergoing severe fracture and collapse.

Mathematical Model of Naive T Cell Division and Survival IL-7 Thresholds.

PubMed

Reynolds, Joseph; Coles, Mark; Lythe, Grant; Molina-París, Carmen

2013-01-01

We develop a mathematical model of the peripheral naive T cell population to study the change in human naive T cell numbers from birth to adulthood, incorporating thymic output and the availability of interleukin-7 (IL-7). The model is formulated as three ordinary differential equations: two describe T cell numbers, in a resting state and progressing through the cell cycle. The third is introduced to describe changes in IL-7 availability. Thymic output is a decreasing function of time, representative of the thymic atrophy observed in aging humans. Each T cell is assumed to possess two interleukin-7 receptor (IL-7R) signaling thresholds: a survival threshold and a second, higher, proliferation threshold. If the IL-7R signaling strength is below its survival threshold, a cell may undergo apoptosis. When the signaling strength is above the survival threshold, but below the proliferation threshold, the cell survives but does not divide. Signaling strength above the proliferation threshold enables entry into cell cycle. Assuming that individual cell thresholds are log-normally distributed, we derive population-average rates for apoptosis and entry into cell cycle. We have analyzed the adiabatic change in homeostasis as thymic output decreases. With a parameter set representative of a healthy individual, the model predicts a unique equilibrium number of T cells. In a parameter range representative of persistent viral or bacterial infection, where naive T cell cycle progression is impaired, a decrease in thymic output may result in the collapse of the naive T cell repertoire.

Inherently unstable networks collapse to a critical point

NASA Astrophysics Data System (ADS)

Sheinman, M.; Sharma, A.; Alvarado, J.; Koenderink, G. H.; MacKintosh, F. C.

2015-07-01

Nonequilibrium systems that are driven or drive themselves towards a critical point have been studied for almost three decades. Here we present a minimalist example of such a system, motivated by experiments on collapsing active elastic networks. Our model of an unstable elastic network exhibits a collapse towards a critical point from any macroscopically connected initial configuration. Taking into account steric interactions within the network, the model qualitatively and quantitatively reproduces results of the experiments on collapsing active gels.

Massive collapse of volcano edifices triggered by hydrothermal pressurization

USGS Publications Warehouse

Reid, M.E.

2004-01-01

Catastrophic collapse of steep volcano flanks threatens lives at stratovolcanoes around the world. Although destabilizing shallow intrusion of magma into the edifice accompanies some collapses (e.g., Mount St. Helens), others have occurred without eruption of juvenile magmatic materials (e.g., Bandai). These latter collapses can be difficult to anticipate. Historic collapses without magmatic eruption are associated with shallow hydrothermal groundwater systems at the time of collapse. Through the use of numerical models of heat and groundwater flow, I evaluate the efficacy of hydrothermally driven collapse. Heating from remote magma intrusion at depth can generate temporarily elevated pore-fluid pressures that propagate upward into an edifice. Effective-stress deformation modeling shows that these pressures are capable of destabilizing the core of an edifice, resulting in massive, deep-seated collapse. Far-field pressurization only occurs with specific rock hydraulic properties; however, data from numerous hydrothermal systems illustrate that this process can transpire in realistic settings. ?? 2004 Geological Society of America.

Probing spontaneous wave-function collapse with entangled levitating nanospheres

NASA Astrophysics Data System (ADS)

Zhang, Jing; Zhang, Tiancai; Li, Jie

2017-01-01

Wave-function collapse models are considered to be the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schrödinger equation, these models (different from standard quantum mechanics) predict that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments, and hence efficient protocols for these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-Pérot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.

Nonstationary magnetosonic wave dynamics in plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2013-08-01

In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.

LISA pathfinder appreciably constrains collapse models

NASA Astrophysics Data System (ADS)

Helou, Bassam; Slagmolen, B. J. J.; McClelland, David E.; Chen, Yanbei

2017-04-01

Spontaneous collapse models are phenomological theories formulated to address major difficulties in macroscopic quantum mechanics. We place significant bounds on the parameters of the leading collapse models, the continuous spontaneous localization (CSL) model, and the Diosi-Penrose (DP) model, by using LISA Pathfinder's measurement, at a record accuracy, of the relative acceleration noise between two free-falling macroscopic test masses. In particular, we bound the CSL collapse rate to be at most (2.96 ±0.12 ) ×10-8 s-1 . This competitive bound explores a new frequency regime, 0.7 to 20 mHz, and overlaps with the lower bound 10-8 ±2 s-1 proposed by Adler in order for the CSL collapse noise to be substantial enough to explain the phenomenology of quantum measurement. Moreover, we bound the regularization cutoff scale used in the DP model to prevent divergences to be at least 40.1 ±0.5 fm , which is larger than the size of any nucleus. Thus, we rule out the DP model if the cutoff is the size of a fundamental particle.

The Multi-Universe Cosmos. The Origin and Fate of our Universe

NASA Astrophysics Data System (ADS)

Velan, Karel

18 billion yers ago our Universe, one of many in the Cosmos, emerged from a hot, dense fireball of matter and energy created in the 4-dimensional cosmic space-time from virtual particles receiving their rest mass from a powerful primordial radiation field, the missing link to any viable theory of creation. The cloud of elementary particles and radiation collapsed by gravity into a fireball until its trappped thermal radiation caused a titanic explosion that initiated the expansion and evolution of ours universe. As the universe expanded and cooled it spawned galaxies, stars, planets and life. Proven laws of physics, observationsl data and mathematical computations support the new cosmological model which proposes a large number of universes in the cosmos in varying stages of evolution

Analysis of collapse in flattening a micro-grooved heat pipe by lateral compression

NASA Astrophysics Data System (ADS)

Li, Yong; He, Ting; Zeng, Zhixin

2012-11-01

The collapse of thin-walled micro-grooved heat pipes is a common phenomenon in the tube flattening process, which seriously influences the heat transfer performance and appearance of heat pipe. At present, there is no other better method to solve this problem. A new method by heating the heat pipe is proposed to eliminate the collapse during the flattening process. The effectiveness of the proposed method is investigated through a theoretical model, a finite element(FE) analysis, and experimental method. Firstly, A theoretical model based on a deformation model of six plastic hinges and the Antoine equation of the working fluid is established to analyze the collapse of thin walls at different temperatures. Then, the FE simulation and experiments of flattening process at different temperatures are carried out and compared with theoretical model. Finally, the FE model is followed to study the loads of the plates at different temperatures and heights of flattened heat pipes. The results of the theoretical model conform to those of the FE simulation and experiments in the flattened zone. The collapse occurs at room temperature. As the temperature increases, the collapse decreases and finally disappears at approximately 130 °C for various heights of flattened heat pipes. The loads of the moving plate increase as the temperature increases. Thus, the reasonable temperature for eliminating the collapse and reducing the load is approximately 130 °C. The advantage of the proposed method is that the collapse is reduced or eliminated by means of the thermal deformation characteristic of heat pipe itself instead of by external support. As a result, the heat transfer efficiency of heat pipe is raised.

Adapting the academic motivation scale for use in pre-tertiary mathematics classrooms

NASA Astrophysics Data System (ADS)

Lim, Siew Yee; Chapman, Elaine

2015-09-01

The Academic Motivation Scale ( ams) is a comprehensive and widely used instrument for assessing motivation based on the self-determination theory. Currently, no such comprehensive instrument exists to assess the different domains of motivation (stipulated by the self-determination theory) in mathematics education at the pre-tertiary level (grades 11 and 12) in Asia. This study adapted the ams for this use and assessed the properties of the adapted instrument with 1610 students from Singapore. Exploratory and confirmatory factor analyses indicated a five-factor structure for the modified instrument (the three original ams intrinsic subscales collapsed into a single factor). Additionally, the modified instrument exhibited good internal consistency (mean α = .88), and satisfactory test-retest reliability over a 1-month interval (mean r xx = .73). The validity of the modified ams was further demonstrated through correlational analyses among scores on its subscales, and with scores on other instruments measuring mathematics attitudes, anxiety and achievement.

Spherical collapse in chameleon models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Ph.; Rosenfeld, R.; Steer, D.A., E-mail: brax@spht.saclay.cea.fr, E-mail: rosenfel@ift.unesp.br, E-mail: daniele.steer@apc.univ-paris7.fr

2010-08-01

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in themore » presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity.« less

Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley.

PubMed

Axtell, Robert L; Epstein, Joshua M; Dean, Jeffrey S; Gumerman, George J; Swedlund, Alan C; Harburger, Jason; Chakravarty, Shubha; Hammond, Ross; Parker, Jon; Parker, Miles

2002-05-14

Long House Valley in the Black Mesa area of northeastern Arizona (U.S.) was inhabited by the Kayenta Anasazi from about 1800 before Christ to about anno Domini 1300. These people were prehistoric ancestors of the modern Pueblo cultures of the Colorado Plateau. Paleoenvironmental research based on alluvial geomorphology, palynology, and dendroclimatology permits accurate quantitative reconstruction of annual fluctuations in potential agricultural production (kg of maize per hectare). The archaeological record of Anasazi farming groups from anno Domini 200-1300 provides information on a millennium of sociocultural stasis, variability, change, and adaptation. We report on a multiagent computational model of this society that closely reproduces the main features of its actual history, including population ebb and flow, changing spatial settlement patterns, and eventual rapid decline. The agents in the model are monoagriculturalists, who decide both where to situate their fields as well as the location of their settlements. Nutritional needs constrain fertility. Agent heterogeneity, difficult to model mathematically, is demonstrated to be crucial to the high fidelity of the model.

Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley

PubMed Central

Axtell, Robert L.; Epstein, Joshua M.; Dean, Jeffrey S.; Gumerman, George J.; Swedlund, Alan C.; Harburger, Jason; Chakravarty, Shubha; Hammond, Ross; Parker, Jon; Parker, Miles

2002-01-01

Long House Valley in the Black Mesa area of northeastern Arizona (U.S.) was inhabited by the Kayenta Anasazi from about 1800 before Christ to about anno Domini 1300. These people were prehistoric ancestors of the modern Pueblo cultures of the Colorado Plateau. Paleoenvironmental research based on alluvial geomorphology, palynology, and dendroclimatology permits accurate quantitative reconstruction of annual fluctuations in potential agricultural production (kg of maize per hectare). The archaeological record of Anasazi farming groups from anno Domini 200-1300 provides information on a millennium of sociocultural stasis, variability, change, and adaptation. We report on a multiagent computational model of this society that closely reproduces the main features of its actual history, including population ebb and flow, changing spatial settlement patterns, and eventual rapid decline. The agents in the model are monoagriculturalists, who decide both where to situate their fields as well as the location of their settlements. Nutritional needs constrain fertility. Agent heterogeneity, difficult to model mathematically, is demonstrated to be crucial to the high fidelity of the model. PMID:12011406

Reliability analysis in interdependent smart grid systems

NASA Astrophysics Data System (ADS)

Peng, Hao; Kan, Zhe; Zhao, Dandan; Han, Jianmin; Lu, Jianfeng; Hu, Zhaolong

2018-06-01

Complex network theory is a useful way to study many real complex systems. In this paper, a reliability analysis model based on complex network theory is introduced in interdependent smart grid systems. In this paper, we focus on understanding the structure of smart grid systems and studying the underlying network model, their interactions, and relationships and how cascading failures occur in the interdependent smart grid systems. We propose a practical model for interdependent smart grid systems using complex theory. Besides, based on percolation theory, we also study the effect of cascading failures effect and reveal detailed mathematical analysis of failure propagation in such systems. We analyze the reliability of our proposed model caused by random attacks or failures by calculating the size of giant functioning components in interdependent smart grid systems. Our simulation results also show that there exists a threshold for the proportion of faulty nodes, beyond which the smart grid systems collapse. Also we determine the critical values for different system parameters. In this way, the reliability analysis model based on complex network theory can be effectively utilized for anti-attack and protection purposes in interdependent smart grid systems.

Human cerebral venous outflow pathway depends on posture and central venous pressure

PubMed Central

Gisolf, J; van Lieshout, J J; van Heusden, K; Pott, F; Stok, W J; Karemaker, J M

2004-01-01

Internal jugular veins are the major cerebral venous outflow pathway in supine humans. In upright humans the positioning of these veins above heart level causes them to collapse. An alternative cerebral outflow pathway is the vertebral venous plexus. We set out to determine the effect of posture and central venous pressure (CVP) on the distribution of cerebral outflow over the internal jugular veins and the vertebral plexus, using a mathematical model. Input to the model was a data set of beat-to-beat cerebral blood flow velocity and CVP measurements in 10 healthy subjects, during baseline rest and a Valsalva manoeuvre in the supine and standing position. The model, consisting of 2 jugular veins, each a chain of 10 units containing nonlinear resistances and capacitors, and a vertebral plexus containing a resistance, showed blood flow mainly through the internal jugular veins in the supine position, but mainly through the vertebral plexus in the upright position. A Valsalva manoeuvre while standing completely re-opened the jugular veins. Results of ultrasound imaging of the right internal jugular vein cross-sectional area at the level of the laryngeal prominence in six healthy subjects, before and during a Valsalva manoeuvre in both body positions, correlate highly with model simulation of the jugular cross-sectional area (R2 = 0.97). The results suggest that the cerebral venous flow distribution depends on posture and CVP: in supine humans the internal jugular veins are the primary pathway. The internal jugular veins are collapsed in the standing position and blood is shunted to an alternative venous pathway, but a marked increase in CVP while standing completely re-opens the jugular veins. PMID:15284348

The timing and intensity of column collapse during explosive volcanic eruptions

NASA Astrophysics Data System (ADS)

Carazzo, Guillaume; Kaminski, Edouard; Tait, Stephen

2015-02-01

Volcanic columns produced by explosive eruptions commonly reach, at some stage, a collapse regime with associated pyroclastic density currents propagating on the ground. The threshold conditions for the entrance into this regime are mainly controlled by the mass flux and exsolved gas content at the source. However, column collapse is often partial and the controls on the fraction of total mass flux that feeds the pyroclastic density currents, defined here as the intensity of collapse, are unknown. To better understand this regime, we use a new experimental apparatus reproducing at laboratory scale the convecting and collapsing behavior of hot particle-laden air jets. We validate the predictions of a 1D theoretical model for the entrance into the regime of partial collapse. Furthermore, we show that where a buoyant plume and a collapsing fountain coexist, the intensity of collapse can be predicted by a universal scaling relationship. We find that the intensity of collapse in the partial collapse regime is controlled by magma gas content and temperature, and always exceeds 40%, independent of peak mass flux and total erupted volume. The comparison between our theoretical predictions and a set of geological data on historic and pre-historic explosive eruptions shows that the model can be used to predict both the onset and intensity of column collapse, hence it can be used for rapid assessment of volcanic hazards notably ash dispersal during eruptive crises.

Correlated random walks induced by dynamical wavefunction collapse

NASA Astrophysics Data System (ADS)

Bedingham, Daniel

2015-03-01

Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.

Stress evolution during caldera collapse

NASA Astrophysics Data System (ADS)

Holohan, E. P.; Schöpfer, M. P. J.; Walsh, J. J.

2015-07-01

The mechanics of caldera collapse are subject of long-running debate. Particular uncertainties concern how stresses around a magma reservoir relate to fracturing as the reservoir roof collapses, and how roof collapse in turn impacts upon the reservoir. We used two-dimensional Distinct Element Method models to characterise the evolution of stress around a depleting sub-surface magma body during gravity-driven collapse of its roof. These models illustrate how principal stress orientations rotate during progressive deformation so that roof fracturing transitions from initial reverse faulting to later normal faulting. They also reveal four end-member stress paths to fracture, each corresponding to a particular location within the roof. Analysis of these paths indicates that fractures associated with ultimate roof failure initiate in compression (i.e. as shear fractures). We also report on how mechanical and geometric conditions in the roof affect pre-failure unloading and post-failure reloading of the reservoir. In particular, the models show how residual friction within a failed roof could, without friction reduction mechanisms or fluid-derived counter-effects, inhibit a return to a lithostatically equilibrated pressure in the magma reservoir. Many of these findings should be transferable to other gravity-driven collapse processes, such as sinkhole formation, mine collapse and subsidence above hydrocarbon reservoirs.

Numeric simulation of relativistic stellar core collapse and the formation of Reissner-Nordstroem black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghezzi, Cristian R.; Letelier, Patricio S.

2007-01-15

The time evolution of a set of 22M{sub {center_dot}} unstable charged stars that collapse is computed integrating the Einstein-Maxwell equations. The model simulates the collapse of a spherical star that had exhausted its nuclear fuel and has or acquires a net electric charge in its core while collapsing. When the charge-to-mass ratio is Q/{radical}(G)M{>=}1, the star does not collapse but spreads. On the other hand, a different physical behavior is observed with a charge-to-mass ratio of 1>Q/{radical}(G)M>0.1. In this case, the collapsing matter forms a bubble enclosing a lower density core. We discuss an immediate astrophysical consequence of these resultsmore » that is a more efficient neutrino trapping during the stellar collapse and an alternative mechanism for powerful supernova explosions. The outer space-time of the star is the Reissner-Nordstroem solution that matches smoothly with our interior numerical solution; thus the collapsing models form Reissner-Nordstroem black holes.« less

Radiating gravitational collapse with shearing motion and bulk viscosity

NASA Astrophysics Data System (ADS)

Chan, R.

2001-03-01

A model is proposed of a collapsing radiating star consisting of a shearing fluid with bulk viscosity undergoing radial heat flow with outgoing radiation. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the bulk viscosity the pressure becomes more and more anisotropic. The behavior of the density, pressure, mass, luminosity, the effective adiabatic index and the Kretschmann scalar is analyzed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 Msun.

Radiating gravitational collapse with shear viscosity

NASA Astrophysics Data System (ADS)

Chan, R.

2000-08-01

A model is proposed of a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial heat flow with outgoing radiation. The pressure of the star, at the beginning of the collapse, is isotropic but owing to the presence of the shear viscosity the pressure becomes more and more anisotropic. The behaviour of the density, pressure, mass, luminosity and the effective adiabatic index is analysed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6Msolar.

Collapse of differentially rotating neutron stars and cosmic censorship

NASA Astrophysics Data System (ADS)

Giacomazzo, Bruno; Rezzolla, Luciano; Stergioulas, Nikolaos

2011-07-01

We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum J/M2, where J and M are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with J/M2<1, i.e. “sub-Kerr” models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves resemble those seen for uniformly rotating stars, although with an overall decrease in the efficiency of gravitational-wave emission. For stellar models with J/M2>1, i.e. “supra-Kerr” models, on the other hand, we were not able to find models that are dynamically unstable and all of the computed supra-Kerr models were found to be far from the stability threshold. For these models a gravitational collapse is possible only after a very severe and artificial reduction of the pressure, which then leads to a torus developing nonaxisymmetric instabilities and eventually contracting to a stable axisymmetric stellar configuration. While this does not exclude the possibility that a naked singularity can be produced by the collapse of a differentially rotating star, it also suggests that cosmic censorship is not violated and that generic conditions for a supra-Kerr progenitor do not lead to a naked singularity.

Dynamics of bubble collapse under vessel confinement in 2D hydrodynamic experiments

NASA Astrophysics Data System (ADS)

Shpuntova, Galina; Austin, Joanna

2013-11-01

One trauma mechanism in biomedical treatment techniques based on the application of cumulative pressure pulses generated either externally (as in shock-wave lithotripsy) or internally (by laser-induced plasma) is the collapse of voids. However, prediction of void-collapse driven tissue damage is a challenging problem, involving complex and dynamic thermomechanical processes in a heterogeneous material. We carry out a series of model experiments to investigate the hydrodynamic processes of voids collapsing under dynamic loading in configurations designed to model cavitation with vessel confinement. The baseline case of void collapse near a single interface is also examined. Thin sheets of tissue-surrogate polymer materials with varying acoustic impedance are used to create one or two parallel material interfaces near the void. Shadowgraph photography and two-color, single-frame particle image velocimetry quantify bubble collapse dynamics including jetting, interface dynamics and penetration, and the response of the surrounding material. Research supported by NSF Award #0954769, ``CAREER: Dynamics and damage of void collapse in biological materials under stress wave loading.''

Targeting HIV services to male migrant workers in southern Africa would not reverse generalized HIV epidemics in their home communities: a mathematical modeling analysis

PubMed Central

Klein, Daniel J.; Eckhoff, Philip A.; Bershteyn, Anna

2015-01-01

Background Migrant populations such as mine workers contributed to the spread of HIV in sub-Saharan Africa. We used a mathematical model to estimate the community-wide impact of targeting treatment and prevention to male migrants. Methods We augmented an individual-based network model, EMOD-HIV v0.8, to include an age-dependent propensity for males to migrate. Migrants were exposed to HIV outside their home community, but continued to participate in HIV transmission in the community during periodic visits. Results Migrant-targeted interventions would have been transformative in the 1980s to 1990s, but post-2015 impacts were more modest. When targetable migrants comprised 2% of adult males, workplace HIV prevention averted 3.5% of community-wide infections over 20 years. Targeted treatment averted 8.5% of all-cause deaths among migrants. When migrants comprised 10% of males, workplace prevention averted 16.2% of infections in the community, one-quarter of which were among migrants. Workplace prevention and treatment acted synergistically, averting 17.1% of community infections and 11.6% of deaths among migrants. These estimates do not include prevention of secondary spread of HIV or tuberculosis at the workplace. Conclusions Though cost-effective, targeting migrants cannot collapse generalized epidemics in their home communities. Such a strategy would only have been possible prior to the early 1990s. However, migrant-targeted interventions synergize with general-population expansion of HIV services. PMID:25733560

Scale-free gravitational collapse as the origin of ρ ˜ r-2 density profile - a possible role of turbulence in regulating gravitational collapse

NASA Astrophysics Data System (ADS)

Li, Guang-Xing

2018-03-01

Astrophysical systems, such as clumps that form star clusters share a density profile that is close to ρ ˜ r-2. We prove analytically this density profile is the result of the scale-free nature of the gravitational collapse. Therefore, it should emerge in many different situations as long as gravity is dominating the evolution for a period that is comparable or longer than the free-fall time, and this does not necessarily imply an isothermal model, as many have previously believed. To describe the collapse process, we construct a model called the turbulence-regulated gravitational collapse model, where turbulence is sustained by accretion and dissipates in roughly a crossing time. We demonstrate that a ρ ˜ r-2 profile emerges due to the scale-free nature the system. In this particular case, the rate of gravitational collapse is regulated by the rate at which turbulence dissipates the kinetic energy such that the infall speed can be 20-50% of the free-fall speed(which also depends on the interpretation of the crossing time based on simulations of driven turbulence). These predictions are consistent with existing observations, which suggests that these clumps are in the stage of turbulence-regulated gravitational collapse. Our analysis provides a unified description of gravitational collapse in different environments.

Gravity induced wave function collapse

NASA Astrophysics Data System (ADS)

Gasbarri, G.; Toroš, M.; Donadi, S.; Bassi, A.

2017-11-01

Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥10-26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤10-20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ˜10-21.

Discriminating the effects of collapse models from environmental diffusion with levitated nanospheres

NASA Astrophysics Data System (ADS)

Li, Jie; Zippilli, Stefano; Zhang, Jing; Vitali, David

2016-05-01

Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because it is nontrivial to discriminate unambiguously their presence in experiments where other hardly controllable sources of noise compete to the overall decoherence. Here we provide a simple procedure that is able to probe the hypothetical presence of the collapse noise with a levitated nanosphere in a Fabry-Pérot cavity. We show that the stationary state of the system is particularly sensitive, under specific experimental conditions, to the interplay between the trapping frequency, the cavity size, and the momentum diffusion induced by the collapse models, allowing one to detect them even in the presence of standard environmental noises.

Practical Methods for the Analysis of Voltage Collapse in Electric Power Systems: a Stationary Bifurcations Viewpoint.

NASA Astrophysics Data System (ADS)

Jean-Jumeau, Rene

1993-03-01

Voltage collapse (VC) is generally caused by either of two types of system disturbances: load variations and contingencies. In this thesis, we study VC resulting from load variations. This is termed static voltage collapse. This thesis deals with this type of voltage collapse in electrical power systems by using a stationary bifurcations viewpoint by associating it with the occurrence of saddle node bifurcations (SNB) in the system. Approximate models are generically used in most VC analyses. We consider the validity of these models for the study of SNB and, thus, of voltage collapse. We justify the use of saddle node bifurcation as a model for VC in power systems. In particular, we prove that this leads to definition of a model and--since load demand is used as a parameter for that model--of a mode of parameterization of that model in order to represent actual power demand variations within the power system network. Ill-conditioning of the set of nonlinear equations defining a dynamical system is a generic occurence near the SNB point. We suggest a reparameterization of the set of nonlinear equations which allows to avoid this problem. A new indicator for the proximity of voltage collapse, the voltage collapse index (VCI), is developed. A new (n + 1)-dimensional set of characteristic equations for the computation of the exact SNB point, replacing the standard (2n + 1)-dimensional one is presented for general parameter -dependent nonlinear dynamical systems. These results are then applied to electric power systems for the analysis and prediction of voltage collapse. The new methods offer the potential of faster computation and greater flexibility. For reasons of theoretical development and clarity, the preceding methodologies are developed under the assumption of the absence of constraints on the system parameters and states, and the full differentiability of the functions defining the power system model. In the latter part of this thesis, we relax these assumptions in order to develop a framework and new formulation for application of the tools previously developed for the analysis and prediction of voltage collapse in practical power system models which include numerous constraints and discontinuities. Illustrations and numerical simulations throughout the thesis support our results.

Could a Mathematics Student Have Prevented the Collapse of the Atlanto-Scandian Herring?

ERIC Educational Resources Information Center

Sigurdsson, Thorir

2006-01-01

Herring in the ocean between Iceland and Norway was one of the largest fish stocks in the world until the fishery crashed in the late 1960s. The catch in 1971 was only 20 thousand metric tons in contrast with the record of 2 million tons in 1966 and the spawning stock declined from 10 million tons to 10 thousand tons in 20 years. After 25 years of…

Robust Intelligence (RI) Under Uncertainty: Mathematical Foundations of Autonomous Hybrid (Human-Machine-Robot) Teams, Organizations and Systems

DTIC Science & Technology

2013-01-01

seeds of chaos. Stability and internal peace bring prosperity; prosperity causes population increase. Demographic growth leads to overpopulation ... overpopulation causes lower wages, higher land rents, and falling per-capita incomes … [Eventually, the] collapse of order brings … famine, war...one of the most innovative, competitive and largest firms in the world (e.g., Investors Business Daily, 2000, 10/31; Bloomberg’s Businessweek, 2001, 9

The effect of giant flank collapses on magma pathways and location of volcanic vents

NASA Astrophysics Data System (ADS)

Maccaferri, Francesco; Richter, Nicole; Walter, Thomas

2017-04-01

Flank collapses have been identified at tall volcanoes and ocean islands worldwide. They are recurrent processes, significantly contributing to the morphological and structural evolution of volcanic edifices, and they often occur in interaction with magmatic activity. Moreover, it has been observed that the intrusion pathways and eruption's sites often differ before and after flank collapses. While it is understood that dyke intrusions might destabilise a volcano flank, and a moving flank might create the space needed for further intrusions, the effect of collapses on the magma pathways has been rarely addressed. Here we use a boundary element model for dyke propagation to study the effect of the stress redistribution due to a flank collapse on the location of eruptive vents. We use our model to simulate the path of magmatic intrusion after the collapse of the eastern flank of Fogo Volcano, Cabe Verde. We find that the competition between loading stress due to the volcanic edifice and unloading due to the collapse of a flank favours magmatic activity to cluster within the collapse scar, displaced with respect to the pre-collapse volcanic centre. Our results are compared with geomorphological observations at Fogo Island and are discussed in the general context of the long-term evolution intraplate volcanic ocean islands worldwide.

Key variables influencing patterns of lava dome growth and collapse

NASA Astrophysics Data System (ADS)

Husain, T.; Elsworth, D.; Voight, B.; Mattioli, G. S.; Jansma, P. E.

2013-12-01

Lava domes are conical structures that grow by the infusion of viscous silicic or intermediate composition magma from a central volcanic conduit. Dome growth can be characterized by repeated cycles of growth punctuated by collapse, as the structure becomes oversized for its composite strength. Within these cycles, deformation ranges from slow long term deformation to sudden deep-seated collapses. Collapses may range from small raveling failures to voluminous and fast-moving pyroclastic flows with rapid and long-downslope-reach from the edifice. Infusion rate and magma rheology together with crystallization temperature and volatile content govern the spatial distribution of strength in the structure. Solidification, driven by degassing-induced crystallization of magma leads to the formation of a continuously evolving frictional talus as a hard outer shell. This shell encapsulates the cohesion-dominated soft ductile core. Here we explore the mechanics of lava dome growth and failure using a two-dimensional particle-dynamics model. This meshless model follows the natural evolution of a brittle carapace formed by loss of volatiles and rheological stiffening and avoids difficulties of hour-glassing and mesh-entangelment typical in meshed models. We test the fidelity of the model against existing experimental and observational models of lava dome growth. The particle-dynamics model follows the natural development of dome growth and collapse which is infeasible using simple analytical models. The model provides insight into the triggers that lead to the transition in collapse mechasnism from shallow flank collapse to deep seated sector collapse. Increase in material stiffness due to decrease in infusion rate results in the transition of growth pattern from endogenous to exogenous. The material stiffness and strength are strongly controlled by the magma infusion rate. Increase in infusion rate decreases the time available for degassing induced crystallization leading to a transition in the growth pattern, while a decrease in infusion rate results in larger crystals causing the material to stiffen leading to formation of spines. Material stiffness controls the growth direction of the viscous plug in the lava dome interior. Material strength and stiffness controled by rate of infusion influence lava dome growth more significantly than coefficient of frictional of the talus.

Finite-element modeling of magma chamber-host rock interactions prior to caldera collapse

NASA Astrophysics Data System (ADS)

Kabele, Petr; Žák, Jiří; Somr, Michael

2017-06-01

Gravity-driven failure of shallow magma chamber roofs and formation of collapse calderas are commonly accompanied by ejection of large volumes of pyroclastic material to the Earth's atmosphere and thus represent severe volcanic hazards. In this respect, numerical analysis has proven as a key tool in understanding the mechanical conditions of caldera collapse. The main objective of this paper is to find a suitable approach to finite-element simulation of roof fracturing and caldera collapse during inflation and subsequent deflation of shallow magma chambers. Such a model should capture the dominant mechanical phenomena, for example, interaction of the host rock with magma and progressive deformation of the chamber roof. To this end, a comparative study, which involves various representations of magma (inviscid fluid, nearly incompressible elastic, or plastic solid) and constitutive models of the host rock (fracture and plasticity), was carried out. In particular, the quasi-brittle fracture model of host rock reproduced well the formation of tension-induced radial and circumferential fractures during magma injection into the chamber (inflation stage), especially at shallow crustal levels. Conversely, the Mohr-Coulomb shear criterion has shown to be more appropriate for greater depths. Subsequent magma withdrawal from the chamber (deflation stage) results in further damage or even collapse of the chamber roof. While most of the previous studies of caldera collapse rely on the elastic stress analysis, the proposed approach advances modeling of the process by incorporating non-linear failure phenomena and nearly incompressible behaviour of magma. This leads to a perhaps more realistic representation of the fracture processes preceding roof collapse and caldera formation.

Modelling Technique for Demonstrating Gravity Collapse Structures in Jointed Rock.

ERIC Educational Resources Information Center

Stimpson, B.

1979-01-01

Described is a base-friction modeling technique for studying the development of collapse structures in jointed rocks. A moving belt beneath weak material is designed to simulate gravity. A description is given of the model frame construction. (Author/SA)

Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems

NASA Astrophysics Data System (ADS)

Simonov, Kyrylo; Hiesmayr, Beatrix C.

2016-11-01

Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons (K meson, D meson, Bd meson, and Bs meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007), 10.1088/1751-8113/40/12/S03] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986), 10.1103/PhysRevD.34.470]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.

Study on Collapse Mechanism of Steel Frame Structure under High Temperature and Blast Loading

NASA Astrophysics Data System (ADS)

Baoxin, Qi; Yan, Shi; Bi, Jialiang

2018-03-01

Numerical simulation analysis for collapsing process and mechanism of steel frame structures under the combined effects of fire and explosion is performed in this paper. First of all, a new steel constitutive model considering fire (high temperature softening effect) and blast (strain rate effect) is established. On the basis of the traditional Johnson-Cook model and the Perzyna model, the relationship between strain and scaled distance as well as the EOUROCODE3 standard heating curve taking into account the temperature effect parameters is introduced, and a modified Johnson-Cook constitutive model is established. Then, the influence of considering the scaled distance is introduced in order to more effectively describe the destruction and collapse phenomena of steel frame structures. Some conclusions are obtained based on the numerical analysis that the destruction will be serious and even progressively collapse with decreasing of the temperature of the steel column for the same scaled distance under the combined effects of fire and blast; the damage will be serious with decreasing of the scaled distance of the steel column under the same temperature under the combined effects of fire and blast; in the case of the combined effects of fire and blast happening in the side-spans, the partial progressive collapse occurs as the scaled distance is less than or equal to 1.28; six kinds of damages which are no damage, minor damage, moderate damage, severe damage, critical collapse, and progressive collapse.

A novel animal model for hyperdynamic airway collapse.

PubMed

Tsukada, Hisashi; O'Donnell, Carl R; Garland, Robert; Herth, Felix; Decamp, Malcolm; Ernst, Armin

2010-12-01

Tracheobronchomalacia (TBM) is increasingly recognized as a condition associated with significant pulmonary morbidity. However, treatment is invasive and complex, and because there is no appropriate animal model, novel diagnostic and treatment strategies are difficult to evaluate. We endeavored to develop a reliable airway model to simulate hyperdynamic airway collapse in humans. Seven 20-kg male sheep were enrolled in this study. Tracheomalacia was created by submucosal resection of > 50% of the circumference of 10 consecutive cervical tracheal cartilage rings through a midline cervical incision. A silicone stent was placed in the trachea to prevent airway collapse during recovery. Tracheal collapsibility was assessed at protocol-specific time points by bronchoscopy and multidetector CT imaging while temporarily removing the stent. Esophageal pressure and flow data were collected to assess flow limitation during spontaneous breathing. All animals tolerated the surgical procedure well and were stented without complications. One sheep died at 2 weeks because of respiratory failure related to stent migration. In all sheep, near-total forced inspiratory airway collapse was observed up to 3 months postprocedure. Esophageal manometry demonstrated flow limitation associated with large negative pleural pressure swings during rapid spontaneous inhalation. Hyperdynamic airway collapse can reliably be induced with this technique. It may serve as a model for evaluation of novel diagnostic and therapeutic strategies for TBM.

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2002-01-01

The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

Stratovolcano stability assessment methods and results from Citlaltepetl, Mexico

USGS Publications Warehouse

Zimbelman, D.R.; Watters, R.J.; Firth, I.R.; Breit, G.N.; Carrasco-Nunez, Gerardo

2004-01-01

Citlaltépetl volcano is the easternmost stratovolcano in the Trans-Mexican Volcanic Belt. Situated within 110 km of Veracruz, it has experienced two major collapse events and, subsequent to its last collapse, rebuilt a massive, symmetrical summit cone. To enhance hazard mitigation efforts we assess the stability of Citlaltépetl's summit cone, the area thought most likely to fail during a potential massive collapse event. Through geologic mapping, alteration mineralogy, geotechnical studies, and stability modeling we provide important constraints on the likelihood, location, and size of a potential collapse event. The volcano's summit cone is young, highly fractured, and hydrothermally altered. Fractures are most abundant within 5–20-m wide zones defined by multiple parallel to subparallel fractures. Alteration is most pervasive within the fracture systems and includes acid sulfate, advanced argillic, argillic, and silicification ranks. Fractured and altered rocks both have significantly reduced rock strengths, representing likely bounding surfaces for future collapse events. The fracture systems and altered rock masses occur non-uniformly, as an orthogonal set with N–S and E–W trends. Because these surfaces occur non-uniformly, hazards associated with collapse are unevenly distributed about the volcano. Depending on uncertainties in bounding surfaces, but constrained by detailed field studies, potential failure volumes are estimated to range between 0.04–0.5 km3. Stability modeling was used to assess potential edifice failure events. Modeled failure of the outer portion of the cone initially occurs as an "intact block" bounded by steeply dipping joints and outwardly dipping flow contacts. As collapse progresses, more of the inner cone fails and the outer "intact" block transforms into a collection of smaller blocks. Eventually, a steep face develops in the uppermost and central portion of the cone. This modeled failure morphology mimics collapse amphitheaters

Migration of cells in a social context

PubMed Central

Vedel, Søren; Tay, Savaş; Johnston, Darius M.; Bruus, Henrik; Quake, Stephen R.

2013-01-01

In multicellular organisms and complex ecosystems, cells migrate in a social context. Whereas this is essential for the basic processes of life, the influence of neighboring cells on the individual remains poorly understood. Previous work on isolated cells has observed a stereotypical migratory behavior characterized by short-time directional persistence with long-time random movement. We discovered a much richer dynamic in the social context, with significant variations in directionality, displacement, and speed, which are all modulated by local cell density. We developed a mathematical model based on the experimentally identified “cellular traffic rules” and basic physics that revealed that these emergent behaviors are caused by the interplay of single-cell properties and intercellular interactions, the latter being dominated by a pseudopod formation bias mediated by secreted chemicals and pseudopod collapse following collisions. The model demonstrates how aspects of complex biology can be explained by simple rules of physics and constitutes a rapid test bed for future studies of collective migration of individual cells. PMID:23251032

Migration of cells in a social context.

PubMed

Vedel, Søren; Tay, Savaş; Johnston, Darius M; Bruus, Henrik; Quake, Stephen R

2013-01-02

In multicellular organisms and complex ecosystems, cells migrate in a social context. Whereas this is essential for the basic processes of life, the influence of neighboring cells on the individual remains poorly understood. Previous work on isolated cells has observed a stereotypical migratory behavior characterized by short-time directional persistence with long-time random movement. We discovered a much richer dynamic in the social context, with significant variations in directionality, displacement, and speed, which are all modulated by local cell density. We developed a mathematical model based on the experimentally identified "cellular traffic rules" and basic physics that revealed that these emergent behaviors are caused by the interplay of single-cell properties and intercellular interactions, the latter being dominated by a pseudopod formation bias mediated by secreted chemicals and pseudopod collapse following collisions. The model demonstrates how aspects of complex biology can be explained by simple rules of physics and constitutes a rapid test bed for future studies of collective migration of individual cells.

Network inoculation: Heteroclinics and phase transitions in an epidemic model

NASA Astrophysics Data System (ADS)

Yang, Hui; Rogers, Tim; Gross, Thilo

2016-08-01

In epidemiological modelling, dynamics on networks, and, in particular, adaptive and heterogeneous networks have recently received much interest. Here, we present a detailed analysis of a previously proposed model that combines heterogeneity in the individuals with adaptive rewiring of the network structure in response to a disease. We show that in this model, qualitative changes in the dynamics occur in two phase transitions. In a macroscopic description, one of these corresponds to a local bifurcation, whereas the other one corresponds to a non-local heteroclinic bifurcation. This model thus provides a rare example of a system where a phase transition is caused by a non-local bifurcation, while both micro- and macro-level dynamics are accessible to mathematical analysis. The bifurcation points mark the onset of a behaviour that we call network inoculation. In the respective parameter region, exposure of the system to a pathogen will lead to an outbreak that collapses but leaves the network in a configuration where the disease cannot reinvade, despite every agent returning to the susceptible class. We argue that this behaviour and the associated phase transitions can be expected to occur in a wide class of models of sufficient complexity.

Advanced collapsible tank for liquid containment

NASA Technical Reports Server (NTRS)

Flanagan, David T.; Hopkins, Robert C.

1993-01-01

Tanks for bulk liquid containment will be required to support advanced planetary exploration programs. Potential applications include storage of potable, process, and waste water, and fuels and process chemicals. The launch mass and volume penalties inherent in rigid tanks suggest that collapsible tanks may be more efficient. Collapsible tanks are made of lightweight flexible material and can be folded compactly for storage and transport. Although collapsible tanks for terrestrial use are widely available, a new design was developed that has significantly less mass and bulk than existing models. Modelled after the shape of a sessible drop, this design features a dual membrane with a nearly uniform stress distribution and a low surface-to-volume ratio. It can be adapted to store a variety of liquids in nearly any environment with constant acceleration field. Three models of 10L, 50L, and 378L capacity have been constructed and tested. The 378L (100 gallon) model weighed less than 10 percent of a commercially available collapsible tank of equivalent capacity, and required less than 20 percent of the storage space when folded for transport.

Collapsible Cubes and Other Curiosities.

ERIC Educational Resources Information Center

Johnson, Scott; Walser, Hans

1997-01-01

Describes some general techniques for making collapsible models, including spiral models, for all the Platonic solids except the cube. Discusses the nature of the dissections of the faces necessary for the construction of the spiral cube. (ASK)

Direct collapse to supermassive black hole seeds: comparing the AMR and SPH approaches.

PubMed

Luo, Yang; Nagamine, Kentaro; Shlosman, Isaac

2016-07-01

We provide detailed comparison between the adaptive mesh refinement (AMR) code enzo-2.4 and the smoothed particle hydrodynamics (SPH)/ N -body code gadget-3 in the context of isolated or cosmological direct baryonic collapse within dark matter (DM) haloes to form supermassive black holes. Gas flow is examined by following evolution of basic parameters of accretion flows. Both codes show an overall agreement in the general features of the collapse; however, many subtle differences exist. For isolated models, the codes increase their spatial and mass resolutions at different pace, which leads to substantially earlier collapse in SPH than in AMR cases due to higher gravitational resolution in gadget-3. In cosmological runs, the AMR develops a slightly higher baryonic resolution than SPH during halo growth via cold accretion permeated by mergers. Still, both codes agree in the build-up of DM and baryonic structures. However, with the onset of collapse, this difference in mass and spatial resolution is amplified, so evolution of SPH models begins to lag behind. Such a delay can have effect on formation/destruction rate of H 2 due to UV background, and on basic properties of host haloes. Finally, isolated non-cosmological models in spinning haloes, with spin parameter λ ∼ 0.01-0.07, show delayed collapse for greater λ, but pace of this increase is faster for AMR. Within our simulation set-up, gadget-3 requires significantly larger computational resources than enzo-2.4 during collapse, and needs similar resources, during the pre-collapse, cosmological structure formation phase. Yet it benefits from substantially higher gravitational force and hydrodynamic resolutions, except at the end of collapse.

Direct collapse to supermassive black hole seeds: comparing the AMR and SPH approaches

NASA Astrophysics Data System (ADS)

Luo, Yang; Nagamine, Kentaro; Shlosman, Isaac

2016-07-01

We provide detailed comparison between the adaptive mesh refinement (AMR) code ENZO-2.4 and the smoothed particle hydrodynamics (SPH)/N-body code GADGET-3 in the context of isolated or cosmological direct baryonic collapse within dark matter (DM) haloes to form supermassive black holes. Gas flow is examined by following evolution of basic parameters of accretion flows. Both codes show an overall agreement in the general features of the collapse; however, many subtle differences exist. For isolated models, the codes increase their spatial and mass resolutions at different pace, which leads to substantially earlier collapse in SPH than in AMR cases due to higher gravitational resolution in GADGET-3. In cosmological runs, the AMR develops a slightly higher baryonic resolution than SPH during halo growth via cold accretion permeated by mergers. Still, both codes agree in the build-up of DM and baryonic structures. However, with the onset of collapse, this difference in mass and spatial resolution is amplified, so evolution of SPH models begins to lag behind. Such a delay can have effect on formation/destruction rate of H2 due to UV background, and on basic properties of host haloes. Finally, isolated non-cosmological models in spinning haloes, with spin parameter λ ˜ 0.01-0.07, show delayed collapse for greater λ, but pace of this increase is faster for AMR. Within our simulation set-up, GADGET-3 requires significantly larger computational resources than ENZO-2.4 during collapse, and needs similar resources, during the pre-collapse, cosmological structure formation phase. Yet it benefits from substantially higher gravitational force and hydrodynamic resolutions, except at the end of collapse.

Numerical investigation of wake-collapse internal waves generated by a submerged moving body

NASA Astrophysics Data System (ADS)

Liang, Jianjun; Du, Tao; Huang, Weigen; He, Mingxia

2017-07-01

The state-of-the-art OpenFOAM technology is used to develop a numerical model that can be devoted to numerically investigating wake-collapse internal waves generated by a submerged moving body. The model incorporates body geometry, propeller forcing, and stratification magnitude of seawater. The generation mechanism and wave properties are discussed based on model results. It was found that the generation of the wave and its properties depend greatly on the body speed. Only when that speed exceeds some critical value, between 1.5 and 4.5 m/s, can the moving body generate wake-collapse internal waves, and with increases of this speed, the time of generation advances and wave amplitude increases. The generated wake-collapse internal waves are confirmed to have characteristics of the second baroclinic mode. As the body speed increases, wave amplitude and length increase and its waveform tends to take on a regular sinusoidal shape. For three linearly temperature-stratified profiles examined, the weaker the stratification, the stronger the wake-collapse internal wave.

Evaluating nuclear physics inputs in core-collapse supernova models

NASA Astrophysics Data System (ADS)

Lentz, E.; Hix, W. R.; Baird, M. L.; Messer, O. E. B.; Mezzacappa, A.

Core-collapse supernova models depend on the details of the nuclear and weak interaction physics inputs just as they depend on the details of the macroscopic physics (transport, hydrodynamics, etc.), numerical methods, and progenitors. We present preliminary results from our ongoing comparison studies of nuclear and weak interaction physics inputs to core collapse supernova models using the spherically-symmetric, general relativistic, neutrino radiation hydrodynamics code Agile-Boltztran. We focus on comparisons of the effects of the nuclear EoS and the effects of improving the opacities, particularly neutrino--nucleon interactions.

Volcano electrical tomography unveils edifice collapse hazard linked to hydrothermal system structure and dynamics

NASA Astrophysics Data System (ADS)

Rosas-Carbajal, Marina; Komorowski, Jean-Christophe; Nicollin, Florence; Gibert, Dominique

2016-07-01

Catastrophic collapses of the flanks of stratovolcanoes constitute a major hazard threatening numerous lives in many countries. Although many such collapses occurred following the ascent of magma to the surface, many are not associated with magmatic reawakening but are triggered by a combination of forcing agents such as pore-fluid pressurization and/or mechanical weakening of the volcanic edifice often located above a low-strength detachment plane. The volume of altered rock available for collapse, the dynamics of the hydrothermal fluid reservoir and the geometry of incipient collapse failure planes are key parameters for edifice stability analysis and modelling that remain essentially hidden to current volcano monitoring techniques. Here we derive a high-resolution, three-dimensional electrical conductivity model of the La Soufrière de Guadeloupe volcano from extensive electrical tomography data. We identify several highly conductive regions in the lava dome that are associated to fluid saturated host-rock and preferential flow of highly acid hot fluids within the dome. We interpret this model together with the existing wealth of geological and geochemical data on the volcano to demonstrate the influence of the hydrothermal system dynamics on the hazards associated to collapse-prone altered volcanic edifices.

Volcano electrical tomography unveils edifice collapse hazard linked to hydrothermal system structure and dynamics

PubMed Central

Rosas-Carbajal, Marina; Komorowski, Jean-Christophe; Nicollin, Florence; Gibert, Dominique

2016-01-01

Catastrophic collapses of the flanks of stratovolcanoes constitute a major hazard threatening numerous lives in many countries. Although many such collapses occurred following the ascent of magma to the surface, many are not associated with magmatic reawakening but are triggered by a combination of forcing agents such as pore-fluid pressurization and/or mechanical weakening of the volcanic edifice often located above a low-strength detachment plane. The volume of altered rock available for collapse, the dynamics of the hydrothermal fluid reservoir and the geometry of incipient collapse failure planes are key parameters for edifice stability analysis and modelling that remain essentially hidden to current volcano monitoring techniques. Here we derive a high-resolution, three-dimensional electrical conductivity model of the La Soufrière de Guadeloupe volcano from extensive electrical tomography data. We identify several highly conductive regions in the lava dome that are associated to fluid saturated host-rock and preferential flow of highly acid hot fluids within the dome. We interpret this model together with the existing wealth of geological and geochemical data on the volcano to demonstrate the influence of the hydrothermal system dynamics on the hazards associated to collapse-prone altered volcanic edifices. PMID:27457494

Volcano electrical tomography unveils edifice collapse hazard linked to hydrothermal system structure and dynamics.

PubMed

Rosas-Carbajal, Marina; Komorowski, Jean-Christophe; Nicollin, Florence; Gibert, Dominique

2016-07-26

Catastrophic collapses of the flanks of stratovolcanoes constitute a major hazard threatening numerous lives in many countries. Although many such collapses occurred following the ascent of magma to the surface, many are not associated with magmatic reawakening but are triggered by a combination of forcing agents such as pore-fluid pressurization and/or mechanical weakening of the volcanic edifice often located above a low-strength detachment plane. The volume of altered rock available for collapse, the dynamics of the hydrothermal fluid reservoir and the geometry of incipient collapse failure planes are key parameters for edifice stability analysis and modelling that remain essentially hidden to current volcano monitoring techniques. Here we derive a high-resolution, three-dimensional electrical conductivity model of the La Soufrière de Guadeloupe volcano from extensive electrical tomography data. We identify several highly conductive regions in the lava dome that are associated to fluid saturated host-rock and preferential flow of highly acid hot fluids within the dome. We interpret this model together with the existing wealth of geological and geochemical data on the volcano to demonstrate the influence of the hydrothermal system dynamics on the hazards associated to collapse-prone altered volcanic edifices.

Generation of Collapsed Cross Sections for Hatch 1 Cycles 1-3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ade, Brian J

2012-11-01

Under NRC JCN V6361, Oak Ridge National Laboratory (ORNL) was tasked to develop and run SCALE/TRITON models for generation of collapsed few-group cross sections and to convert the cross sections to PMAXS format using the GENPMAXS conversion utility for use in PARCS/PATHS simulations of Hatch Unit 1, cycles 1-3. This letter report documents the final models used to produce the Hatch collapsed cross sections.

Evolution of Supernova Remnants

NASA Astrophysics Data System (ADS)

Arbutina, B.

2017-12-01

This book, both a monograph and a graduate textbook, is based on my original research and partly on the materials prepared earlier for the 2007 and 2008 IARS Astrophysics Summer School in Istanbul, AstroMundus course 'Supernovae and Their Remnants' that was held for the first time in 2011 at the Department of Astronomy, Faculty of Mathematics, University of Belgrade, and a graduate course 'Evolution of Supernova Remnants' that I teach at the aforementioned university. The first part Supernovae (introduction, thermonuclear supernovae, core-collapse supernovae) provides introductory information and explains the classification and physics of supernova explosions, while the second part Supernova remnants (introduction, shock waves, cosmic rays and particle acceleration, magnetic fields, synchrotron radiation, hydrodynamic and radio evolution of supernova remnants), which is the field I work in, is more detailed in scope i.e. technical/mathematical. Special attention is paid to details of mathematical derivations that often cannot be found in original works or available literature. Therefore, I believe it can be useful to both, graduate students and researchers interested in the field.

Quantum Measurement and Initial Conditions

NASA Astrophysics Data System (ADS)

Stoica, Ovidiu Cristinel

2016-03-01

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schrödinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schrödinger equation.

On the measurement of time for the quantum harmonic oscillator

NASA Technical Reports Server (NTRS)

Shepard, Scott R.

1992-01-01

A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.

A two-phase flow model for submarine granular flows: With an application to collapse of deeply-submerged granular columns

NASA Astrophysics Data System (ADS)

Lee, Cheng-Hsien; Huang, Zhenhua

2018-05-01

The collapse process of a submerged granular column is strongly affected by its initial packing. Previous models for particle response time, which is used to quantify the drag force between the solid and liquid phases in rheology-based two-phase flow models, have difficulty in simulating the collapse process of granular columns with different initial concentrations (initial packing conditions). This study introduces a new model for particle response time, which enables us to satisfactorily model the drag force between the two phases for a wide range of volume concentration. The present model can give satisfactory results for both loose and dense packing conditions. The numerical results have shown that (i) the initial packing affects the occurrence of contractancy/diltancy behavior during the collapse process, (ii) the general buoyancy and drag force are strongly affected by the initial packing through contractancy and diltancy, and (iii) the general buoyancy and drag force can destabilize the granular material in loose packing condition but stabilize the granular material in dense packing condition. The results have shown that the collapse process of a densely-packed granular column is more sensitive to particle response time than that of a loosely-packed granular column.

CFD simulation of reverse water-hammer induced by collapse of draft-tube cavity in a model pump-turbine during runaway process

NASA Astrophysics Data System (ADS)

Zhang, Xiaoxi; Cheng, Yongguang; Xia, Linsheng; Yang, Jiandong

2016-11-01

This paper reports the preliminary progress in the CFD simulation of the reverse water-hammer induced by the collapse of a draft-tube cavity in a model pump-turbine during the runaway process. Firstly, the Fluent customized 1D-3D coupling model for hydraulic transients and the Schnerr & Sauer cavitation model for cavity development are introduced. Then, the methods are validated by simulating the benchmark reverse water-hammer in a long pipe caused by a valve instant closure. The simulated head history at the valve agrees well with the measured data in literature. After that, the more complicated reverse water-hammer in the draft-tube of a runaway model pump-turbine, which is installed in a model pumped-storage power plant, is simulated. The dynamic processes of a vapor cavity, from generation, expansion, shrink to collapse, are shown. After the cavity collapsed, a sudden increase of pressure can be evidently observed. The process is featured by a locally expending and collapsing vapor cavity that is around the runner cone, which is different from the conventional recognition of violent water- column separation. This work reveals the possibility for simulating the reverse water-hammer phenomenon in turbines by 3D CFD.

Improved Noninterferometric Test of Collapse Models Using Ultracold Cantilevers

NASA Astrophysics Data System (ADS)

Vinante, A.; Mezzena, R.; Falferi, P.; Carlesso, M.; Bassi, A.

2017-09-01

Spontaneous collapse models predict that a weak force noise acts on any mechanical system, as a consequence of the collapse of the wave function. Significant upper limits on the collapse rate have been recently inferred from precision mechanical experiments, such as ultracold cantilevers and the space mission LISA Pathfinder. Here, we report new results from an experiment based on a high-Q cantilever cooled to millikelvin temperatures, which is potentially able to improve the current bounds on the continuous spontaneous localization (CSL) model by 1 order of magnitude. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.

Catastrophic volcanic collapse: relation to hydrothermal processes.

PubMed

López, D L; Williams, S N

1993-06-18

Catastrophic volcanic collapse, without precursory magmatic activity, is characteristic of many volcanic disasters. The extent and locations of hydrothermal discharges at Nevado del Ruiz volcano, Colombia, suggest that at many volcanoes collapse may result from the interactions between hydrothermal fluids and the volcanic edifice. Rock dissolution and hydrothermal mineral alteration, combined with physical triggers such as earth-quakes, can produce volcanic collapse. Hot spring water compositions, residence times, and flow paths through faults were used to model potential collapse at Ruiz. Caldera dimensions, deposits, and alteration mineral volumes are consistent with parameters observed at other volcanoes.

A Generalized Spatial Measure for Resilience of Microbial Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Renslow, Ryan S.; Lindemann, Stephen R.; Song, Hyun-Seob

2016-04-07

The emergent property of resilience is the ability of a system to return to an original state after a disturbance. Resilience may be used as an early warning system for significant or irreversible community transition, i.e., a community with diminishing or low resilience may be close to catastrophic shift in function or an irreversible collapse. Typically, resilience is quantified using recovery time, which may be difficult or impossible to directly measure in microbial systems. A recent study in the literature showed that under certain conditions, a set of spatial-based metrics termed recovery length, can be correlated to recovery time, andmore » thus may be a reasonable alternative measure of resilience. As a limitation, however, this spatial metric of resilience is useful only for step-change perturbations. Building upon the concept of recovery length, we propose a more general form of the spatial metric of resilience that can be applied to any shape of perturbation profiles (i.e., a sharp or smooth gradient). We termed this new spatial measure “perturbation-adjusted spatial metric of resilience” (PASMORE). We demonstrate the applicability of the proposed metric using a mathematical model of a microbial mat. PASMORE can help identify when a system, such as a microbial community, is on the verge of collapse or nearing an irreversible transition across a tipping point.« less

Patterns of recruitment and injury in a heterogeneous airway network model

PubMed Central

Stewart, Peter S.; Jensen, Oliver E.

2015-01-01

In respiratory distress, lung airways become flooded with liquid and may collapse due to surface-tension forces acting on air–liquid interfaces, inhibiting gas exchange. This paper proposes a mathematical multiscale model for the mechanical ventilation of a network of occluded airways, where air is forced into the network at a fixed tidal volume, allowing investigation of optimal recruitment strategies. The temporal response is derived from mechanistic models of individual airway reopening, incorporating feedback on the airway pressure due to recruitment. The model accounts for stochastic variability in airway diameter and stiffness across and between generations. For weak heterogeneity, the network is completely ventilated via one or more avalanches of recruitment (with airways recruited in quick succession), each characterized by a transient decrease in the airway pressure; avalanches become more erratic for airways that are initially more flooded. However, the time taken for complete ventilation of the network increases significantly as the network becomes more heterogeneous, leading to increased stresses on airway walls. The model predicts that the most peripheral airways are most at risk of ventilation-induced damage. A positive-end-expiratory pressure reduces the total recruitment time but at the cost of larger stresses exerted on airway walls. PMID:26423440

A History of Collapse Factor Modeling and Empirical Data for Cryogenic Propellant Tanks

NASA Technical Reports Server (NTRS)

deQuay, Laurence; Hodge, B. Keith

2010-01-01

One of the major technical problems associated with cryogenic liquid propellant systems used to supply rocket engines and their subassemblies and components is the phenomenon of propellant tank pressurant and ullage gas collapse. This collapse is mainly caused by heat transfer from ullage gas to tank walls and interfacing propellant, which are both at temperatures well below those of this gas. Mass transfer between ullage gas and cryogenic propellant can also occur and have minor to significant secondary effects that can increase or decrease ullage gas collapse. Pressurant gas is supplied into cryogenic propellant tanks in order to initially pressurize these tanks and then maintain required pressures as propellant is expelled from these tanks. The net effect of pressurant and ullage gas collapse is increased total mass and mass flow rate requirements of pressurant gases. For flight vehicles this leads to significant and undesirable weight penalties. For rocket engine component and subassembly ground test facilities this results in significantly increased facility hardware, construction, and operational costs. "Collapse Factor" is a parameter used to quantify the pressurant and ullage gas collapse. Accurate prediction of collapse factors, through analytical methods and modeling tools, and collection and evaluation of collapse factor data has evolved over the years since the start of space exploration programs in the 1950 s. Through the years, numerous documents have been published to preserve results of studies associated with the collapse factor phenomenon. This paper presents a summary and selected details of prior literature that document the aforementioned studies. Additionally other literature that present studies and results of heat and mass transfer processes, related to or providing important insights or analytical methods for the studies of collapse factor, are presented.

The capability of the existing network of installations for detecting the antineutrino burst from collapsing stars

NASA Technical Reports Server (NTRS)

Khalchukov, F. F.; Ryassny, V. G.; Ryazhskaya, O. G.; Zatsepin, G. T.

1985-01-01

As the neutrino fluxes can bring information from the internal layers of the collapsing star, the problem of the neutrino burst detection is of importance for both the direct registering of the collapse itself and the investigation of its dynamics. The main characteristics of the neutrino fluxes have been obtained by simulations. The total neutrino flux energy is estimated as 2.5 x 10 to the 53 to 1.4 x 10 to the 54 erg, the energy of NU sub E flux being 10 to the 53 erg. Predictions on neutrino energy spectra are quite different. Two models of the collapse will be used: the model by Bowers and Wilson, hereafter BW, and the model by Nadyozhin and Otroschenko (NO). The NU sub e spectrum in the BW-model reaches the maximum at E max sub NU = 8 MeV. Average energy of NU sub E E sub nu approx. = 10 MeV. The NO-model gives E max sub Nu = 10.5 MeV and E sub nu = 12.6 MeV. The NU sub E-burst duration is DELTA tau sub NU = 20s for the NO-model. As the black hole formation is the result of the star collapse in the BW-model, DELTA tau sub nu is taken to be 5s.

Warm dark matter effects in a spherical collapse model with shear and angular momentum

NASA Astrophysics Data System (ADS)

Marciu, Mihai

2016-03-01

This paper investigates the nonlinear structure formation in a spherical top-hat collapse model based on the pseudo-Newtonian approximation. The system is composed of warm dark matter and dark energy and the dynamical properties of the collapsing region are analyzed for various parametrizations of the dark matter equation of state which are in agreement with current observations. Concerning dark energy, observational constraints of the Chevallier-Polarski-Linder model and the Jassal-Bagla-Padmanabhan equation of state have been considered. During the collapse, the positive dark matter pressure leads to an increase of growth for dark matter and dark energy perturbations and an accelerated expansion for the spherical region. Hence, in the warm dark matter hypothesis, the structure formation is accelerated and the inconsistencies of the Λ CDM model at the galactic scales could be solved. The results obtained are applicable only to adiabatic warm dark matter physical models which are compatible with the pseudo-Newtonian approach.

Internal density waves of shock type induced by chemoconvection in miscible reacting liquids

NASA Astrophysics Data System (ADS)

Bratsun, D. A.

2017-10-01

A theoretical explanation of the phenomenon of spontaneous emergence of density waves experimentally observed recently in bilayered systems of miscible liquids placed in a narrow vertical gap of the Hele-Shaw cell in the gravitational field is provided. Upper and lower layers represent aqueous solutions of acids and bases, respectively, whose contact leads to the beginning of a neutralization reaction. The process is accompanied by a strong dependence of the reagent's diffusion coefficients on their concentrations, giving rise to the generation of local density pockets, in which convection develops. The cavities collapse under certain conditions, causing a density jump, which moves faster than typical perturbations in a medium and takes the form of a shock wave. A mathematical model of the phenomenon is proposed, which can be formally reduced to equations of motion of a compressible gas under certain assumptions. Numerical calculations are given and compared with the experimental data.

LAD Dissertation Prize Talk: Molecular Collisional Excitation in Astrophysical Environments

NASA Astrophysics Data System (ADS)

Walker, Kyle M.

2017-06-01

While molecular excitation calculations are vital in determining particle velocity distributions, internal state distributions, abundances, and ionization balance in gaseous environments, both theoretical calculations and experimental data for these processes are lacking. Reliable molecular collisional data with the most abundant species - H2, H, He, and electrons - are needed to probe material in astrophysical environments such as nebulae, molecular clouds, comets, and planetary atmospheres. However, excitation calculations with the main collider, H2, are computationally expensive and therefore various approximations are used to obtain unknown rate coefficients. The widely-accepted collider-mass scaling approach is flawed, and alternate scaling techniques based on physical and mathematical principles are presented here. The most up-to-date excitation data are used to model the chemical evolution of primordial species in the Recombination Era and produce accurate non-thermal spectra of the molecules H2+, HD, and H2 in a primordial cloud as it collapses into a first generation star.

Response of high-rise and base-isolated buildings to a hypothetical M w 7.0 blind thrust earthquake

USGS Publications Warehouse

Heaton, T.H.; Hall, J.F.; Wald, D.J.; Halling, M.W.

1995-01-01

High-rise flexible-frame buildings are commonly considered to be resistant to shaking from the largest earthquakes. In addition, base isolation has become increasingly popular for critical buildings that should still function after an earthquake. How will these two types of buildings perform if a large earthquake occurs beneath a metropolitan area? To answer this question, we simulated the near-source ground motions of a Mw 7.0 thrust earthquake and then mathematically modeled the response of a 20-story steel-frame building and a 3-story base-isolated building. The synthesized ground motions were characterized by large displacement pulses (up to 2 meters) and large ground velocities. These ground motions caused large deformation and possible collapse of the frame building, and they required exceptional measures in the design of the base-isolated building if it was to remain functional.

Dilatancy and compaction effects on the submerged granular column collapse

NASA Astrophysics Data System (ADS)

Wang, Chun; Wang, Yongqi; Peng, Chong; Meng, Xiannan

2017-10-01

The effects of dilatancy on the collapse dynamics of granular materials in air or in a liquid are studied experimentally and numerically. Experiments show that dilatancy has a critical effect on the collapse of granular columns in the presence of an ambient fluid. Two regimes of the collapse, one being quick and the other being slow, are observed from the experiments and the underlying reasons are analyzed. A two-fluid smoothed particle hydrodynamics model, based on the granular-fluid mixture theory and the critical state theory, is employed to investigate the complex interactions between the solid particles and the ambient water. It is found that dilatancy, resulting in large effective stress and large frictional coefficient between solid particles, helps form the slow regime. Small permeability, representing large inter-phase drag force, also retards the collapse significantly. The proposed numerical model is capable of reproducing these effects qualitatively.

Mechanics of airway and alveolar collapse in human breath-hold diving.

PubMed

Fitz-Clarke, John R

2007-11-15

A computational model of the human respiratory tract was developed to study airway and alveolar compression and re-expansion during deep breath-hold dives. The model incorporates the chest wall, supraglottic airway, trachea, branched airway tree, and elastic alveoli assigned time-dependent surfactant properties. Total lung collapse with degassing of all alveoli is predicted to occur around 235 m, much deeper than estimates for aquatic mammals. Hysteresis of the pressure-volume loop increases with maximum diving depth due to progressive alveolar collapse. Reopening of alveoli occurs stochastically as airway pressure overcomes adhesive and compressive forces on ascent. Surface area for gas exchange vanishes at collapse depth, implying that the risk of decompression sickness should reach a plateau beyond this depth. Pulmonary capillary transmural stresses cannot increase after local alveolar collapse. Consolidation of lung parenchyma might provide protection from capillary injury or leakage caused by vascular engorgement due to outward chest wall recoil at extreme depths.

Blue straggler formation at core collapse

NASA Astrophysics Data System (ADS)

Banerjee, Sambaran

Among the most striking feature of blue straggler stars (BSS) in globular clusters is the presence of multiple sequences of BSSs in the colour-magnitude diagrams (CMDs) of several globular clusters. It is often envisaged that such a multiple BSS sequence would arise due a recent core collapse of the host cluster, triggering a number of stellar collisions and binary mass transfers simultaneously over a brief episode of time. Here we examine this scenario using direct N-body computations of moderately-massive star clusters (of order 104 {M⊙). As a preliminary attempt, these models are initiated with ≈8-10 Gyr old stellar population and King profiles of high concentrations, being ``tuned'' to undergo core collapse quickly. BSSs are indeed found to form in a ``burst'' at the onset of the core collapse and several of such BS-bursts occur during the post-core-collapse phase. In those models that include a few percent primordial binaries, both collisional and binary BSSs form after the onset of the (near) core-collapse. However, there is as such no clear discrimination between the two types of BSSs in the corresponding computed CMDs. We note that this may be due to the less number of BSSs formed in these less massive models than that in actual globular clusters.

Investigation of the Mechanism of Roof Caving in the Jinchuan Nickel Mine, China

NASA Astrophysics Data System (ADS)

Ding, Kuo; Ma, Fengshan; Guo, Jie; Zhao, Haijun; Lu, Rong; Liu, Feng

2018-04-01

On 13 March 2016, a sudden, violent roof caving event with a collapse area of nearly 11,000 m2 occurred in the Jinchuan Nickel Mine and accompanied by air blasts, loud noises and ground vibrations. This collapse event coincided with related, conspicuous surface subsidence across an area of nearly 19,000 m2. This article aims to analyse this collapse event. In previous studies, various mining-induced collapses have been studied, but collapse accidents associated with the filling mining method are very rare and have not been thoroughly studied. The filling method has been regarded as a safe mining method for a long time, so research on associated collapse mechanisms is of considerable significance. In this study, a detailed field investigation of roadway damage was performed, and GPS monitoring results were used to analyse the surface failure. In addition, a numerical model was constructed based on the geometry of the ore body and a major fault. The analysis of the model revealed three failure mechanisms acting during different stages of destruction: double-sided embedded beam deformation, fault activation, and cantilever-articulated rock beam failure. The fault activation and the specific filling method are the key factors of this collapse event. To gain a better understanding of these factors, the shear stress and normal stress along the fault plane were monitored to determine the variation in stress at different failure stages. Discrete element models were established to study two filling methods and to analyse the stability of different filling structures.

Black hole formation from the gravitational collapse of a nonspherical network of structures

NASA Astrophysics Data System (ADS)

Delgado Gaspar, Ismael; Hidalgo, Juan Carlos; Sussman, Roberto A.; Quiros, Israel

2018-05-01

We examine the gravitational collapse and black hole formation of multiple nonspherical configurations constructed from Szekeres dust models with positive spatial curvature that smoothly match to a Schwarzschild exterior. These configurations are made of an almost spherical central core region surrounded by a network of "pancake-like" overdensities and voids with spatial positions prescribed through standard initial conditions. We show that a full collapse into a focusing singularity, without shell crossings appearing before the formation of an apparent horizon, is not possible unless the full configuration becomes exactly or almost spherical. Seeking for black hole formation, we demand that shell crossings are covered by the apparent horizon. This requires very special fine-tuned initial conditions that impose very strong and unrealistic constraints on the total black hole mass and full collapse time. As a consequence, nonspherical nonrotating dust sources cannot furnish even minimally realistic toy models of black hole formation at astrophysical scales: demanding realistic collapse time scales yields huge unrealistic black hole masses, while simulations of typical astrophysical black hole masses collapse in unrealistically small times. We note, however, that the resulting time-mass constraint is compatible with early Universe models of primordial black hole formation, suitable in early dust-like environments. Finally, we argue that the shell crossings appearing when nonspherical dust structures collapse are an indicator that such structures do not form galactic mass black holes but virialize into stable stationary objects.

Modeling of wave processes in blocky media with porous and fluid-saturated interlayers

NASA Astrophysics Data System (ADS)

Sadovskii, Vladimir M.; Sadovskaya, Oxana V.; Lukyanov, Alexander A.

2017-09-01

The wave processes in blocky media are analyzed by applying different mathematical models, wherein the elastic blocks interact with each other via pliant interlayers with the complex mechanical properties. Four versions of constitutive equations are considered. In the first version, an elastic interaction between the blocks is simulated within the framework of linear elasticity theory, and the model of elastic-plastic interlayers is constructed to take into account the appearance of irreversible deformation of interlayers at short time intervals. In the second one, the effects of viscoelastic shear in the interblock interlayers are taken into the consideration using the Poynting-Thomson rheological scheme. In the third option, the model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. In the fourth case, the model of a fluid-saturated material with open pores is examined based on Biot's equations. The collapse of pores is modeled by the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact, which is used to describe the behavior of materials with the different resistance to tension and compression. It was shown that the thermodynamically consistent model is provided, which means that the energy balance equation is fulfilled for an entire blocky structure, where the kinetic and potential energy of the system is the sum of the kinetic and potential energies of the blocks and interlayers. Under numerical implementation of the interlayers models, the dissipationless finite difference Ivanov's method was used. The splitting method by spatial variables in the combination with the Godunov gap decay scheme was applied in the blocks. As a result, robust and stable computational algorithms are built and tested. Using MPI technology, the parallel software was designed for the modeling of wave processes in 2D setting. The numerical results are presented, discussed and future studies are outlined.

Failure Analysis of Overhanging Blocks in the Walls of a Gas Storage Salt Cavern: A Case Study

NASA Astrophysics Data System (ADS)

Wang, Tongtao; Yang, Chunhe; Li, Jianjun; Li, Jinlong; Shi, Xilin; Ma, Hongling

2017-01-01

Most of the rock salt of China is bedded, in which non-salt layers and rock salt layers alternate. Due to the poor solubility of the non-salt layers, many blocks overhang on the walls of the caverns used for gas storage, constructed by water leaching. These overhanging blocks may collapse at any time, which may damage the tubing and casing string, and even cause instability of the cavern. They are one of the main factors threatening the safety of caverns excavated in bedded rock salt formations. In this paper, a geomechanical model of the JJKK-D salt cavern, located in Jintan salt district, Jintan city, Jiangsu province, China, is established to evaluate the stability of the overhanging blocks on its walls. The characters of the target formation, property parameters of the rock mass, and actual working conditions are considered in the geomechanical model. An index system composed of stress, displacement, plastic zone, safety factor, and equivalent strain is used to predict the collapse length of the overhanging blocks, the moment the collapse will take place, and the main factors causing the collapse. The sonar survey data of the JJKK-D salt cavern are used to verify the reliability and accuracy of the proposed geomechanical model. The results show that the proposed geomechanical model has a good reliability and accuracy, and can be used for the collapse prediction of the overhanging blocks on the wall of the JJKK-D salt cavern. The collapse length of the overhanging block is about 8 m. We conclude that the collapse takes place during the debrining. The reason behind the collapse is the sudden decrease of the fluid density, leading to the increase of the self-weight of the overhanging blocks. This study provides a basis for the collapse prediction method of the overhanging blocks of Jintan salt cavern gas storage, and can also serve as a reference for salt cavern gas storage with similar conditions to deal with overhanging blocks.

The 2011 collapse of Puu Oo pit crater, Hawaii: insights from digital image correlation and Discrete Element Method models

NASA Astrophysics Data System (ADS)

Holohan, E. P.; Walter, T. R.; Schöpfer, M. P. J.; Walsh, J. J.; Orr, T.; Poland, M.

2012-04-01

In March 2011, a spectacular fissure eruption on Kilauea was associated with a major collapse event in the highly-active Puu Oo crater. Time-lapse cameras maintained by the Hawaii Volcano Observatory captured views of the crater in the moments before, during, and after the collapse. The 2011 event hence represents a unique opportunity to characterize the surface deformation related to the onset of a pit crater collapse and to understand what factors influence it. To do so, we used two approaches. First, we analyzed the available series of camera images by means of digital image correlation techniques. This enabled us to gain a semi-quantitative (pixel-unit) description of the surface displacements and the structural development of the collapsing crater floor. Secondly, we ran a series of 'true-scale' numerical pit-crater collapse simulations based on the two-dimensional Distinct Element Method (2D-DEM). This enabled us to gain insights into what geometric and mechanical factors could have controlled the observed surface displacement pattern and structural development. Our analysis of the time-lapse images reveals that the crater floor initially gently sagged, and then rapidly collapsed in association with the appearance of a large ring-like fault scarp. The observed structural development and surface displacement patterns of the March 2011 Puu Oo collapse are best reproduced in DEM models with a relatively shallow magma reservoir that is vertically elongated, and with a crater floor rock mass that is reasonably strong. In combining digital image correlation with DEM modeling, our study highlights the future potential of these relatively new techniques for understanding physical processes at active volcanoes.

Collapse events of two-color optical beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sukhinin, Alexey; Aceves, Alejandro B.; Diels, Jean-Claude

2017-03-08

Here in this work, we study optical self-focusing that leads to collapse events for the time-independent model of copropagating beams with different wavelengths. We show that collapse events depend on the combined critical power of two beams for fundamental, vortex, and mixed configurations as well as on the ratio of their individual powers.

Triggering Collapse of the Presolar Dense Cloud Core and Injecting Short-lived Radioisotopes with a Shock Wave. V. Nonisothermal Collapse Regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boss, Alan P., E-mail: aboss@carnegiescience.edu

Recent meteoritical analyses support an initial abundance of the short-lived radioisotope (SLRI) {sup 60}Fe that may be high enough to require nucleosynthesis in a core-collapse supernova, followed by rapid incorporation into primitive meteoritical components, rather than a scenario where such isotopes were inherited from a well-mixed region of a giant molecular cloud polluted by a variety of supernovae remnants and massive star winds. This paper continues to explore the former scenario, by calculating three-dimensional, adaptive mesh refinement, hydrodynamical code (FLASH 2.5) models of the self-gravitational, dynamical collapse of a molecular cloud core that has been struck by a thin shockmore » front with a speed of 40 km s{sup −1}, leading to the injection of shock front matter into the collapsing cloud through the formation of Rayleigh–Taylor fingers at the shock–cloud intersection. These models extend the previous work into the nonisothermal collapse regime using a polytropic approximation to represent compressional heating in the optically thick protostar. The models show that the injection efficiencies of shock front materials are enhanced compared to previous models, which were not carried into the nonisothermal regime, and so did not reach such high densities. The new models, combined with the recent estimates of initial {sup 60}Fe abundances, imply that the supernova triggering and injection scenario remains a plausible explanation for the origin of the SLRIs involved in the formation of our solar system.« less

The Impact of Progenitor Mass Loss on the Dynamical and Spectral Evolution of Supernova Remnants

NASA Astrophysics Data System (ADS)

Patnaude, Daniel J.; Lee, Shiu-Hang; Slane, Patrick O.; Badenes, Carles; Nagataki, Shigehiro; Ellison, Donald C.; Milisavljevic, Dan

2017-11-01

There is now substantial evidence that the progenitors of some core-collapse supernovae undergo enhanced or extreme mass loss prior to explosion. The imprint of this mass loss is observed in the spectra and dynamics of the expanding blast wave on timescales of days to years after core collapse, and the effects on the spectral and dynamical evolution may linger long after the supernova has evolved into the remnant stage. In this paper, we present, for the first time, largely self-consistent end-to-end simulations for the evolution of a massive star from the pre-main sequence, up to and through core collapse, and into the remnant phase. We present three models and compare and contrast how the progenitor mass-loss history impacts the dynamics and spectral evolution of the supernovae and supernova remnants. We study a model that only includes steady mass loss, a model with enhanced mass loss over a period of ˜5000 yr prior to core collapse, and a model with extreme mass loss over a period of ˜500 yr prior to core collapse. The models are not meant to address any particular supernova or supernova remnant, but rather to highlight the important role that the progenitor evolution plays in the observable qualities of supernovae and supernova remnants. Through comparisons of these three different progenitor evolution scenarios, we find that the mass loss in late stages (during and after core carbon burning) can have a profound impact on the dynamics and spectral evolution of the supernova remnant centuries after core collapse.

Two-dimensional Core-collapse Supernova Explosions Aided by General Relativity with Multidimensional Neutrino Transport

NASA Astrophysics Data System (ADS)

O’Connor, Evan P.; Couch, Sean M.

2018-02-01

We present results from simulations of core-collapse supernovae in FLASH using a newly implemented multidimensional neutrino transport scheme and a newly implemented general relativistic (GR) treatment of gravity. We use a two-moment method with an analytic closure (so-called M1 transport) for the neutrino transport. This transport is multienergy, multispecies, velocity dependent, and truly multidimensional, i.e., we do not assume the commonly used “ray-by-ray” approximation. Our GR gravity is implemented in our Newtonian hydrodynamics simulations via an effective relativistic potential that closely reproduces the GR structure of neutron stars and has been shown to match GR simulations of core collapse quite well. In axisymmetry, we simulate core-collapse supernovae with four different progenitor models in both Newtonian and GR gravity. We find that the more compact proto–neutron star structure realized in simulations with GR gravity gives higher neutrino luminosities and higher neutrino energies. These differences in turn give higher neutrino heating rates (upward of ∼20%–30% over the corresponding Newtonian gravity simulations) that increase the efficacy of the neutrino mechanism. Three of the four models successfully explode in the simulations assuming GREP gravity. In our Newtonian gravity simulations, two of the four models explode, but at times much later than observed in our GR gravity simulations. Our results, in both Newtonian and GR gravity, compare well with several other studies in the literature. These results conclusively show that the approximation of Newtonian gravity for simulating the core-collapse supernova central engine is not acceptable. We also simulate four additional models in GR gravity to highlight the growing disparity between parameterized 1D models of core-collapse supernovae and the current generation of 2D models.

Intense electromagnetic outbursts from collapsing hypermassive neutron stars

NASA Astrophysics Data System (ADS)

Lehner, Luis; Palenzuela, Carlos; Liebling, Steven L.; Thompson, Christopher; Hanna, Chad

2012-11-01

We study the gravitational collapse of a magnetized neutron star using a novel numerical approach able to capture both the dynamics of the star and the behavior of the surrounding plasma. In this approach, a fully general relativistic magnetohydrodynamics implementation models the collapse of the star and provides appropriate boundary conditions to a force-free model which describes the stellar exterior. We validate this strategy by comparing with known results for the rotating monopole and aligned rotator solutions and then apply it to study both rotating and nonrotating stellar collapse scenarios and contrast the behavior with what is obtained when employing the electrovacuum approximation outside the star. The nonrotating electrovacuum collapse is shown to agree qualitatively with a Newtonian model of the electromagnetic field outside a collapsing star. We illustrate and discuss a fundamental difference between the force-free and electrovacuum solutions, involving the appearance of large zones of electric-dominated field in the vacuum case. This provides a clear demonstration of how dissipative singularities appear generically in the nonlinear time evolution of force-free fluids. In both the rotating and nonrotating cases, our simulations indicate that the collapse induces a strong electromagnetic transient, which leaves behind an uncharged, unmagnetized Kerr black hole. In the case of submillisecond rotation, the magnetic field experiences strong winding, and the transient carries much more energy. This result has important implications for models of gamma-ray bursts. Even when the neutron star is surrounded by an accretion torus (as in binary merger and collapsar scenarios), a magnetosphere may emerge through a dynamo process operating in a surface shear layer. When this rapidly rotating magnetar collapses to a black hole, the electromagnetic energy released can compete with the later output in a Blandford-Znajek jet. Much less electromagnetic energy is released by a massive magnetar that is (initially) gravitationally stable: its rotational energy is dissipated mainly by internal torques. A distinct plasmoid structure is seen in our nonrotating simulations, which will generate a radio transient with subluminal expansion and greater synchrotron efficiency than is expected in shock models. Closely related phenomena appear to be at work in the giant flares of Galactic magnetars.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jansson, Karl Wahlberg; Johansen, Anders; Syed, Mohtashim Bukhari

Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of millimeter- to centimeter-size pebbles. Such clouds can form, for example, through the streaming instability in protoplanetary disks. We model the collapse process with a statistical model to obtain the internal structure of planetesimals with solid radii between 10 and 1000 km. During the collapse, pebbles collide, and depending on their relative speeds, collisions have different outcomes. A mixture of particle sizes inside a planetesimal leads to better packing capabilities and higher densities. In this paper we apply results from new laboratory experiments of dustmore » aggregate collisions (presented in a companion paper) to model collision outcomes. We find that the internal structure of a planetesimal is strongly dependent on both its mass and the applied fragmentation model. Low-mass planetesimals have no/few fragmenting pebble collisions in the collapse phase and end up as porous pebble piles. The number of fragmenting collisions increases with increasing cloud mass, resulting in wider particle size distributions and higher density. The collapse is nevertheless “cold” in the sense that collision speeds are damped by the high collision frequency. This ensures that a significant fraction of large pebbles survive the collapse in all but the most massive clouds. Our results are in broad agreement with the observed increase in density of Kuiper Belt objects with increasing size, as exemplified by the recent characterization of the highly porous comet 67P/Churyumov–Gerasimenko.« less

Broadband Evaluation of DPRK Explosions, Collapse Event, and Induced Aftershocks

NASA Astrophysics Data System (ADS)

Mayeda, K.; Roman-Nieves, J. I.; Wagner, G.; Jeon, Y. S.

2017-12-01

We report on the past 6 declared DPRK nuclear explosions, a collapse event, and recent associated induced shear dislocation sources using long-period waveform modeling, direct regional phases, and stable P-coda and S-coda spectral ratios. We find that the recent September 3rd, 2017 explosion is well modeled with an MM71 explosion source model at normal scale depth, but the previous 5 smaller yield explosions exhibit much larger relative high frequency radiation, strongly suggesting they are all over buried by varying amounts. The collapse event that occurred 8 minutes following the September 3rd DPRK explosion shares significant similarities with a number of NTS collapse events for explosions of comparable yield, both in absolute amplitude and spectral fall-off. A large number of smaller sources have been observed, which from stable coda spectral analysis and waveform modeling, are consistent with shallow shear dislocations likely caused by stress redistribution following the past nuclear explosions. We conclude with testing of a new discriminant that is specific to this region.

Rapid Configurational Fluctuations in a Model of Methylcellulose

NASA Astrophysics Data System (ADS)

Li, Xiaolan; Dorfman, Kevin

Methylcellulose is a thermoresponsive polymer that undergoes a phase transition at elevated temperature, forming fibrils of a uniform diameter. However, the gelation mechanism is still unclear, in particular at higher polymer concentrations. We have investigated a coarse-grained model for methylcellulose, proposed by Larson and coworkers, that produces collapsed toroids in dilute solution with a radius close to that in experiments. Using Brownian Dynamics simulations, we demonstrate that this model's dihedral potential generates ``flipping events'', which helps the chain to avoid kinetic traps by undergoing a sudden transition between a coiled and a collapsed state. If the dihedral potential is removed, the chains cannot escape from their collapsed configuration, whereas at high dihedral potentials, the chains cannot stabilize the collapsed state. We will present quantitative results on the effect of the dihedral potential on both chain statistics and dynamic behavior, and discuss the implication of our results on the spontaneous formation of high-aspect ratio fibrils in experiments.

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

NASA Astrophysics Data System (ADS)

La Rocca, Michele; Adduce, Claudia; Sciortino, Giampiero; Pinzon, Allen Bateman

2008-10-01

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

Gravitational waves and core-collapse supernovae

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Moiseenko, S. G.

2017-11-01

A mechanism of formation of gravitational waves in the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spheroid of dust and a finite-entropy spheroid. Numerical simulation results on core-collapse supernova explosions are presented for the neutrino and magneto-rotational models. These results are used to estimate the dimensionless amplitude of the gravitational wave with a frequency ν ~ 1300 Hz, radiated during the collapse of the rotating core of a pre-supernova with a mass of 1.2 M⊙ (calculated by the authors in 2D). This estimate agrees well with many other calculations (presented in this paper) that have been done in 2D and 3D settings and which rely on more exact and sophisticated calculations of the gravitational wave amplitude. The formation of the large-scale structure of the Universe in the Zel’dovich pancake model involves the emission of very long-wavelength gravitational waves. The average amplitude of these waves is calculated from the simulation, in the uniform spheroid approximation, of the nonspherical collapse of noncollisional dust matter, which imitates dark matter. It is noted that a gravitational wave radiated during a core-collapse supernova explosion in our Galaxy has a sufficient amplitude to be detected by existing gravitational wave telescopes.

On the implementation of the spherical collapse model for dark energy models

NASA Astrophysics Data System (ADS)

Pace, Francesco; Meyer, Sven; Bartelmann, Matthias

2017-10-01

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δc, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δc for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.

Volcano collapse promoted by progressive strength reduction: New data from Mount St. Helens

USGS Publications Warehouse

Reid, Mark E.; Keith, Terry E.C.; Kayen, Robert E.; Iverson, Neal R.; Iverson, Richard M.; Brien, Dianne

2010-01-01

Rock shear strength plays a fundamental role in volcano flank collapse, yet pertinent data from modern collapse surfaces are rare. Using samples collected from the inferred failure surface of the massive 1980 collapse of Mount St. Helens (MSH), we determined rock shear strength via laboratory tests designed to mimic conditions in the pre-collapse edifice. We observed that the 1980 failure shear surfaces formed primarily in pervasively shattered older dome rocks; failure was not localized in sloping volcanic strata or in weak, hydrothermally altered rocks. Our test results show that rock shear strength under large confining stresses is reduced ∼20% as a result of large quasi-static shear strain, as preceded the 1980 collapse of MSH. Using quasi-3D slope-stability modeling, we demonstrate that this mechanical weakening could have provoked edifice collapse, even in the absence of transiently elevated pore-fluid pressures or earthquake ground shaking. Progressive strength reduction could promote collapses at other volcanic edifices.

How Fast is Collapse of Proteins During Folding?

NASA Astrophysics Data System (ADS)

Chahine, J.; Onuchic, J. N.; Socci, N. D.

1998-03-01

Recent experiments in fast folding proteins are now starting to address the question of how fast is collapse relative to the total folding time. Using minimalist models, we are able to investigate the way in which different scenarios of folding can arise depending on the interplay between the collapse order parameter and the order parameter sensitive to specific tertiary contacts. Most of our earlier studies have focused on the limit that collapse is very fast compared to the total folding time. In this work we focus on the opposite limit, i.e., at the folding temperature, collapse and folding occurs simultaneously. The folding mechanism becomes very different in this limit. Particularly, the non-specific collapse transition, that occurs at temperatures higher than the folding temperature for the fast collapse limit, now occurs between the folding and the glass temperature. We show how this transition can be identified and its consequences for the folding kinetics.

Inexpensive Device for Demonstrating Rock Slope Failure and Other Collapse Phenomena.

ERIC Educational Resources Information Center

Stimpson, B.

1980-01-01

Describes an inexpensive modeling technique for demonstrating large-scale displacement phenomena in rock masses, such as slope collapse and failure of underground openings. Excavation of the model material occurs through openings made in the polyurethane foam in the correct excavation sequence. (Author/SA)

Characteristic density contrasts in the evolution of superclusters. The case of A2142 supercluster

NASA Astrophysics Data System (ADS)

Gramann, Mirt; Einasto, Maret; Heinämäki, Pekka; Teerikorpi, Pekka; Saar, Enn; Nurmi, Pasi; Einasto, Jaan

2015-09-01

Context. The formation and evolution of the cosmic web in which galaxy superclusters are the largest relatively isolated objects is governed by a gravitational attraction of dark matter and antigravity of dark energy (cosmological constant). Aims: We study the characteristic density contrasts in the spherical collapse model for several epochs in the supercluster evolution and their dynamical state. Methods: We analysed the density contrasts for the turnaround, future collapse, and zero gravity in different ΛCDM models and applied them to study the dynamical state of the supercluster A2142 with an almost spherical main body, making it a suitable test object to apply a model that assumes sphericity. Results: We present characteristic density contrasts in the spherical collapse model for different cosmological parameters. The analysis of the supercluster A2142 shows that its high-density core has already started to collapse. The zero-gravity line outlines the outer region of the main body of the supercluster. In the course of future evolution, the supercluster may split into several collapsing systems. Conclusions: The various density contrasts presented in our study and applied to the supercluster A2142 offer a promising way to characterise the dynamical state and expected future evolution of galaxy superclusters.

In silico investigation of blast-induced intracranial fluid cavitation as it potentially leads to traumatic brain injury

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haniff, S.; Taylor, P. A.

In this paper, we conducted computational macroscale simulations predicting blast-induced intracranial fluid cavitation possibly leading to brain injury. To further understanding of this problem, we developed microscale models investigating the effects of blast-induced cavitation bubble collapse within white matter axonal fiber bundles of the brain. We model fiber tracks of myelinated axons whose diameters are statistically representative of white matter. Nodes of Ranvier are modeled as unmyelinated sections of axon. Extracellular matrix envelops the axon fiber bundle, and gray matter is placed adjacent to the bundle. Cavitation bubbles are initially placed assuming an intracranial wave has already produced them. Pressuremore » pulses, of varied strengths, are applied to the upper boundary of the gray matter and propagate through the model, inducing bubble collapse. Simulations, conducted using the shock wave physics code CTH, predict an increase in pressure and von Mises stress in axons downstream of the bubbles after collapse. This appears to be the result of hydrodynamic jetting produced during bubble collapse. Interestingly, results predict axon cores suffer significantly lower shear stresses from proximal bubble collapse than does their myelin sheathing. Finally, simulations also predict damage to myelin sheathing, which, if true, degrades axonal electrical transmissibility and general health of the white matter structures in the brain.« less

In silico investigation of blast-induced intracranial fluid cavitation as it potentially leads to traumatic brain injury

DOE PAGES

Haniff, S.; Taylor, P. A.

2017-10-17

In this paper, we conducted computational macroscale simulations predicting blast-induced intracranial fluid cavitation possibly leading to brain injury. To further understanding of this problem, we developed microscale models investigating the effects of blast-induced cavitation bubble collapse within white matter axonal fiber bundles of the brain. We model fiber tracks of myelinated axons whose diameters are statistically representative of white matter. Nodes of Ranvier are modeled as unmyelinated sections of axon. Extracellular matrix envelops the axon fiber bundle, and gray matter is placed adjacent to the bundle. Cavitation bubbles are initially placed assuming an intracranial wave has already produced them. Pressuremore » pulses, of varied strengths, are applied to the upper boundary of the gray matter and propagate through the model, inducing bubble collapse. Simulations, conducted using the shock wave physics code CTH, predict an increase in pressure and von Mises stress in axons downstream of the bubbles after collapse. This appears to be the result of hydrodynamic jetting produced during bubble collapse. Interestingly, results predict axon cores suffer significantly lower shear stresses from proximal bubble collapse than does their myelin sheathing. Finally, simulations also predict damage to myelin sheathing, which, if true, degrades axonal electrical transmissibility and general health of the white matter structures in the brain.« less

Simulation of the ultrasound-induced growth and collapse of a near-wall bubble

NASA Astrophysics Data System (ADS)

Boyd, Bradley; Becker, Sid

2017-11-01

In this study, we consider the acoustically driven growth and collapse of a cavitation bubble in a fluid medium exposed to an ultrasound field. The bubble dynamics are modelled using a compressible, inviscid, multiphase model. The numerical scheme consists of a conservative interface capturing scheme which uses the fifth-order WENO reconstruction with a maximum-principle-satisfying and positivity-preserving limiter, and the HLLC approximate Riemann flux. To model the ultrasound input, a moving boundary oscillates through a fixed grid of finite-volume cells. The growth phase of the simulation shows the rapid non-spherical growth of the near-wall bubble. Once the bubble reaches its maximum size and the collapse phase begins, the simulation shows the formation of a jet which penetrates the bubble towards the wall at the later stages of the collapse. For a bubble with an initial radius of 50 μ m and an ultrasound pressure amplitude of 200 kPa, the pressure experienced by the wall increased rapidly nearing the end of the collapse, reaching a peak pressure of 13 MPa. This model is an important development in the field as it represents the physics of acoustic cavitation in more detail than before. This work was supported by the Royal Society of New Zealand's Marsden Fund.

In silico investigation of blast-induced intracranial fluid cavitation as it potentially leads to traumatic brain injury

NASA Astrophysics Data System (ADS)

Haniff, S.; Taylor, P. A.

2017-11-01

We conducted computational macroscale simulations predicting blast-induced intracranial fluid cavitation possibly leading to brain injury. To further understanding of this problem, we developed microscale models investigating the effects of blast-induced cavitation bubble collapse within white matter axonal fiber bundles of the brain. We model fiber tracks of myelinated axons whose diameters are statistically representative of white matter. Nodes of Ranvier are modeled as unmyelinated sections of axon. Extracellular matrix envelops the axon fiber bundle, and gray matter is placed adjacent to the bundle. Cavitation bubbles are initially placed assuming an intracranial wave has already produced them. Pressure pulses, of varied strengths, are applied to the upper boundary of the gray matter and propagate through the model, inducing bubble collapse. Simulations, conducted using the shock wave physics code CTH, predict an increase in pressure and von Mises stress in axons downstream of the bubbles after collapse. This appears to be the result of hydrodynamic jetting produced during bubble collapse. Interestingly, results predict axon cores suffer significantly lower shear stresses from proximal bubble collapse than does their myelin sheathing. Simulations also predict damage to myelin sheathing, which, if true, degrades axonal electrical transmissibility and general health of the white matter structures in the brain.

Gravity or turbulence? IV. Collapsing cores in out-of-virial disguise

NASA Astrophysics Data System (ADS)

Ballesteros-Paredes, Javier; Vázquez-Semadeni, Enrique; Palau, Aina; Klessen, Ralf S.

2018-06-01

We study the dynamical state of massive cores by using a simple analytical model, an observational sample, and numerical simulations of collapsing massive cores. From the analytical model, we find that cores increase their column density and velocity dispersion as they collapse, resulting in a time evolution path in the Larson velocity dispersion-size diagram from large sizes and small velocity dispersions to small sizes and large velocity dispersions, while they tend to equipartition between gravity and kinetic energy. From the observational sample, we find that: (a) cores with substantially different column densities in the sample do not follow a Larson-like linewidth-size relation. Instead, cores with higher column densities tend to be located in the upper-left corner of the Larson velocity dispersion σv, 3D-size R diagram, a result explained in the hierarchical and chaotic collapse scenario. (b) Cores appear to have overvirial values. Finally, our numerical simulations reproduce the behavior predicted by the analytical model and depicted in the observational sample: collapsing cores evolve towards larger velocity dispersions and smaller sizes as they collapse and increase their column density. More importantly, however, they exhibit overvirial states. This apparent excess is due to the assumption that the gravitational energy is given by the energy of an isolated homogeneous sphere. However, such excess disappears when the gravitational energy is correctly calculated from the actual spatial mass distribution. We conclude that the observed energy budget of cores is consistent with their non-thermal motions being driven by their self-gravity and in the process of dynamical collapse.

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

The effect of extreme ionization rates during the initial collapse of a molecular cloud core

NASA Astrophysics Data System (ADS)

Wurster, James; Bate, Matthew R.; Price, Daniel J.

2018-05-01

What cosmic ray ionization rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal MHD simulations of the gravitational collapse of rotating, one solar mass, magnetized molecular cloud cores, which include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of ag = 0.1 μm, and our free parameter is the cosmic ray ionization rate, ζcr. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ζcr ≳ 10-13 s-1 are indistinguishable from ideal MHD models, and the evolution of the model with ζcr = 10-14 s-1 matches the evolution of the ideal MHD model within 1 per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of ag. Models with very low ionization rates (ζcr ≲ 10-24 s-1) are required to approach hydrodynamical collapse, and even lower ionization rates may be required for larger ag. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionization rate. However, realistic cosmic ray ionization rates approach neither limit; thus, non-ideal MHD cannot be neglected in star formation simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benetti, Micol; Alcaniz, Jailson S.; Landau, Susana J., E-mail: micolbenetti@on.br, E-mail: slandau@df.uba.ar, E-mail: alcaniz@on.br

The hypothesis of the self-induced collapse of the inflaton wave function was proposed as responsible for the emergence of inhomogeneity and anisotropy at all scales. This proposal was studied within an almost de Sitter space-time approximation for the background, which led to a perfect scale-invariant power spectrum, and also for a quasi-de Sitter background, which allows to distinguish departures from the standard approach due to the inclusion of the collapse hypothesis. In this work we perform a Bayesian model comparison for two different choices of the self-induced collapse in a full quasi-de Sitter expansion scenario. In particular, we analyze themore » possibility of detecting the imprint of these collapse schemes at low multipoles of the anisotropy temperature power spectrum of the Cosmic Microwave Background (CMB) using the most recent data provided by the Planck Collaboration. Our results show that one of the two collapse schemes analyzed provides the same Bayesian evidence of the minimal standard cosmological model ΛCDM, while the other scenario is weakly disfavoured with respect to the standard cosmology.« less

Caldera collapse: Perspectives from comparing Galápagos volcanoes, nuclear-test sinks, sandbox models, and volcanoes on Mars

USGS Publications Warehouse

Howard, K.A.

2010-01-01

The 1968 trapdoor collapse (1.5 km3) of Fernandina caldera in the Galapágos Islands developed the same kinds of structures as found in small sandbox-collapse models and in concentrically zoned sinks formed in desert alluvium by fault subsidence into underground nuclear-explosion cavities. Fernandina’s collapse developed through shear failure in which the roof above the evacuating chamber was lowered mostly intact. This coherent subsidence contrasts to chaotic piecemeal collapse at small, rocky pit craters, underscoring the role of rock strength relative to subsidence size. The zoning at Fernandina implies that the deflated magma chamber underlay a central basin and a bordering inward-dipping monocline, which separates a blind inner reverse fault from an outer zone of normal faulting. Similar concentric zoning patterns can be recognized in coherent subsidence structures ranging over 16 orders of magnitude in size, from sandbox experiments to the giant Olympus Mons caldera on Mars.

Collapse of biodiversity in fractured metacommunities

NASA Astrophysics Data System (ADS)

Fisher, Charles; Mehta, Pankaj

2014-03-01

The increasing threat to global biodiversity from climate change, habitat destruction, and other anthropogenic factors motivates the search for features that increase the resistance of ecological communities to destructive disturbances. Recently, Gibson et al (Science 2013) observed that the damming of the Khlong Saeng river in Thailand caused a rapid collapse of biodiversity in the remaining tropical forests. Using a theoretical model that maps the distribution of coexisting species in an ecological community to a disordered system of Ising spins, we show that fracturing a metacommunity by inhibiting species dispersal leads to a collapse in biodiversity in the constituent local communities. The biodiversity collapse can be modeled as a diffusion on a rough energy landscape, and the resulting estimate for the rate of extinction highlights the role of species functional diversity in maintaining biodiversity following a disturbance.

Collapsing white dwarfs

NASA Technical Reports Server (NTRS)

Baron, E.; Cooperstein, J.; Kahana, S.; Nomoto, K.

1987-01-01

The results of the hydrodynamic collapse of an accreting C + O white dwarf are presented. Collapse is induced by electron captures in the iron core behind a conductive deflagration front. The shock wave produced by the hydrodynamic bounce of the iron core stalls at about 115 km, and thus a neutron star formed in such a model would be formed as an optically quiet event.

Contraction Signatures toward Dense Cores in the Perseus Molecular Cloud

NASA Astrophysics Data System (ADS)

Campbell, J. L.; Friesen, R. K.; Martin, P. G.; Caselli, P.; Kauffmann, J.; Pineda, J. E.

2016-03-01

We report the results of an HCO+ (3-2) and N2D+ (3-2) molecular line survey performed toward 91 dense cores in the Perseus molecular cloud using the James Clerk Maxwell Telescope, to identify the fraction of starless and protostellar cores with systematic radial motions. We quantify the HCO+ asymmetry using a dimensionless asymmetry parameter δv, and identify 20 cores with significant blue or red line asymmetries in optically thick emission indicative of collapsing or expanding motions, respectively. We separately fit the HCO+ profiles with an analytic collapse model and determine contraction (expansion) speeds toward 22 cores. Comparing the δv and collapse model results, we find that δv is a good tracer of core contraction if the optically thin emission is aligned with the model-derived systemic velocity. The contraction speeds range from subsonic (0.03 km s-1) to supersonic (0.4 km s-1), where the supersonic contraction speeds may trace global rather than local core contraction. Most cores have contraction speeds significantly less than their free-fall speeds. Only 7 of 28 starless cores have spectra well-fit by the collapse model, which more than doubles (15 of 28) for protostellar cores. Starless cores with masses greater than the Jeans mass (M/MJ > 1) are somewhat more likely to show contraction motions. We find no trend of optically thin non-thermal line width with M/MJ, suggesting that any undetected contraction motions are small and subsonic. Most starless cores in Perseus are either not in a state of collapse or expansion, or are in a very early stage of collapse.

Bounds on quantum collapse models from matter-wave interferometry: calculational details

NASA Astrophysics Data System (ADS)

Toroš, Marko; Bassi, Angelo

2018-03-01

We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse models: the Ghirardi-Rimini-Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-Markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL), and the Diósi-Penrose (DP) model. We discuss the separability of the dynamics of the collapse models along the three spatial directions, the validity of the paraxial approximation, and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two recent matter-wave experiments: the 2012 far-field experiment of Juffmann T et al (2012 Nat. Nanotechnol. 7 297-300) and the 2013 Kapitza-Dirac-Talbot-Lau (KDTL) near-field experiment of Eibenberger et al (2013 Phys. Chem. Chem. Phys. 15 14696-700). We show the region of the parameter space for each collapse model that is excluded by these experiments. We show that matter-wave experiments provide model-insensitive bounds that are valid for a wide family of dissipative and non-Markovian generalizations.

Physical Invariants of Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Distinct Element modeling of geophysical signatures during sinkhole collapse

NASA Astrophysics Data System (ADS)

Al-Halbouni, Djamil; Holohan, Eoghan P.; Taheri, Abbas; Dahm, Torsten

2017-04-01

A sinkhole forms due to the collapse of rocks or soil near the Earth's surface into an underground cavity. Such cavities represent large secondary pore spaces derived by dissolution and subrosion in the underground. By changing the stress field in the surrounding material, the growth of cavities can lead to a positive feedback, in which expansion and mechanical instability in the surrounding material increases or generates new secondary pore space (e.g. by fracturing), which in turn increases the cavity size, etc. A sinkhole forms due to the eventual subsidence or collapse of the overburden that becomes destabilized and fails all the way to the Earth's surface. Both natural processes like (sub)surface water movement and earthquakes, and human activities, such as mining, construction and groundwater extraction, intensify such feedbacks. The development of models for the mechanical interaction of a growing cavity and fracturing of its surrounding material, thus capturing related precursory geophysical signatures, has been limited, however. Here we report on the advances of a general, simplified approach to simulating cavity growth and sinkhole formation by using 2D Distinct Element Modeling (DEM) PFC5.0 software and thereby constraining pre-, syn- and post-collapse geophysical and geodetic signatures. This physically realistic approach allows for spontaneous cavity development and dislocation of rock mass to be simulated by bonded particle formulation of DEM. First, we present calibration and validation of our model. Surface subsidence above an instantaneously excavated circular cavity is tracked and compared with an incrementally increasing dissolution zone both for purely elastic and non-elastic material.This validation is important for the optimal choice of model dimensions and particles size with respect to simulation time. Second, a cavity growth approach is presented and compared to a well-documented case study, the deliberately intensified sinkhole collapse at Cerville-Buissoncourt in France. The outcomes of our model are compared with available extensiometer, surface-subsidence and microseismicity measurements during the pre- and syn-collapse period. The proposed model development and a possible archive of modeled scenarios may, in combination with a geodetic and seismological sinkhole monitoring, contribute to an early-warning tool for end-users and decision makers in areas affected by natural (e.g. Dead Sea) or man-made sinkhole collapses (mines).

Biological effects of stellar collapse neutrinos

PubMed

Collar, J I

1996-02-05

Massive stars in their final stages of collapse radiate most of their binding energy in the form of MeV neutrinos. The recoil atoms that they produce in elastic scattering off nuclei in organic tissue create radiation damage which is highly effective in the production of irreparable DNA harm, leading to cellular mutation, neoplasia, and oncogenesis. Using a conventional model of the galaxy and of the collapse mechanism, the periodicity of nearby stellar collapses and the radiation dose are calculated. The possible contribution of this process to the paleontological record of mass extinctions is examined.

Rotational Stiffness of Precast Beam-Column Connection using Finite Element Method

NASA Astrophysics Data System (ADS)

Hashim, N.; Agarwal, J.

2018-04-01

Current design practice in structural analysis is to assume the connection as pinned or rigid, however this cannot be relied upon for safety against collapse because during services the actual connection reacts differently where the connection has rotated in relevance. This situation may lead to different reactions and consequently affect design results and other frame responses. In precast concrete structures, connections play an important part in ensuring the safety of the whole structure. Thus, investigates on the actual connection behavior by construct the moment-rotation relationship is significant. Finite element (FE) method is chosen for modeling a 3-dimensional beam-column connection. The model is built in symmetry to reduce analysis time. Results demonstrate that precast billet connection is categorized as semi-rigid connection with Sini of 23,138kNm/rad. This is definitely different from the assumption of pinned or rigid connection used in design practice. Validation were made by comparing with mathematical equation and small differences were achieved that led to the conclusion where precast billet connection using FE method is acceptable.

Gravitational collapse and the vacuum energy

NASA Astrophysics Data System (ADS)

Campos, M.

2014-03-01

To explain the accelerated expansion of the universe, models with interacting dark components (dark energy and dark matter) have been considered recently in the literature. Generally, the dark energy component is physically interpreted as the vacuum energy of the all fields that fill the universe. As the other side of the same coin, the influence of the vacuum energy on the gravitational collapse is of great interest. We study such collapse adopting different parameterizations for the evolution of the vacuum energy. We discuss the homogeneous collapsing star fluid, that interacts with a vacuum energy component, using the stiff matter case as example. We conclude this work with a discussion of the Cahill-McVittie mass for the collapsed object.

Alveolar derecruitment and collapse induration as crucial mechanisms in lung injury and fibrosis.

PubMed

Lutz, Dennis; Gazdhar, Amiq; Lopez-Rodriguez, Elena; Ruppert, Clemens; Mahavadi, Poornima; Günther, Andreas; Klepetko, Walter; Bates, Jason H; Smith, Bradford; Geiser, Thomas; Ochs, Matthias; Knudsen, Lars

2015-02-01

Idiopathic pulmonary fibrosis (IPF) and bleomycin-induced pulmonary fibrosis are associated with surfactant system dysfunction, alveolar collapse (derecruitment), and collapse induration (irreversible collapse). These events play undefined roles in the loss of lung function. The purpose of this study was to quantify how surfactant inactivation, alveolar collapse, and collapse induration lead to degradation of lung function. Design-based stereology and invasive pulmonary function tests were performed 1, 3, 7, and 14 days after intratracheal bleomycin-instillation in rats. The number and size of open alveoli was correlated to mechanical properties. Active surfactant subtypes declined by Day 1, associated with a progressive alveolar derecruitment and a decrease in compliance. Alveolar epithelial damage was more pronounced in closed alveoli compared with ventilated alveoli. Collapse induration occurred on Day 7 and Day 14 as indicated by collapsed alveoli overgrown by a hyperplastic alveolar epithelium. This pathophysiology was also observed for the first time in human IPF lung explants. Before the onset of collapse induration, distal airspaces were easily recruited, and lung elastance could be kept low after recruitment by positive end-expiratory pressure (PEEP). At later time points, the recruitable fraction of the lung was reduced by collapse induration, causing elastance to be elevated at high levels of PEEP. Surfactant inactivation leading to alveolar collapse and subsequent collapse induration might be the primary pathway for the loss of alveoli in this animal model. Loss of alveoli is highly correlated with the degradation of lung function. Our ultrastructural observations suggest that collapse induration is important in human IPF.

On modeling complex interplay in small-scale self-organized socio-hydrological systems

NASA Astrophysics Data System (ADS)

Muneepeerakul, Rachata

2017-04-01

Successful and sustainable socio-hydrological systems, as in any coupled natural human-systems, require effective governance, which depends on the existence of proper infrastructure (both hard and soft). Recent work has addressed systems in which resource users and the organization responsible for maintaining the infrastructure are separate entities. However, many socio-hydrological systems, especially in developing countries, are small and without such formal division of labor; rather, such division of labor typically arises from self-organization within the population. In this work, we modify and mathematically operationalize a conceptual framework by developing a system of differential equations that capture the strategic behavior within such a self-organized population, its interplay with infrastructure characteristics and hydrological dynamics, and feedbacks between these elements. The model yields a number of insightful conditions related to long-term sustainability and collapse of the socio-hydrological system in the form of relationships between biophysical and social factors. These relationships encapsulate nonlinear interactions of these factors. The modeling framework is grounded in a solid conceptual foundation upon which additional modifications and realism can be built for potential reconciliation between socio-hydrology with other related fields and further applications.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Fernandina caldera collapse morphology in geometric and dynamic comparison to sandbox models, subsidence sinks over nuclear-explosion cavities, and some other calderas

NASA Astrophysics Data System (ADS)

Howard, K. A.

2009-12-01

The 1968 collapse structure of Fernandina caldera (1.5 km3 collapsed) and also the smaller Darwin Bay caldera in Galápagos each closely resembles morphologically the structural zoning of features found in depressions collapsed into nuclear-explosion cavities (“sinks” of Houser, 1969) and in coherent sandbox-collapse models. Coherent collapses characterized by faulting, folding, and organized structure contrast with spalled pit craters (and lab experiments with collapsed powder) where disorganized piles of floor rubble result from tensile failure of the roof. Subsidence in coherent mode, whether in weak sand in the lab, stronger desert alluvium for nuclear-test sinks, or in hard rock for calderas, exhibits consistent morphologic zones. Characteristically in the sandbox and the nuclear-test analogs these include a first-formed central plug that drops along annular reverse faults. This plug and a surrounding inward-tilted or monoclinal ring (hanging wall of the reverse fault) contract as the structure expands outward by normal faulting, wherein peripheral rings of distending material widen the upper part of the structure along inward-dipping normal faults and compress inner zones and help keep them intact. In Fernandina, a region between the monocline and the outer zone of normal faulting is interpreted, by comparison to the analogs, to overlie the deflation margin of an underlying magma chamber. The same zoning pattern is recognized in structures ranging from sandbox subsidence features centimeters across, to Alae lave lake and nuclear-test sinks tens to hundreds of meters across, to Fenandina’s 2x4 km-wide collapse, to Martian calderas tens of kilometers across. Simple dimensional analysis using the height of cliffs as a proxie for material strength implies that the geometric analogs are good dynamic analogs, and validates that the pattern of both reverse and normal faulting that has been reported consistently from sandbox modeling applies widely to calderas.

An Experimental Investigation of the Role of Solid Particles on the Collapse of Explosive Volcanic Plumes

NASA Astrophysics Data System (ADS)

Carazzo, G.; Kaminski, E.; Tait, S.

2007-12-01

Pyroclastic density currents generated by the collapse of an explosive volcanic plume represent the most dangerous flows associated with such eruptions. The study of the mechanical processes leading to column collapse is therefore at the heart of current investigations. Fluid dynamic models show that the behavior of a volcanic jet is mainly controlled by the efficiency with which it entrains and heats atmospheric air. The volcanic mixture initially denser than the atmosphere can thus become buoyant if both processes are effective. The complex role of the particle load and heat exchange makes it difficult to study their effect on the jet dynamics other than by sophisticated numerical simulations. Nevertheless to develop an alternative approach, we present an experimental study in which a turbulent 2-phase jet of hot gas and hot particles is propelled into a large chamber of cold air. The jet is initially driven by momentum and naturally collapses, but if the mixing with the surrounding environment is sufficient the buoyancy can reverse to drive a convective plume. We focus on the influence of source particle concentration and source gas velocity on the threshold between the convective and the collapsing regimes. In the range of the source conditions investigated the jet mostly separated into a po sitively buoyant part and a denser collapsing part. We quantify the fraction of the jet collapsed by collecting the particles and we show that the degree of jet collapse is mainly controlled by the initial amount of particles. A 1D model of turbulent jets accounting for the effect of the reversing buoyancy on the turbulent entrainment, the aggregation, the sedimentation and the recycling of particles is presented. The model is found in good agreement with the data. Further work is necessary to understand the fundamental physics behind the semi-empirical parametrization of re-entrainment and aggregation processes.

Building damage assessment from PolSAR data using texture parameters of statistical model

NASA Astrophysics Data System (ADS)

Li, Linlin; Liu, Xiuguo; Chen, Qihao; Yang, Shuai

2018-04-01

Accurate building damage assessment is essential in providing decision support for disaster relief and reconstruction. Polarimetric synthetic aperture radar (PolSAR) has become one of the most effective means of building damage assessment, due to its all-day/all-weather ability and richer backscatter information of targets. However, intact buildings that are not parallel to the SAR flight pass (termed oriented buildings) and collapsed buildings share similar scattering mechanisms, both of which are dominated by volume scattering. This characteristic always leads to misjudgments between assessments of collapsed buildings and oriented buildings from PolSAR data. Because the collapsed buildings and the intact buildings (whether oriented or parallel buildings) have different textures, a novel building damage assessment method is proposed in this study to address this problem by introducing texture parameters of statistical models. First, the logarithms of the estimated texture parameters of different statistical models are taken as a new texture feature to describe the collapse of the buildings. Second, the collapsed buildings and intact buildings are distinguished using an appropriate threshold. Then, the building blocks are classified into three levels based on the building block collapse rate. Moreover, this paper also discusses the capability for performing damage assessment using texture parameters from different statistical models or using different estimators. The RADARSAT-2 and ALOS-1 PolSAR images are used to present and analyze the performance of the proposed method. The results show that using the texture parameters avoids the problem of confusing collapsed and oriented buildings and improves the assessment accuracy. The results assessed by using the K/G0 distribution texture parameters estimated based on the second moment obtain the highest extraction accuracies. For the RADARSAT-2 and ALOS-1 data, the overall accuracy (OA) for these three types of buildings is 73.39% and 68.45%, respectively.

General relativistic considerations of the field shedding model of fast radio bursts

NASA Astrophysics Data System (ADS)

Punsly, Brian; Bini, Donato

2016-06-01

Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.

DEPENDENCE OF THE Sr-TO-Ba AND Sr-TO-Eu RATIO ON THE NUCLEAR EQUATION OF STATE IN METAL-POOR HALO STARS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Famiano, M. A.; Kajino, T.; Aoki, W.

A model is proposed in which the dependence on the equation of state (EOS) of the scatter of [Sr/Ba] in metal-poor stars is studied. Light r-process element enrichment in these stars has been explained via a truncated r-process, or “tr-process.” The truncation of the r-process from a generic core-collapse event followed by a collapse into an accretion-induced black hole is examined in the framework of a galactic chemical evolution model. The constraints on this model imposed by observations of extremely metal-poor stars are explained, and the upper limits in the [Sr/Ba] distributions are found to be related to the nuclearmore » EOS in a collapse scenario. The scatter in [Sr/Ba] and [Sr/Eu] as a function of metallicity has been found to be consistent with turbulent ejection in core-collapse supernovae. Adaptations of this model are evaluated to account for the scatter in isotopic observables. This is done by assuming mixing in ejecta in a supernova event. Stiff EOS are eliminated by this model.« less

Magnetorotatioal Collapse of Supermassive Stars: Black Hole Formation and Jets

NASA Astrophysics Data System (ADS)

Sun, Lunan; Paschalidis, Vasileios; Ruiz, Milton; Shapiro, Stuart

2017-01-01

We perform magnetohydrodynamic simulations in full general relativity of the collapse of radially unstable, uniformly rotating, massive stars to black holes. The stars spin at the mass-shedding limit, account for magnetic fields and obey a Γ = 4/3 EOS. The calculations lift the restriction of axisymmetry imposed in previous simulations. Our simulations model the direct collapse of supermassive stars to supermassive BHs (>=104M⊙) at high cosmological redshifts, which may explain the appearance of supermassive BHs and quasars by z 7. They also crudely model the collapse of massive Pop III stars to massive BHs, which could power some of the long gamma-ray bursts observed by FERMI and SWIFT at z 6-8. We analyze the properties of the electromagnetic and gravitational wave signatures of these events and discuss the detectability of such multimessenger sources.

The Mechanics of Peak-Ring Impact Crater Formation from the IODP-ICDP Expedition 364

NASA Astrophysics Data System (ADS)

Melosh, H.; Collins, G. S.; Morgan, J. V.; Gulick, S. P. S.

2017-12-01

The Chicxulub impact crater is one of very few peak-ring impact craters on Earth. While small (less than 3 km on Earth) impact craters are typically bowl-shaped, larger craters exhibit central peaks, which in still larger (more than about 100 km on Earth) craters expand into mountainous rings with diameters close to half that of the crater rim. The origin of these peak rings has been contentious: Such craters are far too large to create in laboratory experiments and remote sensing of extraterrestrial examples has not clarified the mechanics of their formation. Two principal models of peak ring formation are currently in vogue, the "nested crater" model, in which the peak ring originates at shallow depths in the target, and the "dynamic collapse" model in which the peak ring is uplifted at the base of a collapsing, over-steepened central peak and its rocks originate at mid-crustal depths. IODP-ICDP Expedition 364 sought to elucidate, among other important goals, the mechanics of peak ring formation in the young (66 Myr), fresh, but completely buried Chicxulub impact crater. The cores from this borehole now show unambiguously that the rocks in the Chicxulub peak ring originated at mid-crustal depths, apparently ruling out the nested crater model. These rocks were shocked to pressures on the order of 10-35 GPa and were so shattered that their densities and seismic velocities now resemble those of sedimentary rocks. The morphology of the final crater, its structure as revealed in previous seismic imaging, and the results from the cores are completely consistent with modern numerical models of impact crater excavation and collapse that incorporate a model for post-impact weakening. Subsequent to the opening of a ca. 100 km diameter and 30 km deep transient crater, this enormous hole in the crust collapsed over a period of about 10 minutes. Collapse was enabled by movement of the underlying rocks, which briefly behaved in the manner of a high-viscosity fluid, a brittle deformation state described by the process of "acoustic" fluidization initiated by strong elastic vibrations accompanying the opening and collapse of the crater. The shattered core, cut by both melt rock and clastic dikes, is consistent with the block model of acoustic fluidization supporting its application to crater collapse both on the Earth and on other planets.

Numerical model of ice melange expansion during abrupt ice-shelf collapse

NASA Astrophysics Data System (ADS)

Guttenberg, N.; Abbot, D. S.; Amundson, J. M.; Burton, J. C.; Cathles, L. M.; Macayeal, D. R.; Zhang, W.

2010-12-01

Satellite imagery of the February 2008 Wilkins Ice-Shelf Collapse event reveals that a large percentage of the involved ice shelf was converted to capsized icebergs and broken fragments of icebergs over a relatively short period of time, possibly less than 24 hours. The extreme violence and short time scale of the event, and the considerable reduction of gravitational potential energy between upright and capsized icebergs, suggests that iceberg capsize might be an important driving mechanism controlling both the rate and spatial extent of ice shelf collapse. To investigate this suggestion, we have constructed an idealized, 2-dimensional model of a disintegrating ice shelf composed of a large number (N~100 to >1000) of initially well-packed icebergs of rectangular cross section. The model geometry consists of a longitudinal cross section of the idealized ice shelf from grounding line (or the upstream extent of ice-shelf fragmentation) to seaward ice front, and includes the region beyond the initial ice front to cover the open, ice-free water into which the collapsing ice shelf expands. The seawater in which the icebergs float is treated as a hydrostatic fluid in the computation of iceberg orientation (e.g., the evaluation of buoyancy forces and torques), thereby eliminating the complexities of free-surface waves, but net horizontal drift of the icebergs is resisted by a linear drag law designed to energy dissipation by viscous forces and surface-gravity-wave radiation. Icebergs interact via both elastic and inelastic contacts (typically a corner of one iceberg will scrape along the face of its neighbor). Ice-shelf collapse in the model is embodied by the mass capsize of a large proportion of the initially packed icebergs and the consequent advancement of the ice front (leading edge). Model simulations are conducted to examine (a) the threshold of stability (e.g., what density of initially capsizable icebergs is needed to allow a small perturbation to the system evolve into full-blown collapse of the ice shelf? What proportion of uncapsizable icebergs prevent a collapse?), (b) the rates of mobilization and their dependence on iceberg geometry (e.g., what determines the speed at which the expanding ice melange moves into the open, ice-free water?), and (c) the factors that promote the arrest of the system (e.g., are there circumstances where only partial collapses can occur?). Results of simulations are compared with observational parameters derived from satellite imagery, seismic analysis and laboratory experiment to determine what aspects of the numerical model's physical formulation may have most relevance to the disappearance of ice shelves.

Flow through collapsible tubes at low Reynolds numbers. Applicability of the waterfall model.

PubMed

Lyon, C K; Scott, J B; Wang, C Y

1980-07-01

The applicability of the waterfall model was tested using the Starling resistor and different viscosities of fluids to vary the Reynolds number. The waterfall model proved adequate to describe flow in the Starling resistor model only at very low Reynolds numbers (Reynolds number less than 1). Blood flow characterized by such low Reynolds numbers occurs only in the microvasculature. Thus, it is inappropriate to apply the waterfall model indiscriminately to flow through large collapsible veins.

CONTRACTION SIGNATURES TOWARD DENSE CORES IN THE PERSEUS MOLECULAR CLOUD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campbell, J. L.; Friesen, R. K.; Martin, P. G.

We report the results of an HCO{sup +} (3–2) and N{sub 2}D{sup +} (3–2) molecular line survey performed toward 91 dense cores in the Perseus molecular cloud using the James Clerk Maxwell Telescope, to identify the fraction of starless and protostellar cores with systematic radial motions. We quantify the HCO{sup +} asymmetry using a dimensionless asymmetry parameter δ{sub v}, and identify 20 cores with significant blue or red line asymmetries in optically thick emission indicative of collapsing or expanding motions, respectively. We separately fit the HCO{sup +} profiles with an analytic collapse model and determine contraction (expansion) speeds toward 22more » cores. Comparing the δ{sub v} and collapse model results, we find that δ{sub v} is a good tracer of core contraction if the optically thin emission is aligned with the model-derived systemic velocity. The contraction speeds range from subsonic (0.03 km s{sup −1}) to supersonic (0.4 km s{sup −1}), where the supersonic contraction speeds may trace global rather than local core contraction. Most cores have contraction speeds significantly less than their free-fall speeds. Only 7 of 28 starless cores have spectra well-fit by the collapse model, which more than doubles (15 of 28) for protostellar cores. Starless cores with masses greater than the Jeans mass (M/M{sub J} > 1) are somewhat more likely to show contraction motions. We find no trend of optically thin non-thermal line width with M/M{sub J}, suggesting that any undetected contraction motions are small and subsonic. Most starless cores in Perseus are either not in a state of collapse or expansion, or are in a very early stage of collapse.« less

Black hole formation due to collapsing dark matter in a presence of dark energy in the brane-world scenario

NASA Astrophysics Data System (ADS)

Shah, Hasrat Hussain

In the last three to four decades, various programs have been studied in order to investigate the final fate of gravitational collapse of massive astronomical objects. In the theoretical context, Black Holes (BHs) are the consequence of final stage of the gravitational collapse. In this work, we investigated the gravitational collapse process of a spherically symmetric star constituted of dark matter (DM), ρM, and Dark Energy (DE), ρ in the context of the brane-world scenario. In our model, we discussed the anisotropy of the pressure in a fluid with Equation of State (EoS) pt = kρ and pr = lρ, (l + 2k < ‑1). We briefly discussed various cases of gravitational collapse and it is found that BH can be formed by the gravitational collapse in brane-world regime while in some cases there is only a naked singularity at their end state.

The Influence of AN Interacting Vacuum Energy on the Gravitational Collapse of a Star Fluid

NASA Astrophysics Data System (ADS)

Campos, M.

2014-02-01

To explain the accelerated expansion of the universe, models with interacting dark components has been considered in the literature. Generally, the dark energy component is physically interpreted as the vacuum energy. However, at the other side of the same coin, the influence of the vacuum energy in the gravitational collapse is a topic of scientific interest. Based in a simple assumption on the collapsed rate of the matter fluid density that is altered by the inclusion of a vacuum energy component that interacts with the matter fluid, we study the final fate of the collapse process.

REVIEWS OF TOPICAL PROBLEMS: Neutrinos from stellar core collapses: present status of experiments

NASA Astrophysics Data System (ADS)

Ryazhskaya, Ol'ga G.

2006-10-01

The responses of the existing underground detectors to neutrino bursts from collapsing stars evolving in accordance with various models are considered. The interpretation of the results of detecting neutrino radiation from the SN1987A supernova explosion is discussed. A combination of large scintillation counters interlayered with iron slabs (as a target for the electron neutrino interaction) is suggested as a detector for core collapse neutrinos. Bounds for the galactic rate of core collapses based on 28 years of observations by neutrino telescopes of RAS INR, LSD, and LVD detectors are presented.

Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox

PubMed Central

Marshall, Najja; Timme, Nicholas M.; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M.

2016-01-01

Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of “neural avalanches” (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods—power-law fitting, avalanche shape collapse, and neural complexity—have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842

Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox.

PubMed

Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M

2016-01-01

Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.

Combined collapse by bridging and self-adhesion in a prototypical polymer model inspired by the bacterial nucleoid

NASA Astrophysics Data System (ADS)

Scolari, Vittore F.; Cosentino Lagomarsino, Marco

Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework combining solely these two ingredients, in order to characterize their joint effects. Specifically, we study a simple polymer physics computational model with weak ubiquitous short-ranged self attraction and stronger sparse bridging interactions. Combining theoretical arguments and simulations, we study the general phenomenology of polymer collapse induced by these dual contributions, in the case of regularly-spaced bridging. Our results distinguish a regime of classical Flory-like coil-globule collapse dictated by the interplay of excluded volume and attractive energy and a switch-like collapse where bridging interaction compete with entropy loss terms from the looped arms of a star-like rosette. Additionally, we show that bridging can induce stable compartmentalized domains. In these configurations, different "cores" of bridging proteins are kept separated by star-like polymer loops in an entropically favorable multi-domain configuration, with a mechanism that parallels micellar polysoaps. Such compartmentalized domains are stable, and do not need any intra-specific interactions driving their segregation. Domains can be stable also in presence of uniform attraction, as long as the uniform collapse is above its theta point.

Subsidence and collapse sinkholes in soluble rock: a numerical perspective

NASA Astrophysics Data System (ADS)

Kaufmann, Georg; Romanov, Douchko; Hiller, Thomas

2016-04-01

Soluble rocks such as limestone, gypsum, anhydrite, and salt are prone to subsidence and the sudden creation of collapse sinkholes. The reason for this behaviour stems from the solubility of the rock: Water percolating through fissures and bedding partings can remove material from the rock walls and thus increase the permeability of the host rock by orders of magnitudes. This process occurs on time scales of 1,000-100,000 years, resulting in enlarged fractures, voids and cavities, which then carry flow efficiently through the rock. The enlargement of sub-surface voids to the meter-size within such short times creates mechanical conditions prone to collapse. The collapse initiates at depth, but then propagates to the surface. By means of numerical modelling, we discuss the long-term evolution of secondary porosity in gypsum rocks, resulting in zones of sub-surface voids, which then become mechanically unstable and collapse. We study two real-world case scenarios, in which we can relate field observations to our numerical model: (i) A dam-site scenario, where flow around the dam caused widespread dissolution of gypsum and subsequent subsidence of the dam and a nearby highway. (ii) A natural collapse sinkhole forming as a result of freshwater inflow into a shallow anhydrite formation with rapid evolution of voids in the sub-surface.

Viscoelastic Waves Simulation in a Blocky Medium with Fluid-Saturated Interlayers Using High-Performance Computing

NASA Astrophysics Data System (ADS)

Sadovskii, Vladimir; Sadovskaya, Oxana

2017-04-01

A thermodynamically consistent approach to the description of linear and nonlinear wave processes in a blocky medium, which consists of a large number of elastic blocks interacting with each other via pliant interlayers, is proposed. The mechanical properties of interlayers are defined by means of the rheological schemes of different levels of complexity. Elastic interaction between the blocks is considered in the framework of the linear elasticity theory [1]. The effects of viscoelastic shear in the interblock interlayers are taken into consideration using the Pointing-Thomson rheological scheme. The model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. On the basis of the Biot equations for a fluid-saturated porous medium, a new mathematical model of a blocky medium is worked out, in which the interlayers provide a convective fluid motion due to the external perturbations. The collapse of pores is modeled within the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact [2], which is used to describe the behavior of materials with different resistance to tension and compression. Thermodynamic consistency of the equations in interlayers with the equations in blocks guarantees fulfillment of the energy conservation law for a blocky medium in a whole, i.e. kinetic and potential energy of the system is the sum of kinetic and potential energies of the blocks and interlayers. As a result of discretization of the equations of the model, robust computational algorithm is constructed, that is stable because of the thermodynamic consistency of the finite difference equations at a discrete level. The splitting method by the spatial variables and the Godunov gap decay scheme are used in the blocks, the dissipationless finite difference Ivanov scheme is applied in the interlayers. The parallel program is designed, using the MPI technology. By means of this software, nonlinear wave processes in the case of initial rotation of the central block in a rock mass as well as in the case of concentrated couple stress load, applied at the boundary of a rock mass, are analyzed. Results of computations on the multiprocessor computer systems demonstrate the strong anisotropy of a blocky medium. This work was supported by the Complex Fundamental Research Program no. II.2P "Integration and Development" of Siberian Branch of the Russian Academy of Sciences. References 1. Sadovskii V.M., Sadovskaya O.V. Modeling of Elastic Waves in a Blocky Medium Based on Equations of the Cosserat Continuum // Wave Motion. 2015. V. 52. P. 138-150. 2. Sadovskaya O., Sadovskii V. Mathematical Modeling in Mechanics of Granular Materials. Ser.: Advanced Structured Materials, V. 21. Heidelberg - New York - Dordrecht - London, Springer, 2012. 390 p.

Interplay of Coil–Globule Transition and Surface Adsorption of a Lattice HP Protein Model

PubMed Central

2015-01-01

An end-grafted hydrophobic-polar (HP) model protein chain with alternating H and P monomers is studied to examine interactions between the critical adsorption transition due to surface attraction and the collapse transition due to pairwise attractive H–H interactions. We find that the critical adsorption phenomenon can always be observed; however, the critical adsorption temperature TCAP is influenced by the attractive H–H interactions in some cases. When the collapse temperature Tc is lower than TCAP, the critical adsorption of the HP chain is similar to that of a homopolymer without intrachain attractions and TCAP remains unchanged, whereas the collapse transition is suppressed by the adsorption. In contrast, for cases where Tc is close to or higher than TCAP, TCAP of the HP chain is increased, indicating that a collapsed chain is more easily adsorbed on the surface. The strength of the H–H attraction also influences the statistical size and shape of the polymer, with strong H–H attractions resulting in adsorbed and collapsed chains adopting two-dimensional, circular conformations. PMID:25458556

Weighting of topologically different interactions in a model of two-dimensional polymer collapse.

PubMed

Bedini, Andrea; Owczarek, Aleksander L; Prellberg, Thomas

2013-01-01

We study by computer simulation a recently introduced generalized model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely, crossings where the trail passes across itself and collisions where the lattice path visits the same site without crossing. This model generalizes the canonical interacting self-avoiding trail model of polymer collapse, which has a strongly divergent specific heat at its transition point. We confirm the recent prediction that the asymmetry does not affect the universality class for a range of asymmetry. Certainly, where the weighting of collisions outweighs that of crossings this is well supported numerically. When crossings are weighted heavily relative to collisions, the collapse transition reverts to the canonical θ-point-like behavior found in interacting self-avoiding walks.

Sensing spontaneous collapse and decoherence with interfering Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Schrinski, Björn; Hornberger, Klaus; Nimmrichter, Stefan

2017-12-01

We study how matter-wave interferometry with Bose-Einstein condensates is affected by hypothetical collapse models and by environmental decoherence processes. Motivated by recent atom fountain experiments with macroscopic arm separations, we focus on the observable signatures of first-order and higher-order coherence for different two-mode superposition states, and on their scaling with particle number. This can be used not only to assess the impact of environmental decoherence on many-body coherence, but also to quantify the extent to which macrorealistic collapse models are ruled out by such experiments. We find that interference fringes of phase-coherently split condensates are most strongly affected by decoherence, whereas the quantum signatures of independent interfering condensates are more immune against macrorealistic collapse. A many-body enhanced decoherence effect beyond the level of a single atom can be probed if higher-order correlations are resolved in the interferogram.

Coagulation of grains in static and collapsing protostellar clouds

NASA Technical Reports Server (NTRS)

Weidenschilling, S. J.; Ruzmaikina, T. V.

1993-01-01

The wavelength dependence of extinction in the diffuse interstellar medium implies that it is produced by particles of dominant size of approximately 10(exp -5) cm. There is some indication that in the cores of dense molecular clouds, sub-micron grains can coagulate to form larger particles; this process is probably driven by turbulence. The most primitive meteorites (carbonaceous chondrites) are composed of particles with a bimodal size distribution with peaks near 1 micron (matrix) and 1 mm (chondrules). Models for chondrule formation that involve processing of presolar material by chemical reactions or through an accretion shock during infall assume that aggregates of the requisite mass could form before or during collapse. The effectiveness of coagulation during collapse has been disputed; it appears to depend on specific assumptions. The first results of detailed numerical modeling of spatial and temporal variations of particle sizes in presolar clouds, both static and collapsing, is reported in this article.

Collapsed Dark Matter Structures

NASA Astrophysics Data System (ADS)

Buckley, Matthew R.; DiFranzo, Anthony

2018-02-01

The distributions of dark matter and baryons in the Universe are known to be very different: The dark matter resides in extended halos, while a significant fraction of the baryons have radiated away much of their initial energy and fallen deep into the potential wells. This difference in morphology leads to the widely held conclusion that dark matter cannot cool and collapse on any scale. We revisit this assumption and show that a simple model where dark matter is charged under a "dark electromagnetism" can allow dark matter to form gravitationally collapsed objects with characteristic mass scales much smaller than that of a Milky-Way-type galaxy. Though the majority of the dark matter in spiral galaxies would remain in the halo, such a model opens the possibility that galaxies and their associated dark matter play host to a significant number of collapsed substructures. The observational signatures of such structures are not well explored but potentially interesting.

Collapsed Dark Matter Structures.

PubMed

Buckley, Matthew R; DiFranzo, Anthony

2018-02-02

The distributions of dark matter and baryons in the Universe are known to be very different: The dark matter resides in extended halos, while a significant fraction of the baryons have radiated away much of their initial energy and fallen deep into the potential wells. This difference in morphology leads to the widely held conclusion that dark matter cannot cool and collapse on any scale. We revisit this assumption and show that a simple model where dark matter is charged under a "dark electromagnetism" can allow dark matter to form gravitationally collapsed objects with characteristic mass scales much smaller than that of a Milky-Way-type galaxy. Though the majority of the dark matter in spiral galaxies would remain in the halo, such a model opens the possibility that galaxies and their associated dark matter play host to a significant number of collapsed substructures. The observational signatures of such structures are not well explored but potentially interesting.

The Halo mass function from Excursion Set Theory. II. The Diffusing Barrier

NASA Astrophysics Data System (ADS)

Maggiore, Michele; Riotto, Antonio

2010-07-01

In excursion set theory, the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed function of the variance of the smoothed density field. However, N-body simulations show that dark matter halos grow through a mixture of smooth accretion, violent encounters, and fragmentations, and modeling halo collapse as spherical, or even as ellipsoidal, is a significant oversimplification. In addition, the very definition of what is a dark matter halo, both in N-body simulations and observationally, is a difficult problem. We propose that some of the physical complications inherent to a realistic description of halo formation can be included in the excursion set theory framework, at least at an effective level, by taking into account that the critical value for collapse is not a fixed constant δ c , as in the spherical collapse model, nor a fixed function of the variance σ of the smoothed density field, as in the ellipsoidal collapse model, but rather is itself a stochastic variable, whose scatter reflects a number of complicated aspects of the underlying dynamics. Solving the first-passage time problem in the presence of a diffusing barrier we find that the exponential factor in the Press-Schechter mass function changes from exp{-δ2 c /2σ2} to exp{-aδ2 c /2σ2}, where a = 1/(1 + DB ) and DB is the diffusion coefficient of the barrier. The numerical value of DB , and therefore the corresponding value of a, depends among other things on the algorithm used for identifying halos. We discuss the physical origin of the stochasticity of the barrier and, from recent N-body simulations that studied the properties of the collapse barrier, we deduce a value DB ~= 0.25. Our model then predicts a ~= 0.80, in excellent agreement with the exponential fall off of the mass function found in N-body simulations, for the same halo definition. Combining this result with the non-Markovian corrections computed in Paper I of this series, we derive an analytic expression for the halo mass function for Gaussian fluctuations and we compare it with N-body simulations.

A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility.

PubMed

Moore, Jason H; Gilbert, Joshua C; Tsai, Chia-Ti; Chiang, Fu-Tien; Holden, Todd; Barney, Nate; White, Bill C

2006-07-21

Detecting, characterizing, and interpreting gene-gene interactions or epistasis in studies of human disease susceptibility is both a mathematical and a computational challenge. To address this problem, we have previously developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension (i.e. constructive induction) thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe a comprehensive and flexible framework for detecting and interpreting gene-gene interactions that utilizes advances in information theory for selecting interesting single-nucleotide polymorphisms (SNPs), MDR for constructive induction, machine learning methods for classification, and finally graphical models for interpretation. We illustrate the usefulness of this strategy using artificial datasets simulated from several different two-locus and three-locus epistasis models. We show that the accuracy, sensitivity, specificity, and precision of a naïve Bayes classifier are significantly improved when SNPs are selected based on their information gain (i.e. class entropy removed) and reduced to a single attribute using MDR. We then apply this strategy to detecting, characterizing, and interpreting epistatic models in a genetic study (n = 500) of atrial fibrillation and show that both classification and model interpretation are significantly improved.

Learning topic models by belief propagation.

PubMed

Zeng, Jia; Cheung, William K; Liu, Jiming

2013-05-01

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interest and touches on many important applications in text mining, computer vision and computational biology. This paper represents the collapsed LDA as a factor graph, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great success in learning LDA, the proposed BP is competitive in both speed and accuracy, as validated by encouraging experimental results on four large-scale document datasets. Furthermore, the BP algorithm has the potential to become a generic scheme for learning variants of LDA-based topic models in the collapsed space. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representations.

Habitat fragmentation resulting in overgrazing by herbivores.

PubMed

Kondoh, Michio

2003-12-21

Habitat fragmentation sometimes results in outbreaks of herbivorous insect and causes an enormous loss of primary production. It is hypothesized that the driving force behind such herbivore outbreaks is disruption of natural enemy attack that releases herbivores from top-down control. To test this hypothesis I studied how trophic community structure changes along a gradient of habitat fragmentation level using spatially implicit and explicit models of a tri-trophic (plant, herbivore and natural enemy) food chain. While in spatially implicit model number of trophic levels gradually decreases with increasing fragmentation, in spatially explicit model a relatively low level of habitat fragmentation leads to overgrazing by herbivore to result in extinction of the plant population followed by a total system collapse. This provides a theoretical support to the hypothesis that habitat fragmentation can lead to overgrazing by herbivores and suggests a central role of spatial structure in the influence of habitat fragmentation on trophic communities. Further, the spatially explicit model shows (i) that the total system collapse by the overgrazing can occur only if herbivore colonization rate is high; (ii) that with increasing natural enemy colonization rate, the fragmentation level that leads to the system collapse becomes higher, and the frequency of the collapse is lowered.

An Experimental Investigation on the Ultimate Strength of Partially Infilled: Braced Steel Frames

NASA Astrophysics Data System (ADS)

Dubey, Shailendra Kumar Damodar; Kute, Sunil Y.

2017-12-01

Infilled walls are usually, considered as non-structural elements. However, these walls are effective in carrying lateral loads. In this regard, an experimental investigation was planned and conducted to study the effect of braced and partially infilled steel frames with cement mortar and concrete in comparison to the bare frames. All these frames were tested up to collapse and subjected only to horizontal loads to obtain an effective and possible solution for soft storey which are generally not infilled. In comparison to bare steel frames, partially infilled frames have an increase of lateral load capacity by 45-60%. Central bracing is more effective than that of the corner bracing. For the same load partially infilled frames have significantly less deflection than that of the bare frames. A reduced load factor is suggested for the design of soft storey columns with the partial infills. A mathematical model has been proposed to calculate the theoretical ultimate load for the braced, cement mortar and concrete partial infilled frames.

Experimental study of shock-driven cavity collapse with a single-stage gas gun driver

NASA Astrophysics Data System (ADS)

Anderson, Phillip; Betney, Matthew; Doyle, Hugo; Hawker, Nicholas; Roy, Ronald

2014-10-01

This paper explores experimental studies of shock-driven cavity collapse using a single-stage gas gun. Shocks of up to 1 GPa are generated in a hydrogel with the impact of a planar-faced projectile (50 mm dia.). Within the hydrogel, a pre-formed cavity (5 mm dia.) is cast, which is collapsed by the interaction with the shockwave. The basic collapse process involves the formation of a high-speed transverse jet and then a second collapse phase driven from jet impact. Single-shot multi-frame schlieren imaging is used to show the position and timing of optical emission in relation to the collapse hydrodynamics. Further, temporally and spectrally-resolved measurements of the optical emission are made through simultaneous use of multiple band-passed PMTs and an integrating spectrometer. This reveals three distinct pulses of emission possessing different frequency content. The first corresponds to the trapping of gas during jet impact; the second and third correspond to the further inertial collapse of the now toroidal cavity. Plasma models are used to provide the first indication of the temperature of these inertially confined plasmas.

Gravitational-Wave and Neutrino Signals from Core-Collapse Supernovae with QCD Phase Transition

NASA Astrophysics Data System (ADS)

Zha, Shuai; Leung, Shing Chi; Lin, Lap Ming; Chu, Ming-Chung

Core-collapse supernovae (CCSNe) mark the catastrophic death of massive stars. We simulate CCSNe with a hybrid equations of state (EOS) containing a QCD (quantum chromodynamics) phase transition. The hybrid EOS incorporates the pure hadronic HShen EOS and the MIT Bag Model, with a Gibbs construction. Our two-dimensional hydrodynamics code includes a fifth-order shock capturing scheme WENO and models neutrino transport with the isotropic diffusion source approximation (IDSA). As the proto-neutron-star accretes matter and the core enters the mixed phase, a second collapse takes place due to softening of the EOS. We calculate the gravitational-wave (GW) and neutrino signals for this kind of CCSNe model. Future detection of these signals from CCSNe may help to constrain this scenario and the hybrid EOS.

Preventing the collapse of the Baltic cod stock through an ecosystem-based management approach

PubMed Central

Lindegren, Martin; Möllmann, Christian; Nielsen, Anders; Stenseth, Nils C.

2009-01-01

Worldwide a number of fish stocks have collapsed because of overfishing and climate-induced ecosystem changes. Developing ecosystem-based fisheries management (EBFM) to prevent these catastrophic events in the future requires ecological models incorporating both internal food-web dynamics and external drivers such as fishing and climate. Using a stochastic food-web model for a large marine ecosystem (i.e., the Baltic Sea) hosting a commercially important cod stock, we were able to reconstruct the history of the stock. Moreover we demonstrate that in hindsight the collapse could only have been avoidable by adapting fishing pressure to environmental conditions and food-web interactions. The modeling approach presented here represents a significant advance for EBFM, the application of which is important for sustainable resource management in the future. PMID:19706557

Topographic stress and catastrophic collapse of volcanic islands

NASA Astrophysics Data System (ADS)

Moon, S.; Perron, J. T.; Martel, S. J.

2017-12-01

Flank collapse of volcanic islands can devastate coastal environments and potentially induce tsunamis. Previous studies have suggested that factors such as volcanic eruption events, gravitational spreading, the reduction of material strength due to hydrothermal alteration, steep coastal cliffs, or sea level change may contribute to slope instability and induce catastrophic collapse of volcanic flanks. In this study, we examine the potential influence of three-dimensional topographic stress perturbations on flank collapses of volcanic islands. Using a three-dimensional boundary element model, we calculate subsurface stress fields for the Canary and Hawaiian islands to compare the effects of stratovolcano and shield volcano shapes on topographic stresses. Our model accounts for gravitational stresses from the actual shapes of volcanic islands, ambient stress in the underlying plate, and the influence of pore water pressure. We quantify the potential for slope failure of volcanic flanks using a combined model of three-dimensional topographic stress and slope stability. The results of our analysis show that subsurface stress fields vary substantially depending on the shapes of volcanoes, and can influence the size and spatial distribution of flank failures.

Overlooked possibility of a collapsed Atlantic Meridional Overturning Circulation in warming climate.

PubMed

Liu, Wei; Xie, Shang-Ping; Liu, Zhengyu; Zhu, Jiang

2017-01-01

Changes in the Atlantic Meridional Overturning Circulation (AMOC) are moderate in most climate model projections under increasing greenhouse gas forcing. This intermodel consensus may be an artifact of common model biases that favor a stable AMOC. Observationally based freshwater budget analyses suggest that the AMOC is in an unstable regime susceptible for large changes in response to perturbations. By correcting the model biases, we show that the AMOC collapses 300 years after the atmospheric CO 2 concentration is abruptly doubled from the 1990 level. Compared to an uncorrected model, the AMOC collapse brings about large, markedly different climate responses: a prominent cooling over the northern North Atlantic and neighboring areas, sea ice increases over the Greenland-Iceland-Norwegian seas and to the south of Greenland, and a significant southward rain-belt migration over the tropical Atlantic. Our results highlight the need to develop dynamical metrics to constrain models and the importance of reducing model biases in long-term climate projection.

Overlooked possibility of a collapsed Atlantic Meridional Overturning Circulation in warming climate

PubMed Central

Liu, Wei; Xie, Shang-Ping; Liu, Zhengyu; Zhu, Jiang

2017-01-01

Changes in the Atlantic Meridional Overturning Circulation (AMOC) are moderate in most climate model projections under increasing greenhouse gas forcing. This intermodel consensus may be an artifact of common model biases that favor a stable AMOC. Observationally based freshwater budget analyses suggest that the AMOC is in an unstable regime susceptible for large changes in response to perturbations. By correcting the model biases, we show that the AMOC collapses 300 years after the atmospheric CO2 concentration is abruptly doubled from the 1990 level. Compared to an uncorrected model, the AMOC collapse brings about large, markedly different climate responses: a prominent cooling over the northern North Atlantic and neighboring areas, sea ice increases over the Greenland-Iceland-Norwegian seas and to the south of Greenland, and a significant southward rain-belt migration over the tropical Atlantic. Our results highlight the need to develop dynamical metrics to constrain models and the importance of reducing model biases in long-term climate projection. PMID:28070560

Morphological Expressions of Crater Infill Collapse: Model Simulations of Chaotic Terrains on Mars

NASA Astrophysics Data System (ADS)

Roda, Manuel; Marketos, George; Westerweel, Jan; Govers, Rob

2017-10-01

Martian chaotic terrains are characterized by deeply depressed intensively fractured areas that contain a large number of low-strain tilted blocks. Stronger deformation (e.g., higher number of fractures) is generally observed in the rims when compared to the middle regions of the terrains. The distribution and number of fractures and tilted blocks are correlated with the size of the chaotic terrains. Smaller chaotic terrains are characterized by few fractures between undeformed blocks. Larger terrains show an elevated number of fractures uniformly distributed with single blocks. We investigate whether this surface morphology may be a consequence of the collapse of the infill of a crater. We perform numerical simulations with the Discrete Element Method and we evaluate the distribution of fractures within the crater and the influence of the crater size, infill thickness, and collapsing depth on the final morphology. The comparison between model predictions and the morphology of the Martian chaotic terrains shows strong statistical similarities in terms of both number of fractures and correlation between fractures and crater diameters. No or very weak correlation is observed between fractures and the infill thickness or collapsing depth. The strong correspondence between model results and observations suggests that the collapse of an infill layer within a crater is a viable mechanism for the peculiar morphology of the Martian chaotic terrains.

Modeling Core Collapse Supernovae

NASA Astrophysics Data System (ADS)

Mezzacappa, Anthony

2017-01-01

Core collapse supernovae, or the death throes of massive stars, are general relativistic, neutrino-magneto-hydrodynamic events. The core collapse supernova mechanism is still not in hand, though key components have been illuminated, and the potential for multiple mechanisms for different progenitors exists. Core collapse supernovae are the single most important source of elements in the Universe, and serve other critical roles in galactic chemical and thermal evolution, the birth of neutron stars, pulsars, and stellar mass black holes, the production of a subclass of gamma-ray bursts, and as potential cosmic laboratories for fundamental nuclear and particle physics. Given this, the so called ``supernova problem'' is one of the most important unsolved problems in astrophysics. It has been fifty years since the first numerical simulations of core collapse supernovae were performed. Progress in the past decade, and especially within the past five years, has been exponential, yet much work remains. Spherically symmetric simulations over nearly four decades laid the foundation for this progress. Two-dimensional modeling that assumes axial symmetry is maturing. And three-dimensional modeling, while in its infancy, has begun in earnest. I will present some of the recent work from the ``Oak Ridge'' group, and will discuss this work in the context of the broader work by other researchers in the field. I will then point to future requirements and challenges. Connections with other experimental, observational, and theoretical efforts will be discussed, as well.

Small-angle neutron scattering study of micropore collapse in amorphous solid water.

PubMed

Mitterdorfer, Christian; Bauer, Marion; Youngs, Tristan G A; Bowron, Daniel T; Hill, Catherine R; Fraser, Helen J; Finney, John L; Loerting, Thomas

2014-08-14

Vapor-deposited amorphous solid water (ASW) is the most abundant solid molecular material in space, where it plays a direct role in both the formation of more complex chemical species and the aggregation of icy materials in the earliest stages of planet formation. Nevertheless, some of its low temperature physics such as the collapse of the micropore network upon heating are still far from being understood. Here we characterize the nature of the micropores and their collapse using neutron scattering of gram-quantities of D2O-ASW of internal surface areas up to 230 ± 10 m(2) g(-1) prepared at 77 K. The model-free interpretation of the small-angle scattering data suggests micropores, which remain stable up to 120-140 K and then experience a sudden collapse. The exact onset temperature to pore collapse depends on the type of flow conditions employed in the preparation of ASW and, thus, the specific surface area of the initial deposit, whereas the onset of crystallization to cubic ice is unaffected by the flow conditions. Analysis of the small-angle neutron scattering signal using the Guinier-Porod model suggests that a sudden transition from three-dimensional cylindrical pores with 15 Å radius of gyration to two-dimensional lamellae is the mechanism underlying the pore collapse. The rather high temperature of about 120-140 K of micropore collapse and the 3D-to-2D type of the transition unraveled in this study have implications for our understanding of the processing and evolution of ices in various astrophysical environments.

3D Deformation at the Coso Geothermal Field - Observations and Models

NASA Astrophysics Data System (ADS)

Hetland, E. A.; Hager, B. H.; McClusky, S.; King, R. W.

2001-12-01

Over the past decade, rapid ground deformation has been measured over the Coso geothermal field in Eastern CA using InSAR and GPS. InSAR resolves changes in distance along the line-of-sight (LOS) to the satellite with high spatial coverage. In the Coso geothermal field the maximum LOS displacements are up to 35 mm/yr. The inclination of the LOS is acute (about 20 degrees), hence the majority of the deformation resolved with InSAR is vertical, however LOS displacements are also affected by horizontal displacements. The ratio of the sensitivity of LOS displacements to vertical and horizontal displacements is at most 5 to 2, for horizontal displacements inline with the LOS. GPS is able to resolve large horizontal displacements in this area, leading to the conclusion that the InSAR LOS displacement fields are non-trivially affected by horizontal displacements. Additionally, since the horizontal displacements are large, GPS is also able to resolve vertical displacements. Moreover, the GPS three component velocities are fairly consistent with the LOS displacements from InSAR. This deformation has been largely attributed to subsidence as fluid is extracted from the geothermal reservoir. The reservoir has been previously modeled as deflating elliptical volumes and as collapsing sills. The elliptical volumes are described as Mogi sources, which are mathematically given as point forces along a line. The collapsing sills are treated as Okada dislocations for finite area faults with pure tensile displacements across them. In both of these dislocation models of the reservoir, the elastic moduli of the rock remains constant with changing fluid pressure. Actual reservoirs are more likely composed of regions of rock permeated with fluid-filled cracks and pores. In such a composite material, changing the pore-fluid pressure changes the elastic moduli of the region. These moduli changes cause the region to deform under loading, thus resulting in observed surface displacements. The surface displacements resulting from models with varying moduli of the reservoir rock are markedly different from patterns of surface displacements resulting from models in which the reservoir is treated as dislocations. For a given reservoir size, the differences in displacements from the various models are clearest in the horizontal displacement field, differing by up to a factor of two. We use finite element models with simple reservoir geometries to investigate the sensitivity of both vertical and horizontal displacements to the chosen reservoir model.

Evolution of Spiral and Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone

PubMed Central

Biktashev, Vadim N.; Biktasheva, Irina V.; Sarvazyan, Narine A.

2011-01-01

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue. PMID:21935402

Collapse of the Maya: Could deforestation have contributed?

NASA Astrophysics Data System (ADS)

Oglesby, Robert J.; Sever, Thomas L.; Saturno, William; Erickson, David J.; Srikishen, Jayanthi

2010-06-01

The collapse of the Maya civilization during the ninth century A.D. is a major conundrum in the history of mankind. This civilization reached a spectacular peak but then almost completely collapsed in the space of a few decades. While numerous explanations have been put forth to explain this collapse, in recent years, drought has gained favor. This is because water resources were a key for the Maya, especially to ensure their survival during the lengthy dry season that occurs where they lived. Natural drought is a known, recurring feature of this region, as evidenced by observational data, reconstructions of past times, and global climate model output. Results from simulations with a regional climate model demonstrate that deforestation by the Maya also likely induced warmer, drier, drought-like conditions. It is therefore hypothesized that the drought conditions devastating the Maya resulted from a combination of natural variability and human activities. Neither the natural drought or the human-induced effects alone were sufficient to cause the collapse, but the combination created a situation the Maya could not recover from. These results may have sobering implications for the present and future state of climate and water resources in Mesoamerica as ongoing massive deforestation is again occurring.

Gravitation. [Book on general relativity

NASA Technical Reports Server (NTRS)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

Void collapse under distributed dynamic loading near material interfaces

NASA Astrophysics Data System (ADS)

Shpuntova, Galina; Austin, Joanna

2012-11-01

Collapsing voids cause significant damage in diverse applications from biomedicine to underwater propulsion to explosives. While shock-induced void collapse has been studied extensively, less attention has been devoted to stress wave loading, which will occur instead if there are mechanisms for wave attenuation or if the impact velocity is relatively low. A set of dynamic experiments was carried out in a model experimental setup to investigate the effect of acoustic heterogeneities in the surrounding medium on void collapse. Two tissue-surrogate polymer materials of varying acoustic properties were used to create flowfield geometries involving a boundary and a void. A stress wave, generated by projectile impact, triggered void collapse in the gelatinous polymer medium. When the length scales of features in the flow field were on the same order of magnitude as the stress wave length scale, the presence of the boundary was found to affect the void collapse process relative to collapse in the absence of a boundary. This effect was quantified for a range of geometries and impact conditions using a two-color, single-frame particle image velocimetry technique. Research supported by NSF Award #0954769, ``CAREER: Dynamics and damage of void collapse in biological materials under stress wave loading'' with Prof. Henning Winter as Program Manager.

A Cross-disciplinary Framework for the Description of Contextually Mediated Change

NASA Astrophysics Data System (ADS)

Gabora, Liane; Aerts, Diederik

We present a mathematical framework (referred to as Context-driven Actualization of Potential, or CAP) for describing how entities change over time under the influence of a context. The approach facilitates comparison of change of state of entities studied in different disciplines. Processes are seen to differ according to the degree of nondeterminism, and the degree to which they are sensitive to, internalize, and depend upon a particular context. Our analysis suggests that the dynamical evolution of a quantum entity described by the Schrödinger equation is not fundamentally different from change provoked by a measurement often referred to as collapse but a limiting case, with only one way to collapse. The biological transition to coded replication is seen as a means of preserving structure in the face of context, and sexual replication as a means of increasing potentiality thus enhancing diversity through interaction with context. The framework sheds light on concepts like selection and fitness, reveals how exceptional Darwinian evolution is as a means of 'change of state', and clarifies in what sense culture (and the creative process underlying it) are Darwinian.

Mass tree mortality leads to mangrove peat collapse at Bay Islands, Honduras after Hurricane Mitch

USGS Publications Warehouse

Cahoon, D.R.; Hensel, P.; Rybczyk, J.; McKee, K.L.; Proffitt, C.E.; Perez, B.C.

2003-01-01

We measured sediment elevation and accretion dynamics in mangrove forests on the islands of Guanaja and Roatan, Honduras, impacted by Hurricane Mitch in 1998 to determine if collapse of underlying peat was occurring as a result of mass tree mortality. Little is known about the balance between production and decomposition of soil organic matter in the maintenance of sediment elevation of mangrove forests with biogenic soils. Sediment elevation change measured with the rod surface elevation table from 18 months to 33 months after the storm differed significantly among low, medium and high wind impact sites. Mangrove forests suffering minimal to partial mortality gained elevation at a rate (5 mm yeara??1) greater than vertical accretion (2 mm yeara??1) measured from artificial soil marker horizons, suggesting that root production contributed to sediment elevation. Basin forests that suffered mass tree mortality experienced peat collapse of about 11 mm yeara??1 as a result of decomposition of dead root material and sediment compaction. Low soil shear strength and lack of root growth accompanied elevation decreases. Model simulations using the Relative Elevation Model indicate that peat collapse in the high impact basin mangrove forest would be 37 mm yeara??1 for the 2 years immediately after the storm, as root material decomposed. In the absence of renewed root growth, the model predicts that peat collapse will continue for at least 8 more years at a rate (7 mm yeara??1) similar to that measured (11 mm yeara??1). Mass tree mortality caused rapid elevation loss. Few trees survived and recovery of the high impact forest will thus depend primarily on seedling recruitment. Because seedling establishment is controlled in large part by sediment elevation in relation to tide height, continued peat collapse could further impair recovery rates.

Diversity waves in collapse-driven population dynamics

DOE PAGES

Maslov, Sergei; Sneppen, Kim

2015-09-14

Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe collapses of the entire population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g.more » by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is cyclic ‘‘diversity waves’’ triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances are characterized by a bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak - species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.« less

Diversity waves in collapse-driven population dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maslov, Sergei; Sneppen, Kim

Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe collapses of the entire population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g.more » by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is cyclic ‘‘diversity waves’’ triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances are characterized by a bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak - species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.« less

Naked singularities as particle accelerators. II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patil, Mandar; Joshi, Pankaj S.; Malafarina, Daniele

We generalize here our earlier results on particle acceleration by naked singularities. We showed recently [M. Patil and P. S. Joshi, Phys. Rev. D 82, 104049 (2010).] that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as themore » final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.« less

Constitutive model for porous materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weston, A.M.; Lee, E.L.

1982-01-01

A simple pressure versus porosity compaction model is developed to calculate the response of granular porous bed materials to shock impact. The model provides a scheme for calculating compaction behavior when relatively limited material data are available. While the model was developed to study porous explosives and propellants, it has been applied to a much wider range of materials. The early development of porous material models, such as that of Hermann, required empirical dynamic compaction data. Erkman and Edwards successfully applied the early theory to unreacted porous high explosives using a Gruneisen equation of state without yield behavior and withoutmore » trapped gas in the pores. Butcher included viscoelastic rate dependance in pore collapse. The theoretical treatment of Carroll and Holt is centered on the collapse of a circular pore and includes radial inertia terms and a complex set of stress, strain and strain rate constitutive parameters. Unfortunately data required for these parameters are generally not available. The model described here is also centered on the collapse of a circular pore, but utilizes a simpler elastic-plastic static equilibrium pore collapse mechanism without strain rate dependence, or radial inertia terms. It does include trapped gas inside the pore, a solid material flow stress that creates both a yield point and a variation in solid material pressure with radius. The solid is described by a Mie-Gruneisen type EOS. Comparisons show that this model will accurately estimate major mechanical features which have been observed in compaction experiments.« less

Source Analysis of the Crandall Canyon, Utah, Mine Collapse

DOE PAGES

Dreger, D. S.; Ford, S. R.; Walter, W. R.

2008-07-11

Analysis of seismograms from a magnitude 3.9 seismic event on August 6, 2007 in central Utah reveals an anomalous radiation pattern that is contrary to that expected for a tectonic earthquake, and which is dominated by an implosive component. The results show the seismic event is best modeled as a shallow underground collapse. Interestingly, large transverse surface waves require a smaller additional non-collapse source component that represents either faulting in the rocks above the mine workings or deformation of the medium surrounding the mine.

Can We Recognize an Innovation? Perspective from an Evolving Network Model

NASA Astrophysics Data System (ADS)

Jain, Sanjay; Krishna, Sandeep

"Innovations" are central to the evolution of societies and the evolution of life. But what constitutes an innovation? We can often agree after the event, when its consequences and impact over a long term are known, whether something was an innovation, and whether it was a "big" innovation or a "minor" one. But can we recognize an innovation "on the fly" as it appears? Successful entrepreneurs often can. Is it possible to formalize that intuition? We discuss this question in the setting of a mathematical model of evolving networks. The model exhibits self-organization , growth, stasis, and collapse of a complex system with many interacting components, reminiscent of real-world phenomena. A notion of "innovation" is formulated in terms of graph-theoretic constructs and other dynamical variables of the model. A new node in the graph gives rise to an innovation, provided it links up "appropriately" with existing nodes; in this view innovation necessarily depends upon the existing context. We show that innovations, as defined by us, play a major role in the birth, growth, and destruction of organizational structures. Furthermore, innovations can be categorized in terms of their graph-theoretic structure as they appear. Different structural classes of innovation have potentially different qualitative consequences for the future evolution of the system, some minor and some major. Possible general lessons from this specific model are briefly discussed.

Ecohydrological modeling in agroecosystems: Examples and challenges

DOE PAGES

Porporato, A.; Feng, X.; Manzoni, S.; ...

2015-06-01

We report that human societies are increasingly altering the water and biogeochemical cycles to both improve ecosystem productivity and reduce risks associated with the unpredictable variability of climatic drivers. These alterations, however, often cause large negative environmental consequences, raising the question as to how societies can ensure a sustainable use of natural resources for the future. Here we discuss how ecohydrological modeling may address these broad questions with special attention to agroecosystems. The challenges related to modeling the two-way interaction between society and environment are illustrated by means of a dynamical model in which soil and water quality supports themore » growth of human society but is also degraded by excessive pressure, leading to critical transitions and sustained societal growth-collapse cycles. We then focus on the coupled dynamics of soil water and solutes (nutrients or contaminants), emphasizing the modeling challenges, presented by the strong nonlinearities in the soil and plant system and the unpredictable hydroclimatic forcing, that need to be overcome to quantitatively analyze problems of soil water sustainability in both natural and agricultural ecosystems. Finally, we discuss applications of this framework to problems of irrigation, soil salinization, and fertilization and emphasize how optimal solutions for large-scale, long-term planning of soil and water resources in agroecosystems under uncertainty could be provided by methods from stochastic control, informed by physically and mathematically sound descriptions of ecohydrological and biogeochemical interactions.« less

Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows.

PubMed

Rolland, Joran

2018-02-01

This paper presents a numerical and theoretical study of multistability in two stochastic models of transitional wall flows. An algorithm dedicated to the computation of rare events is adapted on these two stochastic models. The main focus is placed on a stochastic partial differential equation model proposed by Barkley. Three types of events are computed in a systematic and reproducible manner: (i) the collapse of isolated puffs and domains initially containing their steady turbulent fraction; (ii) the puff splitting; (iii) the build-up of turbulence from the laminar base flow under a noise perturbation of vanishing variance. For build-up events, an extreme realization of the vanishing variance noise pushes the state from the laminar base flow to the most probable germ of turbulence which in turn develops into a full blown puff. For collapse events, the Reynolds number and length ranges of the two regimes of collapse of laminar-turbulent pipes, independent collapse or global collapse of puffs, is determined. The mean first passage time before each event is then systematically computed as a function of the Reynolds number r and pipe length L in the laminar-turbulent coexistence range of Reynolds number. In the case of isolated puffs, the faster-than-linear growth with Reynolds number of the logarithm of mean first passage time T before collapse is separated in two. One finds that ln(T)=A_{p}r-B_{p}, with A_{p} and B_{p} positive. Moreover, A_{p} and B_{p} are affine in the spatial integral of turbulence intensity of the puff, with the same slope. In the case of pipes initially containing the steady turbulent fraction, the length L and Reynolds number r dependence of the mean first passage time T before collapse is also separated. The author finds that T≍exp[L(Ar-B)] with A and B positive. The length and Reynolds number dependence of T are then discussed in view of the large deviations theoretical approaches of the study of mean first passage times and multistability, where ln(T) in the limit of small variance noise is studied. Two points of view, local noise of small variance and large length, can be used to discuss the exponential dependence in L of T. In particular, it is shown how a T≍exp[L(A^{'}R-B^{'})] can be derived in a conceptual two degrees of freedom model of a transitional wall flow proposed by Dauchot and Manneville. This is done by identifying a quasipotential in low variance noise, large length limit. This pinpoints the physical effects controlling collapse and build-up trajectories and corresponding passage times with an emphasis on the saddle points between laminar and turbulent states. This analytical analysis also shows that these effects lead to the asymmetric probability density function of kinetic energy of turbulence.

Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows

NASA Astrophysics Data System (ADS)

Rolland, Joran

2018-02-01

This paper presents a numerical and theoretical study of multistability in two stochastic models of transitional wall flows. An algorithm dedicated to the computation of rare events is adapted on these two stochastic models. The main focus is placed on a stochastic partial differential equation model proposed by Barkley. Three types of events are computed in a systematic and reproducible manner: (i) the collapse of isolated puffs and domains initially containing their steady turbulent fraction; (ii) the puff splitting; (iii) the build-up of turbulence from the laminar base flow under a noise perturbation of vanishing variance. For build-up events, an extreme realization of the vanishing variance noise pushes the state from the laminar base flow to the most probable germ of turbulence which in turn develops into a full blown puff. For collapse events, the Reynolds number and length ranges of the two regimes of collapse of laminar-turbulent pipes, independent collapse or global collapse of puffs, is determined. The mean first passage time before each event is then systematically computed as a function of the Reynolds number r and pipe length L in the laminar-turbulent coexistence range of Reynolds number. In the case of isolated puffs, the faster-than-linear growth with Reynolds number of the logarithm of mean first passage time T before collapse is separated in two. One finds that ln(T ) =Apr -Bp , with Ap and Bp positive. Moreover, Ap and Bp are affine in the spatial integral of turbulence intensity of the puff, with the same slope. In the case of pipes initially containing the steady turbulent fraction, the length L and Reynolds number r dependence of the mean first passage time T before collapse is also separated. The author finds that T ≍exp[L (A r -B )] with A and B positive. The length and Reynolds number dependence of T are then discussed in view of the large deviations theoretical approaches of the study of mean first passage times and multistability, where ln(T ) in the limit of small variance noise is studied. Two points of view, local noise of small variance and large length, can be used to discuss the exponential dependence in L of T . In particular, it is shown how a T ≍exp[L (A'R -B') ] can be derived in a conceptual two degrees of freedom model of a transitional wall flow proposed by Dauchot and Manneville. This is done by identifying a quasipotential in low variance noise, large length limit. This pinpoints the physical effects controlling collapse and build-up trajectories and corresponding passage times with an emphasis on the saddle points between laminar and turbulent states. This analytical analysis also shows that these effects lead to the asymmetric probability density function of kinetic energy of turbulence.

Simulation and analysis of collapsing vapor-bubble clusters with special emphasis on potentially erosive impact loads at walls

NASA Astrophysics Data System (ADS)

Ogloblina, Daria; Schmidt, Steffen J.; Adams, Nikolaus A.

2018-06-01

Cavitation is a process where a liquid evaporates due to a pressure drop and re-condenses violently. Noise, material erosion and altered system dynamics characterize for such a process for which shock waves, rarefaction waves and vapor generation are typical phenomena. The current paper presents novel results for collapsing vapour-bubble clusters in a liquid environment close to a wall obtained by computational fluid mechanics (CFD) simulations. The driving pressure initially is 10 MPa in the liquid. Computations are carried out by using a fully compressible single-fluid flow model in combination with a conservative finite volume method (FVM). The investigated bubble clusters (referred to as "clouds") differ by their initial vapor volume fractions, initial stand-off distances to the wall and by initial bubble radii. The effects of collapse focusing due to bubble-bubble interaction are analysed by investigating the intensities and positions of individual bubble collapses, as well as by the resulting shock-induced pressure field at the wall. Stronger interaction of the bubbles leads to an intensification of the collapse strength for individual bubbles, collapse focusing towards the center of the cloud and enhanced re-evaporation. The obtained results reveal collapse features which are common for all cases, as well as case-specific differences during collapse-rebound cycles. Simultaneous measurements of maximum pressures at the wall and within the flow field and of the vapor volume evolution show that not only the primary collapse but also subsequent collapses are potentially relevant for erosion.

a Statistical Texture Feature for Building Collapse Information Extraction of SAR Image

NASA Astrophysics Data System (ADS)

Li, L.; Yang, H.; Chen, Q.; Liu, X.

2018-04-01

Synthetic Aperture Radar (SAR) has become one of the most important ways to extract post-disaster collapsed building information, due to its extreme versatility and almost all-weather, day-and-night working capability, etc. In view of the fact that the inherent statistical distribution of speckle in SAR images is not used to extract collapsed building information, this paper proposed a novel texture feature of statistical models of SAR images to extract the collapsed buildings. In the proposed feature, the texture parameter of G0 distribution from SAR images is used to reflect the uniformity of the target to extract the collapsed building. This feature not only considers the statistical distribution of SAR images, providing more accurate description of the object texture, but also is applied to extract collapsed building information of single-, dual- or full-polarization SAR data. The RADARSAT-2 data of Yushu earthquake which acquired on April 21, 2010 is used to present and analyze the performance of the proposed method. In addition, the applicability of this feature to SAR data with different polarizations is also analysed, which provides decision support for the data selection of collapsed building information extraction.

Precombination Cloud Collapse and Baryonic Dark Matter

NASA Technical Reports Server (NTRS)

Hogan, Craig J.

1993-01-01

A simple spherical model of dense baryon clouds in the hot big bang 'strongly nonlinear primordial isocurvature baryon fluctuations' is reviewed and used to describe the dependence of cloud behavior on the model parameters, baryon mass, and initial over-density. Gravitational collapse of clouds before and during recombination is considered including radiation diffusion and trapping, remnant type and mass, and effects on linear large-scale fluctuation modes. Sufficiently dense clouds collapse early into black holes with a minimum mass of approx. 1 solar mass, which behave dynamically like collisionless cold dark matter. Clouds below a critical over-density, however, delay collapse until recombination, remaining until then dynamically coupled to the radiation like ordinary diffuse baryons, and possibly producing remnants of other kinds and lower mass. The mean density in either type of baryonic remnant is unconstrained by observed element abundances. However, mixed or unmixed spatial variations in abundance may survive in the diffuse baryon and produce observable departures from standard predictions.

Simulating the minimum core for hydrophobic collapse in globular proteins.

PubMed Central

Tsai, J.; Gerstein, M.; Levitt, M.

1997-01-01

To investigate the nature of hydrophobic collapse considered to be the driving force in protein folding, we have simulated aqueous solutions of two model hydrophobic solutes, methane and isobutylene. Using a novel methodology for determining contacts, we can precisely follow hydrophobic aggregation as it proceeds through three stages: dispersed, transition, and collapsed. Theoretical modeling of the cluster formation observed by simulation indicates that this aggregation is cooperative and that the simulations favor the formation of a single cluster midway through the transition stage. This defines a minimum solute hydrophobic core volume. We compare this with protein hydrophobic core volumes determined from solved crystal structures. Our analysis shows that the solute core volume roughly estimates the minimum core size required for independent hydrophobic stabilization of a protein and defines a limiting concentration of nonpolar residues that can cause hydrophobic collapse. These results suggest that the physical forces driving aggregation of hydrophobic molecules in water is indeed responsible for protein folding. PMID:9416609

Stress-mediated Allee effects can cause the sudden collapse of honey bee colonies.

PubMed

Booton, Ross D; Iwasa, Yoh; Marshall, James A R; Childs, Dylan Z

2017-05-07

The recent rapid decline in global honey bee populations could have significant implications for ecological systems, economics and food security. No single cause of honey bee collapse has yet to be identified, although pesticides, mites and other pathogens have all been shown to have a sublethal effect. We present a model of a functioning bee hive and introduce external stress to investigate the impact on the regulatory processes of recruitment to the forager class, social inhibition and the laying rate of the queen. The model predicts that constant density-dependent stress acting through an Allee effect on the hive can result in sudden catastrophic switches in dynamical behaviour and the eventual collapse of the hive. The model proposes that around a critical point the hive undergoes a saddle-node bifurcation, and that a small increase in model parameters can have irreversible consequences for the entire hive. We predict that increased stress levels can be counteracted by a higher laying rate of the queen, lower levels of forager recruitment or lower levels of natural mortality of foragers, and that increasing social inhibition can not maintain the colony under high levels of stress. We lay the theoretical foundation for sudden honey bee collapse in order to facilitate further experimental and theoretical consideration. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Formation of a cavitation cluster in the vicinity of a quasi-empty rupture

NASA Astrophysics Data System (ADS)

Bol'shakova, E. S.; Kedrinskiy, V. K.

2017-09-01

The presentation deals with one of the experimental and numerical models of a quasi-empty rupture in the magma melt. This rupture is formed in the liquid layer of a distilled cavitating fluid under shock loading within the framework of the problem formulation with a small electromagnetic hydrodynamic shock tube. It is demonstrated that the rupture is shaped as a spherical segment, which retains its topology during the entire process of its evolution and collapsing. The dynamic behavior of the quasi-empty rupture is analyzed, and the growth of cavitating nuclei in the form of the boundary layer near the entire rupture interface is found. It is shown that rupture implosion is accompanied by the transformation of the bubble boundary layer to a cavitating cluster, which takes the form of a ring-shaped vortex floating upward to the free surface of the liquid layer. A p-κ mathematical model is formulated, and calculations are performed to investigate the implosion of a quasi-empty spherical cavity in the cavitating liquid, generation of a shock wave by this cavity, and dynamics of the bubble density growth in the cavitating cluster by five orders of magnitude.

Three-dimensional geophysical mapping of shallow water saturated altered rocks at Mount Baker, Washington: Implications for slope stability

NASA Astrophysics Data System (ADS)

Finn, Carol A.; Deszcz-Pan, Maryla; Ball, Jessica L.; Bloss, Benjamin J.; Minsley, Burke J.

2018-05-01

Water-saturated hydrothermal alteration reduces the strength of volcanic edifices, increasing the potential for catastrophic sector collapses that can lead to far traveled and destructive debris flows. Intense hydrothermal alteration significantly lowers the resistivity and magnetization of volcanic rock and therefore hydrothermally altered rocks can be identified with helicopter electromagnetic and magnetic measurements. Geophysical models constrained by rock properties and geologic mapping show that intensely altered rock is restricted to two small (500 m diameter), >150 m thick regions around Sherman Crater and Dorr Fumarole Field at Mount Baker, Washington. This distribution of alteration contrasts with much thicker and widespread alteration encompassing the summits of Mounts Adams and Rainier prior to the 5600 year old Osceola collapse, which is most likely due to extreme erosion and the limited duration of summit magmatism at Mount Baker. In addition, the models suggest that the upper 300 m of rock contains water which could help to lubricate potential debris flows. Slope stability modeling incorporating the geophysically modeled distribution of alteration and water indicates that the most likely and largest ( 0.1 km3) collapses are from the east side of Sherman Crater. Alteration at Dorr Fumarole Field raises the collapse hazard there, but not significantly because of its lower slope angles. Geochemistry and analogs from other volcanoes suggest a model for the edifice hydrothermal system.

On the hyperbolicity and stability of 3+1 formulations of metric f( R) gravity

NASA Astrophysics Data System (ADS)

Mongwane, Bishop

2016-11-01

3+1 formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is plausible that similar considerations could prove fruitful for modified gravity theories. In this article, we pursue from a numerical relativistic viewpoint the 3+1 formulation of metric f( R) gravity as it arises from the fourth order equations of motion, without invoking the dynamical equivalence with Brans-Dicke theories. We present the resulting system of evolution and constraint equations for a generic function f( R), subject to the usual viability conditions. We confirm that the time propagation of the f( R) Hamiltonian and Momentum constraints take the same Mathematical form as in general relativity, irrespective of the f( R) model. We further recast the 3+1 system in a form akin to the BSSNOK formulation of numerical relativity. Without assuming any specific model, we show that the ADM version of f( R) is weakly hyperbolic and is plagued by similar zero speed modes as in the general relativity case. On the other hand the BSSNOK version is strongly hyperbolic and hence a promising formulation for numerical simulations in metric f( R) theories.

Voltage collapse in complex power grids

PubMed Central

Simpson-Porco, John W.; Dörfler, Florian; Bullo, Francesco

2016-01-01

A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow. Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling. However, methods to test for voltage collapse are dominantly simulation-based, offering little theoretical insight into how grid structure influences stability margins. For a simplified power flow model, here we derive a closed-form condition under which a power network is safe from voltage collapse. The condition combines the complex structure of the network with the reactive power demands of loads to produce a node-by-node measure of grid stress, a prediction of the largest nodal voltage deviation, and an estimate of the distance to collapse. We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins. PMID:26887284

Geological constraints of a structural model of sector collapse at Stromboli volcano, Italy

NASA Astrophysics Data System (ADS)

Vezzoli, L.; Corazzato, C.

2016-09-01

This study is focused on the reconstruction of the structure and dynamics of the first lateral collapse that occurred at Stromboli during the Holocene, which represents the structure inherited by all the following collapses that formed the present Sciara del Fuoco depression. The first lateral collapse of Stromboli occurred at the end of the Vancori volcano activity, at about 13 ka ago. The Neostromboli lava cone grew within this collapse amphitheater. Based on a comprehensive geologic and structural analysis of both Vancori and Neostromboli products, we propose an innovative interpretation of the sliding surface. Once considered to be a homogeneous landslide along a deep-seated sliding surface, we demonstrate that the Upper Vancori failure was accommodated by a more complex deformation regime comprising an upper (proximal) domain of tilted megablocks (toreva) and a lower (distal) domain of fragmental landslide transport and deposition.

The collapse of Tacoma Narrows Bridge: a piece to the puzzle

NASA Astrophysics Data System (ADS)

Walther, J. H.; Christensen, D. S.; Malthe, M. G.; Roenne, M.; Spietz, H. J.; Larsen, A.; Larsen, S. V.

2017-11-01

On Nov. 7th 1940 the newly constructed Tacoma Narrows Bridge collapsed due to excessive torsional oscillations caused by the formation and shedding of large coherent vortices. The subsequent wind tunnel tests conducted on both section- and full bridge models concluded that the bridge should have collapsed at a wind speed corresponding to approximately half of the wind speed at the day of the collapse. This discrepancy questions our understanding of the phenomena responsible for the failure of the bridge. The present study aims at clarifying this ``mystery'' by considering historical records made available by the US coast guards, and by performing wind tunnel tests and detailed numerical flow simulations. Our findings indicate that the discrepancy is caused by an until now unnoticed yawed wind direction relative to the bridge, which was present at the day of the collapse. Danish Council for Independent Research Grant No. 4184-00349B.

Seismic precursory patterns before a cliff collapse and critical point phenomena

USGS Publications Warehouse

Amitrano, D.; Grasso, J.-R.; Senfaute, G.

2005-01-01

We analyse the statistical pattern of seismicity before a 1-2 103 m3 chalk cliff collapse on the Normandie ocean shore, Western France. We show that a power law acceleration of seismicity rate and energy in both 40 Hz-1.5 kHz and 2 Hz-10kHz frequency range, is defined on 3 orders of magnitude, within 2 hours from the collapse time. Simultaneously, the average size of the seismic events increases toward the time to failure. These in situ results are derived from the only station located within one rupture length distance from the rock fall rupture plane. They mimic the "critical point" like behavior recovered from physical and numerical experiments before brittle failures and tertiary creep failures. Our analysis of this first seismic monitoring data of a cliff collapse suggests that the thermodynamic phase transition models for failure may apply for cliff collapse. Copyright 2005 by the American Geophysical Union.

The collapse of a cavitation bubble in a corner

NASA Astrophysics Data System (ADS)

Peters, Ivo; Tagawa, Yoshiyuki

2017-11-01

The collapse of cavitation bubbles is influenced by the surrounding geometry. A classic example is the collapse of a bubble near a solid wall, where a fast jet is created towards the wall. The addition of a second wall creates a non-axisymmetric flow field, which influences the displacement and jet formation during the collapse of a bubble. In this experimental study we generate mm-sized vapor bubbles using a focused pulsed laser, giving us full control over the position of the bubble. The corner geometry is formed by two glass slides. High-speed imaging reveals the directional motion of the bubble during the collapse. We find that the bubble displacement cannot be fully described by a simple superposition of the bubble dynamics of the two walls individually. Comparison of our experimental results to a model based on potential flow shows a good agreement for the direction of displacement.

Investigating collapse structures in oceanic islands using magnetotelluric surveys: The case of Fogo Island in Cape Verde

NASA Astrophysics Data System (ADS)

Martínez-Moreno, F. J.; Monteiro Santos, F. A.; Madeira, J.; Pous, J.; Bernardo, I.; Soares, A.; Esteves, M.; Adão, F.; Ribeiro, J.; Mata, J.; Brum da Silveira, A.

2018-05-01

One of the most remarkable natural events on Earth are the large lateral flank collapses of oceanic volcanoes, involving volumes of rock exceeding tens of km3. These collapses are relatively frequent in recent geological times as supported by evidence found in the geomorphology of volcanic island edifices and associated debris flows deposited on the proximal ocean floor. The Island of Fogo in the Cape Verde archipelago is one of the most active and prominent oceanic volcanoes on Earth. The island has an average diameter of 25 km and reaches a maximum elevation of 2829 m above sea level (m a.s.l.) at Pico do Fogo, a young stratovolcano located within a summit depression open eastward due to a large lateral flank collapse. The sudden collapse of the eastern flank of Fogo Island produced a megatsunami 73 ky ago. The limits of the flank collapse were deduced as well from geomorphologic markers within the island. The headwall of the collapse scar is interpreted as either being located beneath the post-collapse volcanic infill of the summit depression or located further west, corresponding to the Bordeira wall that partially surrounds it. The magnetotelluric (MT) method provides a depth distribution of the ground resistivity obtained by the simultaneous measurement of the natural variations of the electric and magnetic field of the Earth. Two N-S magnetotelluric profiles were acquired across the collapsed area to determine its geometry and boundaries. The acquired MT data allowed the determination of the limits of the collapsed area more accurately as well as its morphology at depth and thickness of the post-collapse infill. According to the newly obtained MT data and the bathymetry of the eastern submarine flank of Fogo, the volume involved in the flank collapse is estimated in 110 km3. This volume -the first calculated onshore- stands between the previously published more conservative and excessive calculations -offshore- that were exclusively based in geomorphic evidence. The model for the summit depression proposing two caldera collapses preceding the collapse of the eastern flank of Fogo is supported by the MT data.

A multidisciplinary study of the 2014-2015 Bárðarbunga caldera collapse, Iceland

NASA Astrophysics Data System (ADS)

Tumi Gudmundsson, Magnus; Jonsdóttir, Kristin; Hooper, Andy; Holohan, Eoghan; Halldorsson, Saemundur

2016-04-01

The collapse of the ice-filled Bárðarbunga caldera in central Iceland occurred in autumn and winter, when weather was highly unsettled and conditions for monitoring in many ways difficult. Nevertheless several detailed time series could be obtained on the collapse and to a degree the associated flood-basalt eruption in Holuhraun. This was achieved through applying an array of sensors, that were ground, air and satellite based, partly made possible through the EU-funded FUTUREVOLC supersite project. This slow caldera collapse lasted six months, ending in February 2015. The array of sensors used, coupled with the long duration of the event, allowed unprecedented detail in observing a caldera collapse. The deciphering of the course of events required the use of aircraft altimeter surveys of the ice surface, seismic and GPS monitoring, the installation of a GPS station on the glacier surface in the centre of the caldera that continuously recorded the subsidence. Full Stokes 3-D modelling of the 700-800 m thick ice in the caldera, constrained by observations, was applied to remove the component of ice deformation that had a minor effect on the measured subsidence. The maximum subsidence of the subglacial caldera floor was about 65 meters. The combined interpretation of geochemical geobarometers, subsidence geometry with GPS and InSAR deformation signals, seismicity and distinct element deformation modelling of the subsidence provided unprecedented detail of the process and mechanism of caldera collapse. The collapse involved the re-activation of pre-existing ring faults, and was initiated a few days after magma started to drain from underneath the caldera towards the eventual eruption site in Holuhraun, 45 km to the northeast. The caldera collapse was slow and gradual, and the flow rate from underneath the caldera correlates well with the lava flow rate in Holuhraun, both in terms of total volume and variations in time.

Shock-induced collapse of a bubble inside a deformable vessel

PubMed Central

Coralic, Vedran; Colonius, Tim

2013-01-01

Shockwave lithotripsy repeatedly focuses shockwaves on kidney stones to induce their fracture, partially through cavitation erosion. A typical side effect of the procedure is hemorrhage, which is potentially the result of the growth and collapse of bubbles inside blood vessels. To identify the mechanisms by which shock-induced collapse could lead to the onset of injury, we study an idealized problem involving a preexisting bubble in a deformable vessel. We utilize a high-order accurate, shock- and interface-capturing, finite-volume scheme and simulate the three-dimensional shock-induced collapse of an air bubble immersed in a cylindrical water column which is embedded in a gelatin/water mixture. The mixture is a soft tissue simulant, 10% gelatin by weight, and is modeled by the stiffened gas equation of state. The bubble dynamics of this model configuration are characterized by the collapse of the bubble and its subsequent jetting in the direction of the propagation of the shockwave. The vessel wall, which is defined by the material interface between the water and gelatin/water mixture, is invaginated by the collapse and distended by the impact of the jet. The present results show that the highest measured pressures and deformations occur when the volumetric confinement of the bubble is strongest, the bubble is nearest the vessel wall and/or the angle of incidence of the shockwave reduces the distance between the jet tip and the nearest vessel surface. For a particular case considered, the 40 MPa shockwave utilized in this study to collapse the bubble generated a vessel wall pressure of almost 450 MPa and produced both an invagination and distention of nearly 50% of the initial vessel radius on a 𝒪(10) ns timescale. These results are indicative of the significant potential of shock-induced collapse to contribute to the injury of blood vessels in shockwave lithotripsy. PMID:24015027

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

Timelike naked singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo

We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularitymore » formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture.« less

Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making.

PubMed

Hawkins, Guy E; Forstmann, Birte U; Wagenmakers, Eric-Jan; Ratcliff, Roger; Brown, Scott D

2015-02-11

For nearly 50 years, the dominant account of decision-making holds that noisy information is accumulated until a fixed threshold is crossed. This account has been tested extensively against behavioral and neurophysiological data for decisions about consumer goods, perceptual stimuli, eyewitness testimony, memories, and dozens of other paradigms, with no systematic misfit between model and data. Recently, the standard model has been challenged by alternative accounts that assume that less evidence is required to trigger a decision as time passes. Such "collapsing boundaries" or "urgency signals" have gained popularity in some theoretical accounts of neurophysiology. Nevertheless, evidence in favor of these models is mixed, with support coming from only a narrow range of decision paradigms compared with a long history of support from dozens of paradigms for the standard theory. We conducted the first large-scale analysis of data from humans and nonhuman primates across three distinct paradigms using powerful model-selection methods to compare evidence for fixed versus collapsing bounds. Overall, we identified evidence in favor of the standard model with fixed decision boundaries. We further found that evidence for static or dynamic response boundaries may depend on specific paradigms or procedures, such as the extent of task practice. We conclude that the difficulty of selecting between collapsing and fixed bounds models has received insufficient attention in previous research, calling into question some previous results. Copyright © 2015 the authors 0270-6474/15/352476-09$15.00/0.

Genetic podocyte lineage reveals progressive podocytopenia with parietal cell hyperplasia in a murine model of cellular/collapsing focal segmental glomerulosclerosis.

PubMed

Suzuki, Taisei; Matsusaka, Taiji; Nakayama, Makiko; Asano, Takako; Watanabe, Teruo; Ichikawa, Iekuni; Nagata, Michio

2009-05-01

Focal segmental glomerulosclerosis (FSGS) is a progressive renal disease, and the glomerular visceral cell hyperplasia typically observed in cellular/collapsing FSGS is an important pathological factor in disease progression. However, the cellular features that promote FSGS currently remain obscure. To determine both the origin and phenotypic alterations in hyperplastic cells in cellular/collapsing FSGS, the present study used a previously described FSGS model in p21-deficient mice with visceral cell hyperplasia and identified the podocyte lineage by genetic tagging. The p21-deficient mice with nephropathy showed significantly higher urinary protein levels, extracapillary hyperplastic indices on day 5, and glomerular sclerosis indices on day 14 than wild-type controls. X-gal staining and immunohistochemistry for podocyte and parietal epithelial cell (PEC) markers revealed progressive podocytopenia with capillary collapse accompanied by PEC hyperplasia leading to FSGS. In our investigation, non-tagged cells expressed neither WT1 nor nestin. Ki-67, a proliferation marker, was rarely associated with podocytes but was expressed at high levels in PECs. Both terminal deoxynucleotidyl transferase dUTP nick-end labeling staining and electron microscopy failed to show evidence of significant podocyte apoptosis on days 5 and 14. These findings suggest that extensive podocyte loss and simultaneous PEC hyperplasia is an actual pathology that may contribute to the progression of cellular/collapsing FSGS in this mouse model. Additionally, this is the first study to demonstrate the regulatory role of p21 in the PEC cell cycle.

Simulated Cytoskeletal Collapse via Tau Degradation

PubMed Central

Sendek, Austin; Fuller, Henry R.; Hayre, N. Robert; Singh, Rajiv R. P.; Cox, Daniel L.

2014-01-01

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimers disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundles falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06–0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse. PMID:25162587

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Natural hazard management high education: laboratory of hydrologic and hydraulic risk management and applied geomorphology

NASA Astrophysics Data System (ADS)

Giosa, L.; Margiotta, M. R.; Sdao, F.; Sole, A.; Albano, R.; Cappa, G.; Giammatteo, C.; Pagliuca, R.; Piccolo, G.; Statuto, D.

2009-04-01

The Environmental Engineering Faculty of University of Basilicata have higher-level course for students in the field of natural hazard. The curriculum provides expertise in the field of prediction, prevention and management of earthquake risk, hydrologic-hydraulic risk, and geomorphological risk. These skills will contribute to the training of specialists, as well as having a thorough knowledge of the genesis and the phenomenology of natural risks, know how to interpret, evaluate and monitor the dynamic of environment and of territory. In addition to basic training in the fields of mathematics and physics, the course of study provides specific lessons relating to seismic and structural dynamics of land, environmental and computational hydraulics, hydrology and applied hydrogeology. In particular in this course there are organized two connected examination arguments: Laboratory of hydrologic and hydraulic risk management and Applied geomorphology. These course foresee the development and resolution of natural hazard problems through the study of a real natural disaster. In the last year, the work project has regarded the collapse of two decantation basins of fluorspar, extracted from some mines in Stava Valley, 19 July 1985, northern Italy. During the development of the course, data and event information has been collected, a guided tour to the places of the disaster has been organized, and finally the application of mathematical models to simulate the disaster and analysis of the results has been carried out. The student work has been presented in a public workshop.

Identification of mine collapses, explosions and earthquakes using INSAR: a preliminary investigation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Foxall, B; Sweeney, J J; Walter, W R

1998-07-07

Interferograms constmcted from satellite-borne synthetic aperture radar images have the capability of mapping sub-cm ground surface deformation over areas on the order of 100 x 100 km with a spatial resolution on the order of 10 meters. We investigate the utility of synthetic aperture radar interferomehy (InSAR) used in conjunction with regional seismic methods in detecting and discriminating different types of seismic events in the context of special event analysis for the CTBT. For this initial study, we carried out elastic dislocation modeling of underground explosions, mine collapses and small (M<5.5) shallow earthquakes to produce synthetic interferograms and then analyzedmore » satellite radar data for a large mine collapse. The synthetic modeling shows that, for a given magnitude each type of event produces a distinctive pattern of ground deformation that can be recognized in, and recovered from, the corresponding interferogram. These diagnostic characteristics include not only differences in the polarities of surface displacements but also differences in displacement amplitudes from the different sources. The technique is especially sensitive to source depth, a parameter that is crucial in discriminating earthquakes from the other event types but is often very poorly constrained by regional seismic data alone. The ERS radar data analyzed is from a M L 5.2 seismic event that occurred in southwestern Wyoming on February 3,1995. Although seismic data from the event have some characteristics of an underground explosion, based on seismological and geodetic data it has been identified as being caused by a large underground collapse in the Solvay Mine. Several pairs of before-collapse and after-collapse radar images were phase processed to obtain interferograms. The minimum time separation for a before-collapse and after-collapse pair was 548 days. Even with this long time separation, phase coherence between the image pairs was acceptable and a deformation map was successfully obtained. Two images, separated by 1 day and occurring after the mine collapse, were used to form a digital elevation map (DEM) that was used to correct for topography. The interferograms identify the large deformation at the Solvay Mine as well as some areas of lesser deformation near other mines in the area. The large amount of deformation at the Solvay Mine was identified, but (as predicted by our dislocation modeling) could not be quantified absolutely because of the incoherent interference pattern it produced« less

Evaluation of the 3D Finite Element Method Using a Tantalum Rod for Osteonecrosis of the Femoral Head

PubMed Central

Shi, Jingsheng; Chen, Jie; Wu, Jianguo; Chen, Feiyan; Huang, Gangyong; Wang, Zhan; Zhao, Guanglei; Wei, Yibing; Wang, Siqun

2014-01-01

Background The aim of this study was to contrast the collapse values of the postoperative weight-bearing areas of different tantalum rod implant positions, fibula implantation, and core decompression model and to investigate the advantages and disadvantages of tantalum rod implantation in different ranges of osteonecrosis in comparison with other methods. Material/Methods The 3D finite element method was used to establish the 3D finite element model of normal upper femur, 3D finite element model after tantalum rod implantation into different positions of the upper femur in different osteonecrosis ranges, and other 3D finite element models for simulating fibula implant and core decompression. Results The collapse values in the weight-bearing area of the femoral head of the tantalum rod implant model inside the osteonecrosis area, implant model in the middle of the osteonecrosis area, fibula implant model, and shortening implant model exhibited no statistically significant differences (p>0.05) when the osteonecrosis range was small (60°). The stress values on the artificial bone surface for the tantalum rod implant model inside the osteonecrosis area and the shortening implant model exhibited statistical significance (p<0.01). Conclusions Tantalum rod implantation into the osteonecrosis area can reduce the collapse values in the weight-bearing area when osteonecrosis of the femoral head (ONFH) was in a certain range, thereby obtaining better clinical effects. When ONFH was in a large range (120°), the tantalum rod implantation inside the osteonecrosis area, shortening implant or fibula implant can reduce the collapse values of the femoral head, as assessed by other methods. PMID:25479830

Estimating explosion properties of normal hydrogen-rich core-collapse supernovae

NASA Astrophysics Data System (ADS)

Pejcha, Ondrej

2017-08-01

Recent parameterized 1D explosion models of hundreds of core-collapse supernova progenitors suggest that success and failure are intertwined in a complex pattern that is not a simple function of the progenitor initial mass. This rugged landscape is present also in other explosion properties, allowing for quantitative tests of the neutrino mechanism from observations of hundreds of supernovae discovered every year. We present a new self-consistent and versatile method that derives photospheric radius and temperature variations of normal hydrogen-rich core-collapse supernovae based on their photometric measurements and expansion velocities. We construct SED and bolometric light curves, determine explosion energies, ejecta and nickel masses while taking into account all uncertainties and covariances of the model. We describe the efforts to compare the inferences to the predictions of the neutrino mechanim. The model can be adapted to include more physical assumptions to utilize primarily photometric data coming from surveys such as LSST.

Magnetically regulated collapse in the B335 protostar? I. ALMA observations of the polarized dust emission

NASA Astrophysics Data System (ADS)

Maury, A. J.; Girart, J. M.; Zhang, Q.; Hennebelle, P.; Keto, E.; Rao, R.; Lai, S.-P.; Ohashi, N.; Galametz, M.

2018-06-01

The role of the magnetic field during protostellar collapse is poorly constrained from an observational point of view, although it could be significant if we believe state-of-the-art models of protostellar formation. We present polarimetric observations of the 233 GHz thermal dust continuum emission obtained with ALMA in the B335 Class 0 protostar. Linearly polarized dust emission arising from the circumstellar material in the envelope of B335 is detected at all scales probed by our observations (50 to 1000 au). The magnetic field structure producing the dust polarization has a very ordered topology in the inner envelope, with a transition from a large-scale poloidal magnetic field, in the outflow direction, to strongly pinched in the equatorial direction. This is probably due to magnetic field lines being dragged along the dominating infall direction since B335 does not exhibit prominent rotation. Our data and their qualitative comparison to a family of magnetized protostellar collapse models show that, during the magnetized collapse in B335, the magnetic field is maintaining a high level of organization from scales 1000 au to 50 au: this suggests the field is dynamically relevant and capable of influencing the typical outcome of protostellar collapse, such as regulating the disc size in B335.

Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal Net of the Brain.

PubMed

Wu, Yuan-Ting; Adnan, Ashfaq

2017-07-13

The purpose of this study is to conduct modeling and simulation to understand the effect of shock-induced mechanical loading, in the form of cavitation bubble collapse, on damage to the brain's perineuronal nets (PNNs). It is known that high-energy implosion due to cavitation collapse is responsible for corrosion or surface damage in many mechanical devices. In this case, cavitation refers to the bubble created by pressure drop. The presence of a similar damage mechanism in biophysical systems has long being suspected but not well-explored. In this paper, we use reactive molecular dynamics (MD) to simulate the scenario of a shock wave induced cavitation collapse within the perineuronal net (PNN), which is the near-neuron domain of a brain's extracellular matrix (ECM). Our model is focused on the damage in hyaluronan (HA), which is the main structural component of PNN. We have investigated the roles of cavitation bubble location, shockwave intensity and the size of a cavitation bubble on the structural evolution of PNN. Simulation results show that the localized supersonic water hammer created by an asymmetrical bubble collapse may break the hyaluronan. As such, the current study advances current knowledge and understanding of the connection between PNN damage and neurodegenerative disorders.

The collapse of the Maya: Effects of natural and human-induced drought

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oglesby, Robert J; Erickson III, David J

2010-02-01

The collapse of the Maya civilization during the ninth century A.D. is a major conundrum in the history of mankind. This civilization reached a spectacular peak but then almost completely collapsed in the space of a few decades. While numerous explanations have been put forth to explain this collapse, in recent years, drought has gained favor. This is because water resources were a key for the Maya, especially to ensure their survival during the lengthy dry season that occurs where they lived. Natural drought is a known, recurring feature of this region, as evidenced by observational data, reconstructions of pastmore » times, and global climate model output. Results from simulations with a regional climate model demonstrate that deforestation by the Maya also likely induced warmer, drier, drought-like conditions. It is therefore hypothesized that the drought conditions devastating the Maya resulted from a combination of natural variability and human activities. Neither the natural drought or the human-induced effects alone were sufficient to cause the collapse, but the combination created a situation the Maya could not recover from. These results may have sobering implications for the present and future state of climate and water resources in Mesoamerica as ongoing massive deforestation is again occurring.« less

Formation of Ice-Rich Lobate Debris Aprons Through Regional Icesheet Collapse and Debris-Cover Armoring

NASA Astrophysics Data System (ADS)

Fastook, J. L.; Head, J. W.; Marchant, D. R.

2011-03-01

We use a flowband model to assess development of lobate debris apron sublimation lag thickness and lateral extent beneath scarps. We obtain estimates of the climate in place as the LDAs were forming during collapse of a larger, regional ice sheet.

Gravitational collapse of dark matter interacting with dark energy: Black hole formation

NASA Astrophysics Data System (ADS)

Shah, Hasrat Hussain; Iqbal, Quaid

In this work, we study the gravitational collapsing process of a spherically symmetric star constitute of Dark Matter (DM), ρM, and Dark Energy (DE) ρ. In this model, we use anisotropic pressure with Equation of State (EoS) pt = λρ and pr = lρ, (l + 2λ < -1). It reveals that gravitational collapse of DM and DE with interaction leads to the formation of the black hole. When l + 2λ < -3 (phantoms), dust and phantoms could be ejected from the death of white hole. This emitted matter again undergoes to collapsing process and becomes the black hole. This study gives the generalization for isotropy of pressure in the fluid to anisotropy when there will be interaction between DM and DE.

The 3D Death of a Massive Star

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2015-07-01

What happens at the very end of a massive star's life, just before its core's collapse? A group led by Sean Couch (California Institute of Technology and Michigan State University) claim to have carried out the first three-dimensional simulations of these final few minutes — revealing new clues about the factors that can lead a massive star to explode in a catastrophic supernova at the end of its life. A Giant Collapses In dying massive stars, in-falling matter bounces off the of collapsed core, creating a shock wave. If the shock wave loses too much energy as it expands into the star, it can stall out — but further energy input can revive it and result in a successful explosion of the star as a core-collapse supernova. In simulations of this process, however, theorists have trouble getting the stars to consistently explode: the shocks often stall out and fail to revive. Couch and his group suggest that one reason might be that these simulations usually start at core collapse assuming spherical symmetry of the progenitor star. Adding Turbulence Couch and his collaborators suspect that the key is in the final minutes just before the star collapses. Models that assume a spherically-symmetric star can't include the effects of convection as the final shell of silicon is burned around the core — and those effects might have a significant impact! To test this hypothesis, the group ran fully 3D simulations of the final three minutes of the life of a 15 solar-mass star, ending with core collapse, bounce, and shock-revival. The outcome was striking: the 3D modeling introduced powerful turbulent convection (with speeds of several hundred km/s!) in the last few minutes of silicon-shell burning. As a result, the initial structure and motions in the star just before core collapse were very different from those in core-collapse simulations that use spherically-symmetric initial conditions. The turbulence was then further amplified during collapse and formation of the shock, generating pressure that aided the shock expansion — which should ultimately help the star explode! The group cautions that their simulations are still very idealized, but these results clearly indicate that the 3D structure of massive stellar cores has an important impact on the core-collapse supernova mechanism. Citation Sean M. Couch et al. 2015 ApJ 808 L21 doi:10.1088/2041-8205/808/1/L21

Multiscale Analysis of a Collapsible Respiratory Airway

NASA Astrophysics Data System (ADS)

Ghadiali, Samir; Bell, E. David; Swarts, J. Douglas

2006-11-01

The Eustachian tube (ET) is a collapsible respiratory airway that connects the nasopharynx with the middle ear (ME). The ET normally exists in a collapsed state and must be periodically opened to maintain a healthy and sterile ME. Although the inability to open the ET (i.e. ET dysfunction) is the primary etiology responsible for several common ME diseases (i.e. Otitis Media), the mechanisms responsible for ET dysfunction are not well established. To investigate these mechanisms, we developed a multi-scale model of airflow in the ET and correlated model results with experimental data obtained in healthy and diseased subjects. The computational models utilized finite-element methods to simulate fluid-structure interactions and molecular dynamics techniques to quantify the adhesive properties of mucus glycoproteins. Results indicate that airflow in the ET is highly sensitive to both the dynamics of muscle contraction and molecular adhesion forces within the ET lumen. In addition, correlation of model results with experimental data obtained in diseased subjects was used to identify the biomechanical mechanisms responsible for ET dysfunction.

Infill Walls Contribution on the Progressive Collapse Resistance of a Typical Mid-rise RC Framed Building

NASA Astrophysics Data System (ADS)

Besoiu, Teodora; Popa, Anca

2017-10-01

This study investigates the effect of the autoclaved aerated concrete infill walls on the progressive collapse resistance of a typical RC framed structure. The 13-storey building located in Brăila (a zone with high seismic risk in Romania) was designed according to the former Romanian seismic code P13-70 (1970). Two models of the structure are generated in the Extreme Loading® for Structures computer software: a model with infill walls and a model without infill walls. Following GSA (2003) Guidelines, a nonlinear dynamic procedure is used to determine the progressive collapse risk of the building when a first-storey corner column is suddenly removed. It was found that, the structure is not expected to fail under the standard GSA loading: DL+0.25LL. Moreover, if the infill walls are introduced in the model, the maximum vertical displacement of the node above the removed column is reduced by about 48%.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Austin, Ryan A.; Barton, Nathan R.; Reaugh, John E.

A numerical model is developed to study the shock wave ignition of HMX crystal. The model accounts for the coupling between crystal thermal/mechanical responses and chemical reactions that are driven by the temperature field. This allows for the direct numerical simulation of decomposition reactions in the hot spots formed by shock/impact loading. The model is used to simulate intragranular pore collapse under shock wave loading. In a reference case: (i) shear-enabled micro-jetting is responsible for a modest extent of reaction in the pore collapse region, and (ii) shear banding is found to be an important mode of localization. The shearmore » bands, which are filled with molten HMX, grow out of the pore collapse region and serve as potential ignition sites. The model predictions of shear banding and reactivity are found to be quite sensitive to the respective flow strengths of the solid and liquid phases. In this regard, it is shown that reasonable assumptions of liquid-HMX viscosity can lead to chemical reactions within the shear bands on a nanosecond time scale.« less

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Anomalous critical behavior in the polymer collapse transition of three-dimensional lattice trails.

PubMed

Bedini, Andrea; Owczarek, Aleksander L; Prellberg, Thomas

2012-07-01

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separated by a multicritical point. A kinetic growth process of trails (KGTs) was conjectured to map precisely to this multicritical point. Two types of low-temperature phases, a globule phase and a maximally dense phase, were encountered. Here we investigate the collapse properties of a similar extended model of interacting lattice trails on the simple cubic lattice with separate weights for doubly and triply visited sites. Again we find first- and second-order collapse transitions dependent on the relative sizes of the doubly and triply visited energies. However, we find no evidence of a low-temperature maximally dense phase with only the globular phase in existence. Intriguingly, when the ratio of the energies is precisely that which separates the first-order from the second-order regions anomalous finite-size scaling appears. At the finite-size location of the rounded transition clear evidence exists for a first-order transition that persists in the thermodynamic limit. This location moves as the length increases, with its limit apparently at the point that maps to a KGT. However, if one fixes the temperature to sit at exactly this KGT point, then only a critical point can be deduced from the data. The resolution of this apparent contradiction lies in the breaking of crossover scaling and the difference in the shift and transition width (crossover) exponents.

Collapse and coexistence for a molecular braid with an attractive interaction component subject to mechanical forces.

PubMed

Lee, Dominic J O'

2015-04-15

Dual mechanical braiding experiments provide a useful tool with which to investigate the nature of interactions between rod-like molecules, for instance actin and DNA. In conditions close to molecular condensation, one would expect an appearance of a local minimum in the interaction potential between the two molecules. We investigate this situation, introducing an attractive component into the interaction potential, using a model developed for describing such experiments. We consider both attractive interactions that do not depend on molecular structure and those which depend on a DNA-like helix structure. In braiding experiments, an attractive term may lead to certain effects. A local minimum may cause molecules to collapse from a loosely braided configuration into a tight one, occurring at a critical value of the moment applied about the axis of the braid. For a fixed number of braid pitches, this may lead to coexistence between the two braiding states, tight and loose. Coexistence implies certain proportions of the braid are in each state, their relative size depending on the number of braid pitches. This manifests itself as a linear dependence in numerically calculated quantities as functions of the number of braid pitches. Also, in the collapsed state, the braid radius stays roughly constant. Furthermore, if the attractive interaction is helix dependent, the left-right handed braid symmetry is broken. For a DNA like charge distribution, using the Kornyshev-Leikin interaction model, our results suggest that significant braid collapse and coexistence only occurs for left handed braids. Regardless of the interaction model, the study highlights the possible qualitative physics of braid collapse and coexistence; and the role helix specific forces might play, if important. The model could be used to connect other microscopic theories of interaction with braiding experiments.

Revisiting Higgs inflation in the context of collapse theories

NASA Astrophysics Data System (ADS)

Rodriguez, Saul; Sudarsky, Daniel

2018-03-01

In this work we consider the Higgs inflation scenario, but in contrast with past works, the present analysis is done in the context of a spontaneous collapse theory for the quantum state of the inflaton field. In particular, we will rely on a previously studied adaptation of the Continuous Spontaneous Localization model for the treatment of inflationary cosmology. We will show that with the introduction of the dynamical collapse hypothesis, some of the most serious problems of the Higgs inflation proposal can be resolved in a natural way.

Avalanches and scaling collapse in the large-N Kuramoto model

NASA Astrophysics Data System (ADS)

Coleman, J. Patrick; Dahmen, Karin A.; Weaver, Richard L.

2018-04-01

We study avalanches in the Kuramoto model, defined as excursions of the order parameter due to ephemeral episodes of synchronization. We present scaling collapses of the avalanche sizes, durations, heights, and temporal profiles, extracting scaling exponents, exponent relations, and scaling functions that are shown to be consistent with the scaling behavior of the power spectrum, a quantity independent of our particular definition of an avalanche. A comprehensive scaling picture of the noise in the subcritical finite-N Kuramoto model is developed, linking this undriven system to a larger class of driven avalanching systems.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Magnetorotational collapse of supermassive stars: Black hole formation, gravitational waves, and jets

NASA Astrophysics Data System (ADS)

Sun, Lunan; Paschalidis, Vasileios; Ruiz, Milton; Shapiro, Stuart L.

2017-08-01

We perform magnetohydrodynamic simulations in full general relativity of uniformly rotating stars that are marginally unstable to collapse. These simulations model the direct collapse of supermassive stars (SMSs) to seed black holes that can grow to become the supermassive black holes at the centers of quasars and active galactic nuclei. They also crudely model the collapse of massive Population III stars to black holes, which could power a fraction of distant, long gamma-ray bursts. The initial stellar models we adopt are Γ =4 /3 polytropes initially with a dynamically unimportant dipole magnetic field. We treat initial magnetic-field configurations either confined to the stellar interior or extending out from the stellar interior into the exterior. We find that the black hole formed following collapse has mass MBH≃0.9 M (where M is the mass of the initial star) and dimensionless spin parameter aBH/MBH≃0.7 . A massive, hot, magnetized torus surrounds the remnant black hole. At Δ t ˜400 - 550 M ≈2000 -2700 (M /106 M⊙)s following the gravitational wave peak amplitude, an incipient jet is launched. The disk lifetime is Δ t ˜105(M /106 M⊙)s , and the outgoing Poynting luminosity is LEM˜1 051 -52 ergs /s . If≳1 %-10 % of this power is converted into gamma rays, Swift and Fermi could potentially detect these events out to large redshifts z ˜20 . Thus, SMSs could be sources of ultra-long gamma-ray bursts (ULGRBs), and massive Population III stars could be the progenitors that power a fraction of the long GRBs observed at redshift z ˜5 - 8 . Gravitational waves are copiously emitted during the collapse and peak at ˜15 (106 M⊙/M ) mHz [˜0.15 (104 M⊙/M ) Hz ], i.e., in the LISA (DECIGO/BBO) band; optimally oriented SMSs could be detectable by LISA (DECIGO/BBO) at z ≲3 (z ≲11 ). Hence, 1 04 M⊙ SMSs collapsing at z ˜10 are promising multimessenger sources of coincident gravitational and electromagnetic waves.

The Fogo's Collapse-triggered Megatsunami: Evidence-calibrated Numerical Simulations of Tsunamigenic Potential and Coastal Impact

NASA Astrophysics Data System (ADS)

Omira, Rachid; Ramalho, Ricardo S.; Quartau, Rui; Ramalho, Inês; Madeira, José; Baptista, Maria Ana

2017-04-01

Volcanic Ocean Islands are very prominent and dynamic features involving several constructive and destructive phases during their life-cycles. Large-scale gravitational flank collapses are one of the most destructive processes and can present a major source of hazard, since it has been shown that these events are capable of triggering megatsunamis with significant coastal impact. The Fogo volcanic island, Cape Verde, presents evidence for giant edifice mass-wasting, as attested by both onshore and offshore evidence. A recent study by Ramalho et al. (2015) revealed the presence of tsunamigenic deposits that attest the generation of a megatsunami with devastating impact on the nearby Santiago Island, following Fogo's catastrophic collapse. Evidence from northern Santiago implies local minimum run-ups of 270 m, providing a unique physical framework to test collapse-triggered tsunami numerical simulations. In this study, we investigate the tsunamigenic potential associated with Fogo's flank collapse, and its impact on the Islands of the Cape Verde archipelago using field evidence-calibrated numerical simulations. We first reconstruct the pre-event island morphology, and then employ a multilayer numerical model to simulate the flank failure flow towards and under the sea, the ensuing tsunami generation, propagation and coastal impact. We use a digital elevation model that considers the coastline configuration and the sea level at the time of the event. Preliminary numerical modeling results suggest that collapsed volumes of 90-150 km3, in one single event, generate numerical solutions that are compatible with field evidence. Our simulations suggest that Fogo's collapse triggered a megatsunami that reached the coast of Santiago in 8 min, and with wave heights in excess of 250 m. The tsunami waves propagated with lower amplitudes towards the Cape Verde Islands located northward of Fogo. This study will contribute to more realistically assess the scale of risks associated with these extremely rare but very high impact natural disasters. This work is supported by the EU project ASTARTE -Grant 603839, 7th FP (ENV.2013, 6.4-3), the EU project TSUMAPS-NEAM -Agreement Number: ECHO/SUB/2015/718568/PREV26, and the IF/01641/2015 MEGAWAVE - FCT project.

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Itinerancy of money

NASA Astrophysics Data System (ADS)

Yasutomi, Ayumu

2003-09-01

Previously, I studied [Physica D 82, 180-194 (1995)] the emergence and collapse of money in a computer simulation model. In this paper I will revisit the same topic, building a model in the same line. I discuss this problem from the viewpoint of chaotic itinerancy. Money is the most popular system for evading the difficulty of exchange under division of labor. It emerges autonomously from exchanges among selfish agents which behave as automata. And such emergent money collapses autonomously. I describe money as a structure in economic space, explaining its autonomous emergence and collapse as two phases of the same phenomenon. The key element in this phenomenon is the switch of the meaning of strategies. This is caused by the drastic change of environment caused by the emergence of a structure. This dynamics shares some aspects with chaotic itinerancy.

Prediction of seismic collapse risk of steel moment frame mid-rise structures by meta-heuristic algorithms

NASA Astrophysics Data System (ADS)

Jough, Fooad Karimi Ghaleh; Şensoy, Serhan

2016-12-01

Different performance levels may be obtained for sideway collapse evaluation of steel moment frames depending on the evaluation procedure used to handle uncertainties. In this article, the process of representing modelling uncertainties, record to record (RTR) variations and cognitive uncertainties for moment resisting steel frames of various heights is discussed in detail. RTR uncertainty is used by incremental dynamic analysis (IDA), modelling uncertainties are considered through backbone curves and hysteresis loops of component, and cognitive uncertainty is presented in three levels of material quality. IDA is used to evaluate RTR uncertainty based on strong ground motion records selected by the k-means algorithm, which is favoured over Monte Carlo selection due to its time saving appeal. Analytical equations of the Response Surface Method are obtained through IDA results by the Cuckoo algorithm, which predicts the mean and standard deviation of the collapse fragility curve. The Takagi-Sugeno-Kang model is used to represent material quality based on the response surface coefficients. Finally, collapse fragility curves with the various sources of uncertainties mentioned are derived through a large number of material quality values and meta variables inferred by the Takagi-Sugeno-Kang fuzzy model based on response surface method coefficients. It is concluded that a better risk management strategy in countries where material quality control is weak, is to account for cognitive uncertainties in fragility curves and the mean annual frequency.

Seasonal reproduction leads to population collapse and an Allee effect in a stage-structured consumer-resource biomass model when mortality rate increases

PubMed Central

de Roos, André M.

2017-01-01

Many populations collapse suddenly when reaching low densities even if they have abundant food conditions, a phenomenon known as an Allee effect. Such collapses can have disastrous consequences, for example, for loss of biodiversity. In this paper, we formulate a stage-structured consumer-resource biomass model in which adults only reproduce at the beginning of each growing season, and investigate the effect of an increasing stage-independent background mortality rate of the consumer. As the main difference with previously studied continuous-time models, seasonal reproduction can result in an Allee effect and consumer population collapses at high consumer mortality rate. However, unlike the mechanisms reported in the literature, in our model the Allee effect results from the time difference between the maturation of juveniles and the reproduction of adults. The timing of maturation plays a crucial role because it not only determines the body size of the individuals at maturation but also influences the duration of the period during which adults can invest in reproductive energy, which together determine the reproductive output at the end of the season. We suggest that there exists an optimal timing of maturation and that consumer persistence is promoted if individuals mature later in the season at a larger body size, rather than maturing early, despite high food availability supporting rapid growth. PMID:29088273

Airborne Astronomy Program

NASA Technical Reports Server (NTRS)

Butner, Harold M.

1999-01-01

Our understanding about the inter-relationship between the collapsing cloud envelope and the disk has been greatly altered. While the dominant star formation models invoke free fall collapse and r(sup -1.5) density profile, other star formation models are possible. These models invoke either different cloud starting conditions or the mediating effects of magnetic fields to alter the cloud geometry during collapse. To test these models, it is necessary to understand the envelope's physical structure. The discovery of disks, based on millimeter observations around young stellar objects, however makes a simple interpretation of the emission complicated. Depending on the wavelength, the disk or the envelope could dominate emission from a star. In addition, the discovery of planets around other stars has made understanding the disks in their own right quite important. Many star formation models predict disks should form naturally as the star is forming. In many cases, the information we derive about disk properties depends implicitly on the assumed envelope properties. How to understand the two components and their interaction with each other is a key problem of current star formation.

Characterizing ground motions that collapse steel special moment-resisting frames or make them unrepairable

USGS Publications Warehouse

Olsen, Anna H.; Heaton, Thomas H.; Hall, John F.

2015-01-01

This work applies 64,765 simulated seismic ground motions to four models each of 6- or 20-story, steel special moment-resisting frame buildings. We consider two vector intensity measures and categorize the building response as “collapsed,” “unrepairable,” or “repairable.” We then propose regression models to predict the building responses from the intensity measures. The best models for “collapse” or “unrepairable” use peak ground displacement and velocity as intensity measures, and the best models predicting peak interstory drift ratio, given that the frame model is “repairable,” use spectral acceleration and epsilon (ϵ) as intensity measures. The more flexible frame is always more likely than the stiffer frame to “collapse” or be “unrepairable.” A frame with fracture-prone welds is substantially more susceptible to “collapse” or “unrepairable” damage than the equivalent frame with sound welds. The 20-story frames with fracture-prone welds are more vulnerable to P-delta instability and have a much higher probability of collapse than do any of the 6-story frames.

Three-dimensional geophysical mapping of shallow water saturated altered rocks at Mount Baker, Washington: Implications for slope stability

USGS Publications Warehouse

Finn, Carol A.; Deszcz-Pan, Maria; Ball, Jessica L.; Bloss, Benjamin J.; Minsley, Burke J.

2018-01-01

Water-saturated hydrothermal alteration reduces the strength of volcanic edifices, increasing the potential for catastrophic sector collapses that can lead to far traveled and destructive debris flows. Intense hydrothermal alteration significantly lowers the resistivity and magnetization of volcanic rock and therefore hydrothermally altered rocks can be identified with helicopter electromagnetic and magnetic measurements. Geophysical models constrained by rock properties and geologic mapping show that intensely altered rock is restricted to two small (500 m diameter), >150 m thick regions around Sherman Crater and Dorr Fumarole Field at Mount Baker, Washington. This distribution of alteration contrasts with much thicker and widespread alteration encompassing the summits of Mounts Adams and Rainier prior to the 5600 year old Osceola collapse, which is most likely due to extreme erosion and the limited duration of summit magmatism at Mount Baker. In addition, the models suggest that the upper ~300 m of rock contains water which could help to lubricate potential debris flows. Slope stability modeling incorporating the geophysically modeled distribution of alteration and water indicates that the most likely and largest (~0.1 km3) collapses are from the east side of Sherman Crater. Alteration at Dorr Fumarole Field raises the collapse hazard there, but not significantly because of its lower slope angles. Geochemistry and analogs from other volcanoes suggest a model for the edifice hydrothermal system.

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Quantum walks in brain microtubules--a biomolecular basis for quantum cognition?

PubMed

Hameroff, Stuart

2014-01-01

Cognitive decisions are best described by quantum mathematics. Do quantum information devices operate in the brain? What would they look like? Fuss and Navarro () describe quantum lattice registers in which quantum superpositioned pathways interact (compute/integrate) as 'quantum walks' akin to Feynman's path integral in a lattice (e.g. the 'Feynman quantum chessboard'). Simultaneous alternate pathways eventually reduce (collapse), selecting one particular pathway in a cognitive decision, or choice. This paper describes how quantum walks in a Feynman chessboard are conceptually identical to 'topological qubits' in brain neuronal microtubules, as described in the Penrose-Hameroff 'Orch OR' theory of consciousness. Copyright © 2013 Cognitive Science Society, Inc.

The SPH consistency problem and some astrophysical applications

NASA Astrophysics Data System (ADS)

Klapp, Jaime; Sigalotti, Leonardo; Rendon, Otto; Gabbasov, Ruslan; Torres, Ayax

2017-11-01

We discuss the SPH kernel and particle consistency problem and demonstrate that SPH has a limiting second-order convergence rate. We also present a solution to the SPH consistency problem. We present examples of how SPH implementations that are not mathematically consistent may lead to erroneous results. The new formalism has been implemented into the Gadget 2 code, including an improved scheme for the artificial viscosity. We present results for the ``Standard Isothermal Test Case'' of gravitational collapse and fragmentation of protostellar molecular cores that produce a very different evolution than with the standard SPH theory. A further application of accretion onto a black hole is presented.

A family of models of partially relaxed stellar systems. II. Comparison with the products of collisionless collapse

NASA Astrophysics Data System (ADS)

Trenti, M.; Bertin, G.; van Albada, T. S.

2005-04-01

N-body simulations of collisionless collapse have offered important clues for the construction of realistic stellar dynamical models of elliptical galaxies. Understanding this idealized and relatively simple process, by which stellar systems can reach partially relaxed equilibrium configurations (characterized by isotropic central regions and radially anisotropic envelopes), is a prerequisite to more ambitious attempts at constructing physically justified models of elliptical galaxies in which the problem of galaxy formation is set in the generally accepted cosmological context of hierarchical clustering. In a previous paper we have discussed the dynamical properties of a family of models of partially relaxed stellar systems (the f(ν) models), designed to incorporate the qualitative properties of the products of collisionless collapse at small and at large radii. Here we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of such family of models and those of the products of collisionless collapse found in N-body simulations that we have run for the purpose. Surprisingly, the models thus identified are able to match the simulated density distributions over nine orders of magnitude and also to provide an excellent fit to the anisotropy profiles and a good representation of the overall structure in phase space. The end-products of the simulations and the best-fitting models turn out to be characterized by a level of pressure anisotropy close to the threshold for the onset of the radial-orbit instability. The conservation of Q, a third quantity that is argued to be approximately conserved in addition to total energy and total number of particles as a basis for the construction of the f(ν) family, is discussed and tested numerically.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Lung deformations and radiation-induced regional lung collapse in patients treated with stereotactic body radiation therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diot, Quentin, E-mail: quentin.diot@ucdenver.edu; Kavanagh, Brian; Vinogradskiy, Yevgeniy

2015-11-15

Purpose: To differentiate radiation-induced fibrosis from regional lung collapse outside of the high dose region in patients treated with stereotactic body radiation therapy (SBRT) for lung tumors. Methods: Lung deformation maps were computed from pre-treatment and post-treatment computed tomography (CT) scans using a point-to-point translation method. Fifty anatomical landmarks inside the lung (vessel or airway branches) were matched on planning and follow-up scans for the computation process. Two methods using the deformation maps were developed to differentiate regional lung collapse from fibrosis: vector field and Jacobian methods. A total of 40 planning and follow-ups CT scans were analyzed for 20more » lung SBRT patients. Results: Regional lung collapse was detected in 15 patients (75%) using the vector field method, in ten patients (50%) using the Jacobian method, and in 12 patients (60%) by radiologists. In terms of sensitivity and specificity the Jacobian method performed better. Only weak correlations were observed between the dose to the proximal airways and the occurrence of regional lung collapse. Conclusions: The authors presented and evaluated two novel methods using anatomical lung deformations to investigate lung collapse and fibrosis caused by SBRT treatment. Differentiation of these distinct physiological mechanisms beyond what is usually labeled “fibrosis” is necessary for accurate modeling of lung SBRT-induced injuries. With the help of better models, it becomes possible to expand the therapeutic benefits of SBRT to a larger population of lung patients with large or centrally located tumors that were previously considered ineligible.« less

Shock response of nanoporous Cu--A molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Zhao, Fengpeng

2015-06-01

Shock response of porous materials can be of crucial significance for shock physics and bears many practical applications in materials synthesis and engineering. Molecular dynamics simulations are carried out to investigate shock response of nanoporous metal materials, including elastic-plastic deformation, Hugoniot states, shock-induced melting, partial or complete void collapse, hotspot formation, nanojetting, and vaporization. A model nanoporous Cu with cylindrical voids and a high porosity under shocking is established to investigate such physical properties as velocity, temperature, density, stress and von Mises stress at different stages of compression and release. The elastic-plastic and overtaking shocks are observed at different shock strengths. A modified power-law P- α model is proposed to describe the Hugoniot states. The Grüneisen equation of state is validated. Shock-induced melting shows no clear signs of bulk premelting or superheating. Void collapse via plastic flow nucleated from voids, and the exact processes are shock strength dependent. With increasing shock strengths, void collapse transits from the ``geometrical'' mode (collapse of a void is dominated by crystallography and void geometry and can be different from that of one another) to ``hydrodynamic'' mode (collapse of a void is similar to one another). The collapse may be achieved predominantly by plastic flows along the {111} slip planes, by way of alternating compression and tension zones, by means of transverse flows, via forward and transverse flows, or through forward nano-jetting. The internal jetting induces pronounced shock front roughening, leading to internal hotspot formation and sizable high speed jets on atomically flat free surfaces. P. O. Box 919-401, Mianyang, 621900, Sichuan, PRC.

On the implementation of the spherical collapse model for dark energy models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pace, Francesco; Meyer, Sven; Bartelmann, Matthias, E-mail: francesco.pace@manchester.ac.uk, E-mail: sven.meyer@uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapsemore » model: the linear critical overdensity δ{sub c}, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ{sub c} for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.« less

Modelling of Coke Layer Collapse during Ore Charging in Ironmaking Blast Furnace by DEM

NASA Astrophysics Data System (ADS)

Narita, Yoichi; Mio, Hiroshi; Orimoto, Takashi; Nomura, Seiji

2017-06-01

A technical issue in an ironmaking blast furnace operation is to realize the optimum layer thickness and the radial distribution of burden (ore and coke) to enhance its efficiency and productivity. When ore particles are charged onto the already-embedded coke layer, the coke layer-collapse phenomenon occurs. The coke layer-collapse phenomenon has a significant effect on the distribution of ore and coke layer thickness in the radial direction. In this paper, the mechanical properties of coke packed bed under ore charging were investigated by the impact-loading test and the large-scale direct shear test. Experimental results show that the coke particle is broken by the impact force of ore charging, and the particle breakage leads to weaken of coke-layer strength. The expression of contact force for coke in Discrete Element Method (DEM) was modified based on the measured data, and it followed by the 1/3-scaled experiment on coke's collapse phenomena. Comparing a simulation by modified model to the 1/3-scaled experiment, they agreed well in the burden distribution.

Application of 3D Laser Scanner to Forensic Engineering.

PubMed

Park, Chan-Seong; Jeon, Hong-Pil; Choi, Kwang-Soo; Kim, Jin-Pyo; Park, Nam-Kyu

2018-05-01

In the case of building collapses and overturned structures, a three-dimensional (3D) collapse or overturn model is required to reconstruct the accident. As construction sites become increasingly complex and large, 3D laser scanning is sometimes the best tool to accurately document and store the site conditions. This case report presents one case of a structure collapse and one case of an overturned crane reconstructed by a 3D laser scanner. In the case of structural collapse of a prefabricated shoring system, a 3D model reconstructed all the members successfully, a task that is nearly impossible using a scale such as a tape measure. The reconstructed prefabricated shoring system was verified through a structural analysis through comparison with the construction drawings to investigate faults in construction. In the case of the overturned crane, the jib angle and other major dimensions were successfully acquired through 3D laser scanning and used to estimate the working radius. As a result, the propriety of the working radius with the given lifting load was successfully determined. © 2017 American Academy of Forensic Sciences.

Reversible Leaf Xylem Collapse: A Potential “Circuit Breaker” against Cavitation1[OPEN

PubMed Central

Zhang, Yong-Jiang; Rockwell, Fulton E.; Graham, Adam C.; Alexander, Teressa; Holbrook, N. Michele

2016-01-01

We report a novel form of xylem dysfunction in angiosperms: reversible collapse of the xylem conduits of the smallest vein orders that demarcate and intrusively irrigate the areoles of red oak (Quercus rubra) leaves. Cryo-scanning electron microscopy revealed gradual increases in collapse from approximately −2 MPa down to −3 MPa, saturating thereafter (to −4 MPa). Over this range, cavitation remained negligible in these veins. Imaging of rehydration experiments showed spatially variable recovery from collapse within 20 s and complete recovery after 2 min. More broadly, the patterns of deformation induced by desiccation in both mesophyll and xylem suggest that cell wall collapse is unlikely to depend solely on individual wall properties, as mechanical constraints imposed by neighbors appear to be important. From the perspective of equilibrium leaf water potentials, petioles, whose vessels extend into the major veins, showed a vulnerability to cavitation that overlapped in the water potential domain with both minor vein collapse and buckling (turgor loss) of the living cells. However, models of transpiration transients showed that minor vein collapse and mesophyll capacitance could effectively buffer major veins from cavitation over time scales relevant to the rectification of stomatal wrong-way responses. We suggest that, for angiosperms, whose subsidiary cells give up large volumes to allow large stomatal apertures at the cost of potentially large wrong-way responses, vein collapse could make an important contribution to these plants’ ability to transpire near the brink of cavitation-inducing water potentials. PMID:27733514

The Interplay of Opacities and Rotation in Promoting the Explosion of Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Vartanyan, David; Burrows, Adam; Radice, David

2018-01-01

For over five decades, the mechanism of explosion in core-collapse supernovae has been a central unsolved problem in astrophysics, challenging both our computational capabilities and our understanding of relevant physics. Current simulations often produce explosions, but they are at times underenergetic. The neutrino mechanism, wherein a fraction of emitted neutrinos is absorbed in the mantle of the star to reignite the stalled shock, remains the dominant model for reviving explosions in massive stars undergoing core collapse. We present here a diverse suite of 2D axisymmetric simulations produced by FORNAX, a highly parallelizable multidimensional supernova simulation code. We explore the effects of various corrections, including the many-body correction, to neutrino-matter opacities and the possible role of rotation in promoting explosion amongst various core-collapse progenitors.

Interacting partially directed self-avoiding walk: a probabilistic perspective

NASA Astrophysics Data System (ADS)

Carmona, Philippe; Nguyen, Gia Bao; Pétrélis, Nicolas; Torri, Niccolò

2018-04-01

We review some recent results obtained in the framework of the 2D interacting self-avoiding walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the interacting partially directed self-avoiding walk (IPDSAW), a model introduced in Zwanzig and Lauritzen (1968 J. Chem. Phys. 48 3351) to decrease the mathematical complexity of ISAW. In the first part of the paper, we discuss how a new probabilistic approach based on a random walk representation (see Nguyen and Pétrélis (2013 J. Stat. Phys. 151 1099–120)) allowed for a sharp determination of the asymptotics of the free energy close to criticality (see Carmona et al (2016 Ann. Probab. 44 3234–90)). Some scaling limits of IPDSAW were conjectured in the physics literature (see e.g. Brak et al (1993 Phys. Rev. E 48 2386–96)). We discuss here the fact that all limits are now proven rigorously, i.e. for the extended regime in Carmona and Pétrélis (2016 Electron. J. Probab. 21 1–52), for the collapsed regime in Carmona et al (2016 Ann. Probab. 44 3234–90) and at criticality in Carmona and Pétrélis (2017b arxiv:1709.06448). The second part of the paper starts with the description of four open questions related to physically relevant extensions of IPDSAW. Among such extensions is the interacting prudent self-avoiding walk (IPSAW) whose configurations are those of the 2D prudent walk. We discuss the main results obtained in Pétrélis and Torri (2016 Ann. Inst. Henri Poincaré D) about IPSAW and in particular the fact that its collapse transition is proven to exist rigorously.

Influence of West Antarctic Ice Sheet collapse on Antarctic surface climate

NASA Astrophysics Data System (ADS)

Steig, Eric J.; Huybers, Kathleen; Singh, Hansi A.; Steiger, Nathan J.; Ding, Qinghua; Frierson, Dargan M. W.; Popp, Trevor; White, James W. C.

2015-06-01

Climate model simulations are used to examine the impact of a collapse of the West Antarctic Ice Sheet (WAIS) on the surface climate of Antarctica. The lowered topography following WAIS collapse produces anomalous cyclonic circulation with increased flow of warm, maritime air toward the South Pole and cold-air advection from the East Antarctic plateau toward the Ross Sea and Marie Byrd Land, West Antarctica. Relative to the background climate, areas in East Antarctica that are adjacent to the WAIS warm, while substantial cooling (several °C) occurs over parts of West Antarctica. Anomalously low isotope-paleotemperature values at Mount Moulton, West Antarctica, compared with ice core records in East Antarctica, are consistent with collapse of the WAIS during the last interglacial period, Marine Isotope Stage 5e. More definitive evidence might be recoverable from an ice core record at Hercules Dome, East Antarctica, which would experience significant warming and positive oxygen isotope anomalies if the WAIS collapsed.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity.

PubMed

Biasi, Anxo F; Mas, Javier; Paredes, Angel

2017-03-01

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

Cerium; crystal structure and position in the periodic table.

PubMed

Johansson, Börje; Luo, Wei; Li, Sa; Ahuja, Rajeev

2014-09-17

The properties of the cerium metal have intrigued physicists and chemists for many decades. In particular a lot of attention has been directed towards its high pressure behavior, where an isostructural volume collapse (γ phase → α phase) has been observed. Two main models of the electronic aspect of this transformation have been proposed; one where the 4f electron undergoes a change from being localized into an itinerant metallic state, and one where the focus is on the interaction between the 4f electron and the conduction electrons, often referred to as the Kondo volume collapse model. However, over the years it has been repeatedly questioned whether the cerium collapse really is isostructural. Most recently, detailed experiments have been able to remove this worrisome uncertainty. Therefore the isostructural aspect of the α-γ transition has now to be seriously addressed in the theoretical modeling, something which has been very much neglected. A study of this fundamental characteristic of the cerium volume collapse is made in present paper and we show that the localized [rlhar2 ] delocalized 4f electron picture provides an adequate description of this unique behavior. This agreement makes it possible to suggest that an appropriate crossroad position for cerium in The Periodic Table.

Cerium; Crystal Structure and Position in The Periodic Table

PubMed Central

Johansson, Börje; Luo, Wei; Li, Sa; Ahuja, Rajeev

2014-01-01

The properties of the cerium metal have intrigued physicists and chemists for many decades. In particular a lot of attention has been directed towards its high pressure behavior, where an isostructural volume collapse (γ phase → α phase) has been observed. Two main models of the electronic aspect of this transformation have been proposed; one where the 4f electron undergoes a change from being localized into an itinerant metallic state, and one where the focus is on the interaction between the 4f electron and the conduction electrons, often referred to as the Kondo volume collapse model. However, over the years it has been repeatedly questioned whether the cerium collapse really is isostructural. Most recently, detailed experiments have been able to remove this worrisome uncertainty. Therefore the isostructural aspect of the α-γ transition has now to be seriously addressed in the theoretical modeling, something which has been very much neglected. A study of this fundamental characteristic of the cerium volume collapse is made in present paper and we show that the localized ⇌ delocalized 4f electron picture provides an adequate description of this unique behavior. This agreement makes it possible to suggest that an appropriate crossroad position for cerium in The Periodic Table. PMID:25227991

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Global radiative adjustment after a collapse of the Atlantic meridional overturning circulation

NASA Astrophysics Data System (ADS)

Drijfhout, Sybren S.

2015-10-01

The transient climate response to a collapse of the Atlantic meridional overturning circulation (AMOC) is analysed from the difference between two ensembles of climate model simulations with ECHAM5/MPI-OM, one with hosing and the other without hosing. The primary effect of the collapse is to redistribute heat over the two hemispheres. However, Northern Hemisphere sea ice increase in response to the AMOC collapse induces a hemisphere-wide cooling, amplified by atmospheric feedbacks, in particular water vapour. The Southern Hemisphere warming is governed by slower processes. After 25 years the global cooling peaks. Thereafter, the response is characterised by a gradual readjustment of global mean temperature. During the AMOC collapse a downward radiation anomaly arises at the top of the atmosphere (TOA), heating the earth's surface. The net downward radiation anomaly at TOA arises from reduced longwave emission by the atmosphere, overcompensating the increased net upward anomalies in shortwave and longwave radiation at the surface. This radiation anomaly is associated with net ocean heat uptake: cooling of the overlying atmosphere results from reduced ocean heat release through the increase of sea-ice cover in the North Atlantic. The change in energy flow arises from the reduction in latent and sensible heat flux, which dominate the surface radiation budget. Similar experiments with a climate model of intermediate complexity reveal a stronger shortwave response that acts to reduce the net downward radiation anomaly at TOA. The net shortwave and longwave radiation anomalies at TOA always decrease during the first 100 years after the AMOC collapse, but in the intermediate complexity model this is associated with a sign change after 90 years when the net radiation anomaly at TOA becomes upward, accompanied by net ocean heat loss. After several hundred years the longwave and shortwave anomalies increase again, while the net residual at TOA remains small. This radiative adjustment is associated with the transition to a colder climate.

Risk factor analysis for predicting vertebral body re-collapse after posterior instrumented fusion in thoracolumbar burst fracture.

PubMed

Jang, Hae-Dong; Bang, Chungwon; Lee, Jae Chul; Soh, Jae-Wan; Choi, Sung-Woo; Cho, Hyeung-Kyu; Shin, Byung-Joon

2018-02-01

In the posterior instrumented fusion surgery for thoracolumbar (T-L) burst fracture, early postoperative re-collapse of well-reduced vertebral body fracture could induce critical complications such as correction loss, posttraumatic kyphosis, and metal failure, often leading to revision surgery. Furthermore, re-collapse is quite difficult to predict because of the variety of risk factors, and no widely accepted accurate prediction systems exist. Although load-sharing classification has been known to help to decide the need for additional anterior column support, this radiographic scoring system has several critical limitations. (1) To evaluate risk factors and predictors for postoperative re-collapse in T-L burst fractures. (2) Through the decision-making model, we aimed to predict re-collapse and prevent unnecessary additional anterior spinal surgery. Retrospective comparative study. Two-hundred and eight (104 men and 104 women) consecutive patients with T-L burst fracture who underwent posterior instrumented fusion were reviewed retrospectively. Burst fractures caused by high-energy trauma (fall from a height and motor vehicle accident) with a minimum 1-year follow-up were included. The average age at the time of surgery was 45.9 years (range, 15-79). With respect to the involved spinal level, 95 cases (45.6%) involved L1, 51 involved T12, 54 involved L2, and 8 involved T11. Mean fixation segments were 3.5 (range, 2-5). Pedicle screw instrumentation including fractured vertebra had been performed in 129 patients (62.3%). Clinical data using self-report measures (visual analog scale score), radiographic measurements (plain radiograph, computed tomography, and magnetic resonance image), and functional measures using the Oswestry Disability Index were evaluated. Body height loss of fractured vertebra, body wedge angle, and Cobb angle were measured in serial plain radiographs. We assigned patients to the re-collapse group if their body height loss progressed greater than 20% at any follow-up time compared with immediate postoperative body height loss; we assigned the remaining patients to the well-maintained group. The chi-square test and t test of SPSS were used for comparison of differences between two groups and multiple logistic regression analysis for risk factor evaluation. Through the decision tree analysis of statistical package R, a decision-making model was composed, and a cutoff value of revealed risk factors and re-collapse rate of each subgroup were identified. The present study wassupported by the University College of Medicine Research Fund (university to which authors belong). There was no external funding source for this study. The authors have no conflict of interest to declare. Re-collapse occurred in 31 of 208 patients (14.9%). In this group, age, the proportion of male gender, preoperative height loss, and preoperative wedge angle were significantly greater than the well-maintained group. Multivariable logistic regression analysis identified two independent risk factors: age (adjusted odds ratio 1.084, p=.002) and body height loss (adjusted odds ratio 1.065, p=.003). According to the decision-making tree, age (>43 years) was the most discriminating variable, andpreoperative body height loss (>54%) was the second. In this model, the re-collapse rate was zero in ages less than 43 years, and among those remaining, nearly 80% patients with greater than 54% of body height loss belonged to the re-collapse group. The independent predictors of re-collapse after posterior instrumented fusion for T-L burst fracture were the age at operation (>43 years old) and preoperative body height loss (>54%). Careful assessment using our decision-making model could help to predict re-collapse and prevent unnecessary additional spinal surgery for anterior column support, especially in young patients. Copyright © 2017 Elsevier Inc. All rights reserved.

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

Collapse dynamics of ultrasound contrast agent microbubbles

NASA Astrophysics Data System (ADS)

King, Daniel Alan

Ultrasound contrast agents (UCAs) are micron-sized gas bubbles encapsulated with thin shells on the order of nanometers thick. The damping effects of these viscoelastic coatings are widely known to significantly alter the bubble dynamics for linear and low-amplitude behavior; however, their effects on strongly nonlinear and destruction responses are much less studied. This dissertation examines the behaviors of single collapsing shelled microbubbles using experimental and theoretical methods. The study of their dynamics is particularly relevant for emerging experimental uses of UCAs which seek to leverage localized mechanical forces to create or avoid specialized biomedical effects. The central component in this work is the study of postexcitation rebound and collapse, observed acoustically to identify shell rupture and transient inertial cavitation of single UCA microbubbles. This time-domain analysis of the acoustic response provides a unique method for characterization of UCA destruction dynamics. The research contains a systematic documentation of single bubble postexcitation collapse through experimental measurement with the double passive cavitation detection (PCD) system at frequencies ranging from 0.9 to 7.1 MHz and peak rarefactional pressure amplitudes (PRPA) ranging from 230 kPa to 6.37 MPa. The double PCD setup is shown to improve the quality of collected data over previous setups by allowing symmetric responses from a localized confocal region to be identified. Postexcitation signal percentages are shown to generally follow trends consistent with other similar cavitation metrics such as inertial cavitation, with greater destruction observed at both increased PRPA and lower frequency over the tested ranges. Two different types of commercially available UCAs are characterized and found to have very different collapse thresholds; lipid-shelled Definity exhibits greater postexcitation at lower PRPAs than albumin-shelled Optison. Furthermore, by altering the size distributions of these UCAs, it is shown that the shell material has a large influence on the occurrence of postexcitation rebound at all tested frequencies while moderate alteration of the size distribution may only play a significant role within certain frequency ranges. Finally, the conditions which generate the experimental postexcitation signal are examined theoretically using several forms of single bubble models. Evidence is provided for the usefulness of modeling this large amplitude UCA behavior with a size-varying surface tension as described in the Marmottant model; better agreement for lipid-shelled Definity UCAs is obtained by considering the dynamic response with a rupturing shell rather than either a non-rupturing or nonexistent shell. Moreover, the modeling indicates that maximum radial expansion from the initial UCA size is a suitable metric to predict postexcitation collapse, and that both shell rupture and inertial cavitation are necessary conditions to generate this behavior. Postexcitation analysis is found to be a beneficial characterization metric for studying the destruction behaviors of single UCAs when measured with the double PCD setup. This work provides quantitative documentation of UCA collapse, exploration into UCA material properties which affect this collapse, and comparison of existing single bubble models with experimentally measured postexcitation signals.

Comparing models of Red Knot population dynamics

USGS Publications Warehouse

McGowan, Conor P.

2015-01-01

Predictive population modeling contributes to our basic scientific understanding of population dynamics, but can also inform management decisions by evaluating alternative actions in virtual environments. Quantitative models mathematically reflect scientific hypotheses about how a system functions. In Delaware Bay, mid-Atlantic Coast, USA, to more effectively manage horseshoe crab (Limulus polyphemus) harvests and protect Red Knot (Calidris canutus rufa) populations, models are used to compare harvest actions and predict the impacts on crab and knot populations. Management has been chiefly driven by the core hypothesis that horseshoe crab egg abundance governs the survival and reproduction of migrating Red Knots that stopover in the Bay during spring migration. However, recently, hypotheses proposing that knot dynamics are governed by cyclical lemming dynamics garnered some support in data analyses. In this paper, I present alternative models of Red Knot population dynamics to reflect alternative hypotheses. Using 2 models with different lemming population cycle lengths and 2 models with different horseshoe crab effects, I project the knot population into the future under environmental stochasticity and parametric uncertainty with each model. I then compare each model's predictions to 10 yr of population monitoring from Delaware Bay. Using Bayes' theorem and model weight updating, models can accrue weight or support for one or another hypothesis of population dynamics. With 4 models of Red Knot population dynamics and only 10 yr of data, no hypothesis clearly predicted population count data better than another. The collapsed lemming cycle model performed best, accruing ~35% of the model weight, followed closely by the horseshoe crab egg abundance model, which accrued ~30% of the weight. The models that predicted no decline or stable populations (i.e. the 4-yr lemming cycle model and the weak horseshoe crab effect model) were the most weakly supported.

Gravitational collapse of colloidal gels: Origins of the tipping point

NASA Astrophysics Data System (ADS)

Padmanabhan, Poornima; Zia, Roseanna

2016-11-01

Reversible colloidal gels are soft viscoelastic solids in which durable but reversible bonds permit on-demand transition from solidlike to liquidlike behavior; these O(kT) bonds also lead to ongoing coarsening and age stiffening, making their rheology inherently time dependent. To wit, such gels may remain stable for an extended time, but then suddenly collapse, sedimenting to the bottom of the container (or creaming to the top) and eliminating any intended functionality of the material. Although this phenomenon has been studied extensively in the experimental literature, the microscopic mechanism underlying the collapse is not well understood. Effects of gel age, interparticle attraction strength, and wall effects all have been shown to affect collapse behavior, but the microstructural transformations underlying the 'tipping point' remain murky. To study this behavior, we conduct large-scale dynamic simulation to model the structural and rheological evolution of colloidal gels subjected to various gravitational stresses, examining the detailed micromechanics in three temporal regimes: slow sedimentation prior to collapse; the tipping point leading to the onset of rapid collapse; and the subsequent compaction of the material as it approaches its final bed height. Acknowledgment for funding and support from the Office of Naval Research; the National Science Foundation; and NSF XSEDE.

Numerical studies of cavitation erosion on an elastic-plastic material caused by shock-induced bubble collapse

NASA Astrophysics Data System (ADS)

Turangan, C. K.; Ball, G. J.; Jamaluddin, A. R.; Leighton, T. G.

2017-09-01

We present a study of shock-induced collapse of single bubbles near/attached to an elastic-plastic solid using the free-Lagrange method, which forms the latest part of our shock-induced collapse studies. We simulated the collapse of 40 μm radius single bubbles near/attached to rigid and aluminium walls by a 60 MPa lithotripter shock for various scenarios based on bubble-wall separations, and the collapse of a 255 μm radius bubble attached to aluminium foil with a 65 MPa lithotripter shock. The coupling of the multi-phases, compressibility, axisymmetric geometry and elastic-plastic material model within a single solver has enabled us to examine the impingement of high-speed liquid jets from the shock-induced collapsing bubbles, which imposes an extreme compression in the aluminium that leads to pitting and plastic deformation. For certain scenarios, instead of the high-speed jet, a radially inwards flow along the aluminium surface contracts the bubble to produce a `mushroom shape'. This work provides methods for quantifying which parameters (e.g. bubble sizes and separations from the solid) might promote or inhibit erosion on solid surfaces.

High energy radiation precursors to the collapse of black holes binaries based on resonating plasma modes

NASA Astrophysics Data System (ADS)

Coppi, B.

2018-05-01

The presence of well organized plasma structures around binary systems of collapsed objects [1,2] (black holes and neutron stars) is proposed in which processes can develop [3] leading to high energy electromagnetic radiation emission immediately before the binary collapse. The formulated theoretical model supporting this argument shows that resonating plasma collective modes can be excited in the relevant magnetized plasma structure. Accordingly, the collapse of the binary approaches, with the loss of angular momentum by emission of gravitational waves [2], the resonance conditions with vertically standing plasma density and magnetic field oscillations are met. Then, secondary plasma modes propagating along the magnetic field are envisioned to be sustained with mode-particle interactions producing the particle populations responsible for the observable electromagnetic radiation emission. Weak evidence for a precursor to the binary collapse reported in Ref. [2], has been offered by the Agile X-γ-ray observatory [4] while the August 17 (2017) event, identified first by the LIGO-Virgo detection of gravitational waves and featuring the inferred collapse of a neutron star binary, improves the evidence of such a precursor. A new set of experimental observations is needed to reassess the presented theory.

On the Maximum Mass of Differentially Rotating Neutron Stars

NASA Astrophysics Data System (ADS)

Baumgarte, Thomas W.; Shapiro, Stuart L.; Shibata, Masaru

2000-01-01

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations that are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Modelling cavitation erosion using fluid–material interaction simulations

PubMed Central

Chahine, Georges L.; Hsiao, Chao-Tsung

2015-01-01

Material deformation and pitting from cavitation bubble collapse is investigated using fluid and material dynamics and their interaction. In the fluid, a novel hybrid approach, which links a boundary element method and a compressible finite difference method, is used to capture non-spherical bubble dynamics and resulting liquid pressures efficiently and accurately. The bubble dynamics is intimately coupled with a finite-element structure model to enable fluid/structure interaction simulations. Bubble collapse loads the material with high impulsive pressures, which result from shock waves and bubble re-entrant jet direct impact on the material surface. The shock wave loading can be from the re-entrant jet impact on the opposite side of the bubble, the fast primary collapse of the bubble, and/or the collapse of the remaining bubble ring. This produces high stress waves, which propagate inside the material, cause deformation, and eventually failure. A permanent deformation or pit is formed when the local equivalent stresses exceed the material yield stress. The pressure loading depends on bubble dynamics parameters such as the size of the bubble at its maximum volume, the bubble standoff distance from the material wall and the pressure driving the bubble collapse. The effects of standoff and material type on the pressure loading and resulting pit formation are highlighted and the effects of bubble interaction on pressure loading and material deformation are preliminarily discussed. PMID:26442140

The characteristic black hole mass resulting from direct collapse in the early Universe

NASA Astrophysics Data System (ADS)

Latif, M. A.; Schleicher, D. R. G.; Schmidt, W.; Niemeyer, J. C.

2013-12-01

Black holes of a billion solar masses are observed in the infant Universe a few hundred million years after the big bang. The direct collapse of protogalactic gas clouds in primordial haloes with Tvir ≥ 104 K provides the most promising way to assemble massive black holes. In this study, we aim to determine the characteristic mass scale of seed black holes and the time evolution of the accretion rates resulting from the direct collapse model. We explore the formation of supermassive black holes via cosmological large eddy simulations (LES) by employing sink particles and following their evolution for 20 000 yr after the formation of the first sink. As the resulting protostars were shown to have cool atmospheres in the presence of strong accretion, we assume here that UV feedback is negligible during this calculation. We confirm this result in a comparison run without sinks. Our findings show that black hole seeds with characteristic mass of 105 M⊙ are formed in the presence of strong Lyman-Werner flux which leads to an isothermal collapse. The characteristic mass is about two times higher in LES compared to the implicit large eddy simulations. The accretion rates increase with time and reach a maximum value of 10 M⊙ yr-1 after 104 yr. Our results show that the direct collapse model is clearly feasible as it provides the expected mass of the seed black holes.

The direct collapse of a massive black hole seed under the influence of an anisotropic Lyman-Werner source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Regan, John A.; Johansson, Peter H.; Wise, John H., E-mail: john.regan@helsinki.fi

2014-11-10

The direct collapse model of supermassive black hole seed formation requires that the gas cools predominantly via atomic hydrogen. To this end we simulate the effect of an anisotropic radiation source on the collapse of a halo at high redshift. The radiation source is placed at a distance of 3 kpc (physical) from the collapsing object and is set to emit monochromatically in the center of the Lyman-Werner (LW) band. The LW radiation emitted from the high redshift source is followed self-consistently using ray tracing techniques. Due to self-shielding, a small amount of H{sub 2} is able to form atmore » the very center of the collapsing halo even under very strong LW radiation. Furthermore, we find that a radiation source, emitting >10{sup 54} (∼ 10{sup 3} J{sub 21}) photons s{sup –1}, is required to cause the collapse of a clump of M ∼ 10{sup 5} M {sub ☉}. The resulting accretion rate onto the collapsing object is ∼0.25 M {sub ☉} yr{sup –1}. Our results display significant differences, compared to the isotropic radiation field case, in terms of the H{sub 2} fraction at an equivalent radius. These differences will significantly affect the dynamics of the collapse. With the inclusion of a strong anisotropic radiation source, the final mass of the collapsing object is found to be M ∼ 10{sup 5} M {sub ☉}. This is consistent with predictions for the formation of a supermassive star or quasi-star leading to a supermassive black hole.« less

Cavitation erosion prediction based on analysis of flow dynamics and impact load spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mihatsch, Michael S., E-mail: michael.mihatsch@aer.mw.tum.de; Schmidt, Steffen J.; Adams, Nikolaus A.

2015-10-15

Cavitation erosion is the consequence of repeated collapse-induced high pressure-loads on a material surface. The present paper assesses the prediction of impact load spectra of cavitating flows, i.e., the rate and intensity distribution of collapse events based on a detailed analysis of flow dynamics. Data are obtained from a numerical simulation which employs a density-based finite volume method, taking into account the compressibility of both phases, and resolves collapse-induced pressure waves. To determine the spectrum of collapse events in the fluid domain, we detect and quantify the collapse of isolated vapor structures. As reference configuration we consider the expansion ofmore » a liquid into a radially divergent gap which exhibits unsteady sheet and cloud cavitation. Analysis of simulation data shows that global cavitation dynamics and dominant flow events are well resolved, even though the spatial resolution is too coarse to resolve individual vapor bubbles. The inviscid flow model recovers increasingly fine-scale vapor structures and collapses with increasing resolution. We demonstrate that frequency and intensity of these collapse events scale with grid resolution. Scaling laws based on two reference lengths are introduced for this purpose. We show that upon applying these laws impact load spectra recorded on experimental and numerical pressure sensors agree with each other. Furthermore, correlation between experimental pitting rates and collapse-event rates is found. Locations of high maximum wall pressures and high densities of collapse events near walls obtained numerically agree well with areas of erosion damage in the experiment. The investigation shows that impact load spectra of cavitating flows can be inferred from flow data that captures the main vapor structures and wave dynamics without the need for resolving all flow scales.« less

Finite-Difference Time-Domain Analysis of Tapered Photonic Crystal Fiber

NASA Astrophysics Data System (ADS)

Ali, M. I. Md; Sanusidin, S. N.; Yusof, M. H. M.

2018-03-01

This paper brief about the simulation of tapered photonic crystal fiber (PCF) LMA-8 single-mode type based on correlation of scattering pattern at wavelength of 1.55 μm, analyzation of transmission spectrum at wavelength over the range of 1.0 until 2.5 μm and correlation of transmission spectrum with the refractive index change in photonic crystal holes with respect to taper size of 0.1 until 1.0 using Optiwave simulation software. The main objective is to simulate using Finite-Difference Time-Domain (FDTD) technique of tapered LMA-8 PCF and for sensing application by improving the capabilities of PCF without collapsing the crystal holes. The types of FDTD techniques used are scattering pattern and transverse transmission and principal component analysis (PCA) used as a mathematical tool to model the data obtained by MathCad software. The simulation results showed that there is no obvious correlation of scattering pattern at a wavelength of 1.55 μm, a correlation obtained between taper sizes with a transverse transmission and there is a parabolic relationship between the refractive index changes inside the crystal structure.

A Delayed Choice Quantum Eraser Explained by the Transactional Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Fearn, H.

2016-01-01

This paper explains the delayed choice quantum eraser of Kim et al. (A delayed choice quantum eraser, 1999) in terms of the transactional interpretation (TI) of quantum mechanics by Cramer (Rev Mod Phys 58:647, 1986, The quantum handshake, entanglement, nonlocality and transactions, 1986). It is kept deliberately mathematically simple to help explain the transactional technique. The emphasis is on a clear understanding of how the instantaneous "collapse" of the wave function due to a measurement at a specific time and place may be reinterpreted as a relativistically well-defined collapse over the entire path of the photon and over the entire transit time from slit to detector. This is made possible by the use of a retarded offer wave, which is thought to travel from the slits (or rather the small region within the parametric crystal where down-conversion takes place) to the detector and an advanced counter wave traveling backward in time from the detector to the slits. The point here is to make clear how simple the transactional picture is and how much more intuitive the collapse of the wave function becomes if viewed in this way. Also, any confusion about possible retro-causal signaling is put to rest. A delayed choice quantum eraser does not require any sort of backward in time communication. This paper makes the point that it is preferable to use the TI over the usual Copenhagen interpretation for a more intuitive understanding of the quantum eraser delayed choice experiment. Both methods give exactly the same end results and can be used interchangeably.

Assessment of the Damage Tolerance of Postbuckled Hat-Stiffened Panels Using Single-Stringer Specimens

NASA Technical Reports Server (NTRS)

Bisagni, Chiara; Vescovini, Riccardo; Davila, Carlos G.

2010-01-01

A procedure is proposed for the assessment of the damage tolerance and collapse of stiffened composite panels using a single-stringer compression specimen. The dimensions of the specimen are determined such that the specimen s nonlinear response and collapse are representative of an equivalent multi-stringer panel in compression. Experimental tests are conducted on specimens with and without an embedded delamination. A shell-based finite element model with intralaminar and interlaminar damage capabilities is developed to predict the postbuckling response as well as the damage evolution from initiation to collapse.

Understanding Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Hix, W. R.; Lentz, E. J.; Baird, M.; Messer, O. E. B.; Mezzacappa, A.; Lee, C.-T.; Bruenn, S. W.; Blondin, J. M.; Marronetti, P.

2010-03-01

Our understanding of core-collapse supernovae continues to improve as better microphysics is included in increasingly realistic neutrino-radiationhydrodynamic simulations. Recent multi-dimensional models with spectral neutrino transport, which slowly develop successful explosions for a range of progenitors between 12 and 25 solar mass, have motivated changes in our understanding of the neutrino reheating mechanism. In a similar fashion, improvements in nuclear physics, most notably explorations of weak interactions on nuclei and the nuclear equation of state, continue to refine our understanding of how supernovae explode. Recent progresses on both the macroscopic and microscopic effects that affect core-collapse supernovae are discussed.

Lifetime of Bubble Rafts: Cooperativity and Avalanches

NASA Astrophysics Data System (ADS)

Ritacco, Hernán; Kiefer, Flavien; Langevin, Dominique

2007-06-01

We have studied the collapse of pseudo-bi-dimensional foams. These foams are made of uniformly sized soap bubbles packed in an hexagonal lattice sitting at the top of a liquid surface. The collapse process follows the sequence: (1) rupture of a first bubble, driven by thermal fluctuations and (2) a cascade of bursting bubbles. We present a simple numerical model which captures the main characteristics of the dynamics of foam collapse. We show that in a certain range of viscosities of the foaming solutions, the size distribution of the avalanches follows power laws as in self-organized criticality processes.

Lifetime of bubble rafts: cooperativity and avalanches.

PubMed

Ritacco, Hernán; Kiefer, Flavien; Langevin, Dominique

2007-06-15

We have studied the collapse of pseudo-bi-dimensional foams. These foams are made of uniformly sized soap bubbles packed in an hexagonal lattice sitting at the top of a liquid surface. The collapse process follows the sequence: (1) rupture of a first bubble, driven by thermal fluctuations and (2) a cascade of bursting bubbles. We present a simple numerical model which captures the main characteristics of the dynamics of foam collapse. We show that in a certain range of viscosities of the foaming solutions, the size distribution of the avalanches follows power laws as in self-organized criticality processes.

Moment tensor analysis of the 3 September 2017 DPRK announced nuclear explosion and collapse aftershock

NASA Astrophysics Data System (ADS)

Ichinose, G. A.; Ford, S. R.; Chiang, A.; Walter, W. R.; Dreger, D. S.

2017-12-01

The Democratic People's Republic of Korea (DPRK) conducted its sixth announced nuclear test on 3 September 2017, 03:30:00 with a magnitude of 6.1 (IDC mb). At 03:38:27, there was an aftershock of magnitude 4.1 (IDC mb). Moment tensor analysis using regional long-period surface waves was performed to identify the source type of these two events. The first event was an explosive isotropic source with total seismic moment magnitude of Mw 5.34 (Mo=1.16e+17 Nm) with strong 66% isotropic component (eigenvalues: 1.30e+17, 0.75e+17, 0.44e+17 Nm). The second event was a closing crack source with an Mw 4.64 (Mo=1.04e+17 Nm) also with a strong 68% isotropic component (eigenvalues: -4.82e+16, -5.33e+16, -10.93e+16 Nm). We used the same stations within 360-1140 km for inversion of both events (stations: IC.MDJ, IC.BJT, IC.HIA) and predict the long-period displacements at KG.TJN and IU.INCN. We used a 1-D velocity model appropriate for active tectonic regions and band pass the data between periods of 20 and 100 sec. Waveform time-shifts were incorporated from previous event-station pairs to account for velocity model inadequacies. Both DPRK events source-types plot within the population of other NNSS nuclear and western US collapse events (Ford et al., 2009) on the fundamental lune (Tape and Tape, 2012). The DPRK collapse event is similar to the hole collapse 0h21m26s after the 5 September 1982 Atrisco shot at NNSS (Springer et al., 2002; DOE NV-209). The DPRK collapse could be explained by a complete or partial apical cavity collapse. The estimated collapse volume is 122000-277000 m3 and crack radius is 30-40 m given the seismic moment, elastic moduli for granite and a closing crack model (Mueller, 2001). In comparison to Denny and Johnson (1994) cavity-yield scaling in granite, the cavity radius ranges from 40 to 60 m given an explosion yield range of 140-400 kT. This collapse event is noteworthy because large aftershocks are rare in nuclear testing and even more rare are collapses in granite. Analysis of surface wave relative amplitude and phase anomalies between the recent and previous DPRK events indicates no anomalies in the ratios with the 20160106 and 20160909 tests beneath the Mt. Mantap and large anomalies with ratios between the 2009 and 2013 tests beneath the mountain slope. Prepared by LLNL under Contract DE-AC52-07NA27344.

Dykes and structures of the NE rift of Tenerife, Canary Islands: a record of stabilisation and destabilisation of ocean island rift zones

NASA Astrophysics Data System (ADS)

Delcamp, A.; Troll, V. R.; van Wyk de Vries, B.; Carracedo, J. C.; Petronis, M. S.; Pérez-Torrado, F. J.; Deegan, F. M.

2012-07-01

Many oceanic island rift zones are associated with lateral sector collapses, and several models have been proposed to explain this link. The North-East Rift Zone (NERZ) of Tenerife Island, Spain offers an opportunity to explore this relationship, as three successive collapses are located on both sides of the rift. We have carried out a systematic and detailed mapping campaign on the rift zone, including analysis of about 400 dykes. We recorded dyke morphology, thickness, composition, internal textural features and orientation to provide a catalogue of the characteristics of rift zone dykes. Dykes were intruded along the rift, but also radiate from several nodes along the rift and form en échelon sets along the walls of collapse scars. A striking characteristic of the dykes along the collapse scars is that they dip away from rift or embayment axes and are oblique to the collapse walls. This dyke pattern is consistent with the lateral spreading of the sectors long before the collapse events. The slump sides would create the necessary strike-slip movement to promote en échelon dyke patterns. The spreading flank would probably involve a basal decollement. Lateral flank spreading could have been generated by the intense intrusive activity along the rift but sectorial spreading in turn focused intrusive activity and allowed the development of deep intra-volcanic intrusive complexes. With continued magma supply, spreading caused temporary stabilisation of the rift by reducing slopes and relaxing stress. However, as magmatic intrusion persisted, a critical point was reached, beyond which further intrusion led to large-scale flank failure and sector collapse. During the early stages of growth, the rift could have been influenced by regional stress/strain fields and by pre-existing oceanic structures, but its later and mature development probably depended largely on the local volcanic and magmatic stress/strain fields that are effectively controlled by the rift zone growth, the intrusive complex development, the flank creep, the speed of flank deformation and the associated changes in topography. Using different approaches, a similar rift evolution has been proposed in volcanic oceanic islands elsewhere, showing that this model likely reflects a general and widespread process. This study, however, shows that the idea that dykes orient simply parallel to the rift or to the collapse scar walls is too simple; instead, a dynamic interplay between external factors (e.g. collapse, erosion) and internal forces (e.g. intrusions) is envisaged. This model thus provides a geological framework to understand the evolution of the NERZ and may help to predict developments in similar oceanic volcanoes elsewhere.

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Acoustic fluidization and the scale dependence of impact crater morphology

NASA Technical Reports Server (NTRS)

Melosh, H. J.; Gaffney, E. S.

1983-01-01

A phenomenological Bingham plastic model has previously been shown to provide an adequate description of the collapse of impact craters. This paper demonstrates that the Bingham parameters may be derived from a model in which acoustic energy generated during excavation fluidizes the rock debris surrounding the crater. Experimental support for the theoretical flow law is presented. Although the Bingham yield stress cannot be computed without detailed knowledge of the initial acoustic field, the Bingham viscosity is derived from a simple argument which shows that it increases as the 3/2 power of crater diameter, consistent with observation. Crater collapse may occur in material with internal dissipation Q as low as 100, comparable to laboratory observations of dissipation in granular materials. Crater collapse thus does not require that the acoustic field be regenerated during flow.

Convective radiation fluid-dynamics: formation and early evolution of ultra low-mass objects

NASA Astrophysics Data System (ADS)

Wuchterl, G.

2005-12-01

The formation process of ultra low-mass objects is some kind of extension of the star formation process. The physical changes towards lower mass are discussed by investigating the collapse of cloud cores that are modelled as Bonnor-Ebert spheres. Their collapse is followed by solving the equations of fluid dynamics with radiation and a model of time-dependent convection that has been calibrated to the Sun. For a sequence of cloud-cores with 1 to 0.01 solar masses, evolutionary tracks and isochrones are shown in the mass-radius diagram, the Hertzsprung-Russel diagram and the effective temperature-surface gravity or Kiel diagram. The collapse and the early hydrostatic evolution to ages of few Ma are briefly discussed and compared to observations of objects in Upper Scorpius and the low-mass components of GG Tau.

The development of neutrino-driven convection in core-collapse supernovae: 2D vs 3D

NASA Astrophysics Data System (ADS)

Kazeroni, R.; Krueger, B. K.; Guilet, J.; Foglizzo, T.

2017-12-01

A toy model is used to study the non-linear conditions for the development of neutrino-driven convection in the post-shock region of core-collapse supernovae. Our numerical simulations show that a buoyant non-linear perturbation is able to trigger self-sustained convection only in cases where convection is not linearly stabilized by advection. Several arguments proposed to interpret the impact of the dimensionality on global core-collapse supernova simulations are discussed in the light of our model. The influence of the numerical resolution is also addressed. In 3D a strong mixing to small scales induces an increase of the neutrino heating efficiency in a runaway process. This phenomenon is absent in 2D and this may indicate that the tridimensional nature of the hydrodynamics could foster explosions.

Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica.

PubMed

Joughin, Ian; Smith, Benjamin E; Medley, Brooke

2014-05-16

Resting atop a deep marine basin, the West Antarctic Ice Sheet has long been considered prone to instability. Using a numerical model, we investigated the sensitivity of Thwaites Glacier to ocean melt and whether its unstable retreat is already under way. Our model reproduces observed losses when forced with ocean melt comparable to estimates. Simulated losses are moderate (<0.25 mm per year at sea level) over the 21st century but generally increase thereafter. Except possibly for the lowest-melt scenario, the simulations indicate that early-stage collapse has begun. Less certain is the time scale, with the onset of rapid (>1 mm per year of sea-level rise) collapse in the different simulations within the range of 200 to 900 years. Copyright © 2014, American Association for the Advancement of Science.

Numerical Simulation of Slag Eye Formation and Slag Entrapment in a Bottom-Blown Argon-Stirred Ladle

NASA Astrophysics Data System (ADS)

Liu, Wei; Tang, Haiyan; Yang, Shufeng; Wang, Minghui; Li, Jingshe; Liu, Qing; Liu, Jianhui

2018-06-01

A transient mathematical model is developed for simulating the bubble-steel-slag-top gas four-phase flow in a bottom-blown argon-stirred ladle with a 70-ton capacity. The Lagrangian discrete phase model (DPM) is used for describing the moving behavior of bubbles in the steel and slag. To observe the formation process of slag eye, the volume of fluid (VOF) model is used to track the interfaces between three incompressible phases: metal/slag, metal/gas, and slag/gas. The complex multiphase turbulent flow induced by bubble-liquid interactions is solved by a large eddy simulation (LES) model. Slag eye area and slag droplet dispersion are investigated under different gas flow rates. The results show that the movement of bubbles, formation and collapse of slag eye, volatility of steel/slag interface and behavior of slag entrapment can be properly predicted in the current model. When the gas flow rate is 300 L/min, the circulation driven by the bubble plume will stir the entire ladle adequately and form a slag eye of the right size. At the same time, it will not cause strong erosion to the ladle wall, and the fluctuation of the interface is of adequate intensity, which will be helpful for improving the desulfurization efficiency; the slag entrapment behavior can also be decreased. Interestingly, with the motion of liquid steel circulation, the collision and coalescence of dispersed slag droplets occur during the floating process in the vicinity of the wall.

A model for the evaluation of systemic risk in stock markets

NASA Astrophysics Data System (ADS)

Caetano, Marco Antonio Leonel; Yoneyama, Takashi

2011-06-01

Systemic risk refers to the possibility of a collapse of an entire financial system or market, differing from the risk associated with any particular individual or a group pertaining to the system, which may include banks, government, brokers, and creditors. After the 2008 financial crisis, a significant amount of effort has been directed to the study of systemic risk and its consequences around the world. Although it is very difficult to predict when people begin to lose confidence in a financial system, it is possible to model the relationships among the stock markets of different countries and perform a Monte Carlo-type analysis to study the contagion effect. Because some larger and stronger markets influence smaller ones, a model inspired by a catalytic chemical model is proposed. In chemical reactions, reagents with higher concentrations tend to favor their conversion to products. In order to modulate the conversion process, catalyzers may be used. In this work, a mathematical modeling is proposed with bases on the catalytic chemical reaction model. More specifically, the Hang Seng and Dow Jones indices are assumed to dominate Ibovespa (the Brazilian Stock Market index), such that the indices of strong markets are taken as being analogous to the concentrations of the reagents and the indices of smaller markets as concentrations of products. The role of the catalyst is to model the degree of influence of one index on another. The actual data used to fit the model parameter consisted of the Hang Seng index, Dow Jones index, and Ibovespa, since 1993. “What if” analyses were carried out considering some intervention policies.

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

Dynamical properties of a family of collisionless models of elliptical galaxies

NASA Astrophysics Data System (ADS)

Bertin, G.; Trenti, M.

2004-04-01

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago, the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations.

Anomalous polymer collapse winding angle distributions

NASA Astrophysics Data System (ADS)

Narros, A.; Owczarek, A. L.; Prellberg, T.

2018-03-01

In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of winding angle distributions, where simulations of interacting self-avoiding walks show that the winding angle distribution for N-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as Clog N . Here we extend this work by considering interacting self-avoiding trails which are believed to be a model representative of some of the more complex behaviour. We provide robust evidence that, while the high temperature swollen state of this model has a winding angle distribution that is also Gaussian, this breaks down at the polymer collapse point and at low temperatures. Moreover, we provide some evidence that the distributions are well modelled by stretched/compressed exponentials, in contradistinction to the behaviour found in interacting self-avoiding walks. Dedicated to Professor Stu Whittington on the occasion of his 75th birthday.

Modeling bubble dynamics and radical kinetics in ultrasound induced microalgal cell disruption.

PubMed

Wang, Meng; Yuan, Wenqiao

2016-01-01

Microalgal cell disruption induced by acoustic cavitation was simulated through solving the bubble dynamics in an acoustical field and their radial kinetics (chemical kinetics of radical species) occurring in the bubble during its oscillation, as well as calculating the bubble wall pressure at the collapse point. Modeling results indicated that increasing ultrasonic intensity led to a substantial increase in the number of bubbles formed during acoustic cavitation, however, the pressure generated when the bubbles collapsed decreased. Therefore, cumulative collapse pressure (CCP) of bubbles was used to quantify acoustic disruption of a freshwater alga, Scenedesmus dimorphus, and a marine alga, Nannochloropsis oculata and compare with experimental results. The strong correlations between CCP and the intracellular lipid fluorescence density, chlorophyll-a fluorescence density, and cell particle/debris concentration were found, which suggests that the developed models could accurately predict acoustic cell disruption, and can be utilized in the scale up and optimization of the process. Copyright © 2015 Elsevier B.V. All rights reserved.

Direct numerical simulation of shear localization and decomposition reactions in shock-loaded HMX crystal

DOE PAGES

Austin, Ryan A.; Barton, Nathan R.; Reaugh, John E.; ...

2015-05-14

A numerical model is developed to study the shock wave ignition of HMX crystal. The model accounts for the coupling between crystal thermal/mechanical responses and chemical reactions that are driven by the temperature field. This allows for the direct numerical simulation of decomposition reactions in the hot spots formed by shock/impact loading. The model is used to simulate intragranular pore collapse under shock wave loading. In a reference case: (i) shear-enabled micro-jetting is responsible for a modest extent of reaction in the pore collapse region, and (ii) shear banding is found to be an important mode of localization. The shearmore » bands, which are filled with molten HMX, grow out of the pore collapse region and serve as potential ignition sites. The model predictions of shear banding and reactivity are found to be quite sensitive to the respective flow strengths of the solid and liquid phases. In this regard, it is shown that reasonable assumptions of liquid-HMX viscosity can lead to chemical reactions within the shear bands on a nanosecond time scale.« less

Collapsing lattice animals and lattice trees in two dimensions

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Grassberger, Peter

2005-06-01

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second-order transitions from an extended to a collapsed phase in the resulting two-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond-driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P* where a transition line between two collapsed phases (one bond driven and the other contact driven) sparks off. This point P* seems to be attractive (in the renormalization group sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

2017-12-01

The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Geophysical observations at cavity collapse

NASA Astrophysics Data System (ADS)

Jousset, Philippe; Bazargan-Sabet, Behrooz; Lebert, François; Bernardie, Séverine; Gourry, Jean-Christophe

2010-05-01

In Lorraine region (France) salt layers at about 200 meters depth are exploited by Solvay using solution mining methodology which consists in extracting the salt by dissolution, collapsing the cavern overburden during the exploitation phase and finally reclaiming the landscape by creating a water area. In this process, one of the main challenges for the exploiting company is to control the initial 120-m diameter collapse so as to minimize possible damages. In order to detect potential precursors and understand processes associated with such collapses, a wide series of monitoring techniques including micro seismics, broad-band seismology, hydro-acoustic, electromagnetism, gas probing, automatic leveling, continuous GPS, continuous gravity and borehole extensometry was set-up in the frame of an in-situ study carried out by the "Research Group for the Impact and Safety of Underground Works" (GISOS, France). Equipments were set-up well before the final collapse, giving a unique opportunity to analyze a great deal of information prior to and during the collapse process which has been successfully achieved on February the 13th, 2009 by controlling the cavity internal pressure. In this work, we present the results of data recorded by a network of 3 broadband seismometers, 2 accelerometers, 2 tilt-meters and a continuously gravity meter. We relate the variations of the brine pumping rate with the evolutions of the induced geophysical signals and finally we propose a first mechanical model for describing the controlled collapse. Beyond the studied case, extrapolation of the results obtained might contribute to the understanding of uncontrolled cavity collapses, such as pit-craters or calderas at volcanoes.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

Driven neutron star collapse: Type I critical phenomena and the initial black hole mass distribution

NASA Astrophysics Data System (ADS)

Noble, Scott C.; Choptuik, Matthew W.

2016-01-01

We study the general relativistic collapse of neutron star (NS) models in spherical symmetry. Our initially stable models are driven to collapse by the addition of one of two things: an initially ingoing velocity profile, or a shell of minimally coupled, massless scalar field that falls onto the star. Tolman-Oppenheimer-Volkoff (TOV) solutions with an initially isentropic, gamma-law equation of state serve as our NS models. The initial values of the velocity profile's amplitude and the star's central density span a parameter space which we have surveyed extensively and which we find provides a rich picture of the possible end states of NS collapse. This parameter space survey elucidates the boundary between Type I and Type II critical behavior in perfect fluids which coincides, on the subcritical side, with the boundary between dispersed and bound end states. For our particular model, initial velocity amplitudes greater than 0.3 c are needed to probe the regime where arbitrarily small black holes can form. In addition, we investigate Type I behavior in our system by varying the initial amplitude of the initially imploding scalar field. In this case we find that the Type I critical solutions resemble TOV solutions on the 1-mode unstable branch of equilibrium solutions, and that the critical solutions' frequencies agree well with the fundamental mode frequencies of the unstable equilibria. Additionally, the critical solution's scaling exponent is shown to be well approximated by a linear function of the initial star's central density.

Constraints on core collapse from the black hole mass function

NASA Astrophysics Data System (ADS)

Kochanek, C. S.

2015-01-01

We model the observed black hole mass function under the assumption that black hole formation is controlled by the compactness of the stellar core at the time of collapse. Low-compactness stars are more likely to explode as supernovae and produce neutron stars, while high-compactness stars are more likely to be failed supernovae that produce black holes with the mass of the helium core of the star. Using three sequences of stellar models and marginalizing over a model for the completeness of the black hole mass function, we find that the compactness ξ2.5 above which 50% of core collapses produce black holes is ξ _{2.5}^{50%}=0.24 (0.15 < ξ _{2.5}^{50%} < 0.37 at 90% confidence). The models also predict that f = 0.18 (0.09 < f < 0.39) of core collapses fail. We tested four other criteria for black hole formation based on ξ2.0 and ξ3.0, the compactnesses at enclosed masses of 2.0 or 3.0 rather than 2.5 M⊙, the mass of the iron core MFe, and the mass inside the oxygen burning shell MO. We found that ξ2.0 works as well as ξ2.5, while ξ3.0, MFe and MO are significantly worse. As expected from the high compactness of 20-25 M⊙ stars, black hole formation in this mass range provides a natural explanation of the red supergiant problem.

Triggering collapse of the presolar dense cloud core and injecting short-lived radioisotopes with a shock wave. III. Rotating three-dimensional cloud cores

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boss, Alan P.; Keiser, Sandra A., E-mail: boss@dtm.ciw.edu

2014-06-10

A key test of the supernova triggering and injection hypothesis for the origin of the solar system's short-lived radioisotopes is to reproduce the inferred initial abundances of these isotopes. We present here the most detailed models to date of the shock wave triggering and injection process, where shock waves with varied properties strike fully three-dimensional, rotating, dense cloud cores. The models are calculated with the FLASH adaptive mesh hydrodynamics code. Three different outcomes can result: triggered collapse leading to fragmentation into a multiple protostar system; triggered collapse leading to a single protostar embedded in a protostellar disk; or failure tomore » undergo dynamic collapse. Shock wave material is injected into the collapsing clouds through Rayleigh-Taylor fingers, resulting in initially inhomogeneous distributions in the protostars and protostellar disks. Cloud rotation about an axis aligned with the shock propagation direction does not increase the injection efficiency appreciably, as the shock parameters were chosen to be optimal for injection even in the absence of rotation. For a shock wave from a core-collapse supernova, the dilution factors for supernova material are in the range of ∼10{sup –4} to ∼3 × 10{sup –4}, in agreement with recent laboratory estimates of the required amount of dilution for {sup 60}Fe and {sup 26}Al. We conclude that a type II supernova remains as a promising candidate for synthesizing the solar system's short-lived radioisotopes shortly before their injection into the presolar cloud core by the supernova's remnant shock wave.« less

[The injection of acrylic bone cement prevents bone collapse in the intercalar bones lacking bony support: an experimental sheep semilunar bone model].

PubMed

Unsal, Murat; Tetik, Cihangir; Erol, Bülent; Cabukoğlu, Cengiz

2003-01-01

In a sheep semilunar bone model, we investigated whether collapse in the intercalar bones lacking bony support could be prevented by the injection of acrylic bone cement. The study included 16 limbs of eight sheep. Preoperatively, anteroposterior and lateral views of the carpal joints in the fore limbs were obtained. The animals were divided into four groups. In group 1 (n=3) no surgical procedure was performed in the right semilunar bones, whereas the periosteum on the contralateral side was elevated (group 2; n=3). The first two groups were left as controls. In Group 3 (n=5) the left semilunar bones were filled with acrylic bone cement following decancellation of the bone, while the right semilunar bones were left decancellated (group 4; n=5). The sheep were monitored for three months. Radiographs of the carpal joints were obtained to evaluate collapse occurrence in the semilunar bones. Thereafter, the animals were sacrificed and the semilunar bones were excised for biomechanical and histological examinations. Osteonecrosis and cartilage damage were sought and resistance to compressive forces was investigated. Radiologically, the extent of collapse was statistically significant in the semilunar bones in group 4 (p<0.05). The use of acrylic bone cement was found to prevent collapse in group 3, with no significant difference being noted between preoperative and postoperative semilunar bone heights (p>0.05). Biomechanically, the least resistance to compressive forces was measured in group 4 (p<0.05). Histologically, cartilage damage and osteonecrosis were only seen in group 4. Our data suggest that the use of acrylic bone cement prevents collapse in the semilunar bones, without inducing any cartilage damage or osteonecrosis.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Continuum viscoplastic simulation of a granular column collapse on large slopes : μ(I) rheology and lateral wall effects

NASA Astrophysics Data System (ADS)

Martin, Nathan; Mangeney, Anne; Ionescu, Ioan; Bouchut, Francois

2016-04-01

The description of the mechanical behaviour of granular flows and in particular of the static/flowing transition is still an open and challenging issue with strong implication for hazard assessment [{Delannay et al.}, 2016]. In particular, {detailed quantitative} comparison between numerical models and observations is necessary to go further in this direction. We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (from horizontal to 22^o) and compare precisely the results with laboratory experiments performed by {Mangeney et al.} [2010] and {Farin et al.} [2014]. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes higher than 10o whereas it remains of little effect on horizontal slope [{Martin et al.}, 2016]. We show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order [{Ionescu et al.}, 2015]. However, only a fine tuning of the constant viscosity (η = 1 Pa.s) makes it possible to predict the slow propagation phase observed experimentally on large slopes. This was not possible when using, without tuning, the variable viscosity calculated from the μ(I) rheology with the parameters estimated from experiments. Finally, we discuss the well-posedness of the model with variable and constant viscosity based in particular on the development of shear bands observed in the numerical simulations. References Delannay, R., Valance, A., Mangeney, A., Roche, O., and Richard, P., 2016. Granular and particle-laden flows: from laboratory experiments to field observations, {J. Phys. D: Appl. Phys.}, submitted. Farin, M., Mangeney, A., and Roche, O., 2014. Dynamics, deposit and erosion processes in granular collapse over sloping beds, {J. Geophys. Res. Earth Surf.}, 119(3), 504-532. Ionescu, I., Mangeney, A., Bouchut, F., and Roche, O., 2015. Viscoplastic modelling of granular column collapse with pressure and rate dependent viscosity, {J. Non-Newtonian Fluid Mech.}, 219, 1-18. Mangeney, A., Roche, O., Hungr, O., Mangold, Faccanoni, G., and Lucas, A., 2010. Erosion and mobility in granular collapse over sloping beds, {J. Geophys. Res.-Earth Surf.}, 115, F03040. Martin, N., Ionescu, I. R., Mangeney, A., Bouchut, F. and Farin, M., Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects, submitted.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Effects of high shock pressures and pore morphology on hot spot mechanisms in HMX

NASA Astrophysics Data System (ADS)

Springer, H. K.; Tarver, C. M.; Bastea, S.

2017-01-01

The shock initiation and detonation behavior of heterogeneous solid explosives is governed by its microstructure and reactive properties. New additive manufacturing techniques offer unprecedented control of explosive microstructures previously impossible, enabling us to develop novel explosives with tailored shock sensitivity and detonation properties. Since microstructure-performance relationships are not well established for explosives, there is little material design guidance for these manufacturing techniques. In this study, we explore the effects of high shock pressures (15-38 GPa) with long shock durations and different pore morphologies on hot spot mechanisms in HMX. HMX is chosen as the model material because we have experimental data on many of the chemical-thermal-mechanical properties required for pore collapse simulations. Our simulations are performed using the multi-physics arbitrary Lagrangian Eulerian finite element hydrocode, ALE3D, with Cheetah-based models for the unreacted and the product equation-of-states. We use a temperature-dependent specific heat with the unreacted equation-of-state and a temperature-dependent viscosity model to ensure accurate shock temperatures for subsequent chemistry. The Lindemann Law model is used for shock melting in HMX. In contrast to previous pore collapse studies at lower shock pressures (≤10 GPa) in HMX and shorter post-collapse burning times, our calculations show that shock melting occurs above 15 GPa due to higher bulk heating and a prominent elongated ("jet-like") hot spot region forms at later times. The combination of the elongated, post-collapse hot spot region and the higher bulk heating with increasing pressure dramatically increases the growth rate of reaction. Our calculations show that the reaction rate, dF/dt, increases with increasing shock pressure. We decompose the reaction rate into ignition ((dF/dt)ig) and growth ((dF/dt)gr) phases to better analyze our results. We define the ignition phase to primarily include pore collapse and growth phase to primarily include post-collapse grain burning. We are able to track late-time, post-collapse burning due to the unique loading conditions employed in these calculations. We find that (dF/dt)gr > (dF/dt)ig for all pressures considered. (dF/dt)gr changes more significantly from 25 to 38 GPa (from 0.05/µs to >10-100/µs) than from 15 to 25 GPa (from 0.005/µs to 0.05/µs). There is a three order-of-magnitude difference in the reaction from 15 to 38 GPa just after pore collapse. This is qualitatively consistent with fitting the (macroscopic) Ignition and Growth model to high pressure shock initiation data, where much larger reaction fractions are needed to capture the early stages of reaction. Calculated burn rates demonstrate better agreement with data at intermediate times in the growth phase for 15 to 25 GPa and late times for 30 GPa then at any time in the growth phase for 38 GPa. Our calculations are much higher than burn rate data at the earliest times in the growth phase for all pressures, which may reflect the higher localized pressures and temperatures just after pore collapse in the ignition phase. Our calculations with spherical, conical, and elliptical pores show that the influence of morphology on reaction rate is pressure dependent and the most influential pore shapes at lower pressures aren't the same at higher pressures in the regime studied. Altogether these studies provide the basis for developing microstructure-aware models that can be used to design new explosives with optimal performance-safety characteristics. Such models can be used to guide additive manufacturing of explosives and fully exploit their disruptive nature.

Solid-solid collapse transition in a two dimensional model molecular system.

PubMed

Singh, Rakesh S; Bagchi, Biman

2013-11-21

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains.

Solid-solid collapse transition in a two dimensional model molecular system

NASA Astrophysics Data System (ADS)

Singh, Rakesh S.; Bagchi, Biman

2013-11-01

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains.

NEW EQUATIONS OF STATE IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hempel, M.; Liebendoerfer, M.; Fischer, T.

2012-03-20

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer and Swesty. The systematic comparison shows that themore » model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium, is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison with the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows the determination of the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.« less

Block oscillation model for impact crater collapse

NASA Astrophysics Data System (ADS)

Ivanov, B. A.; Kostuchenko, V. N.

1997-03-01

Previous investigations of the impact crater formation mechanics have shown that the late stage, a transient cavity collapse in a gravity field, may be modeled with a traditional rock mechanics if one ascribes very specific mechanical properties of rock in the vicinity of a crater: an effective strength of rock needed is around 30 bar, and effective angle of internal friction below 5 deg. The rock media with such properties may be supposed 'temporary fluidized'. The nature of this fluidization is now poorly understood; an acoustic (vibration) nature of this fluidization has been suggested. This model now seems to be the best approach to the problem. The open question is how to implement the model (or other possible models) in a hydrocode for numerical simulation of a dynamic crater collapse. We study more relevant models of mechanical behavior of rocks during cratering. The specific of rock deformation is that the rock media deforms not as a plastic metal-like continuum, but as a system of discrete rock blocks. The deep drilling of impact craters revealed the system of rock blocks of 50 m to 200 m in size. We used the model of these block oscillations to formulate the appropriate rheological law for the subcrater flow during the modification stage.

Core groups, antimicrobial resistance and rebound in gonorrhoea in North America.

PubMed

Chan, Christina H; McCabe, Caitlin J; Fisman, David N

2012-04-01

Genital tract infections caused by Neisseria gonorrhoeae are a major cause of sexually transmitted disease worldwide. Surveillance data suggest that incidence has increased in recent years after initially falling in the face of intensified control efforts. The authors sought to evaluate the potential contribution of antimicrobial resistance to such rebound and to identify optimal treatment strategies in the face of resistance using a mathematical model of gonorrhoea. The authors built risk-structured 'susceptible-infectious-susceptible' models with and without the possibility of antibiotic resistance and used these models as a platform for the evaluation of competing plausible treatment strategies, including changing antimicrobial choice when resistance prevalence surpassed fixed thresholds, random assignment of treatment and use of combination antimicrobial therapy. Absent antimicrobial resistance, strategies that focus on treatment of highest risk individuals (the so-called core group) result in collapse of disease transmission. When antimicrobial resistance exists, a focus on the core group causes rebound in incidence, with maximal dissemination of antibiotic resistance. Random assignment of antimicrobial treatment class outperformed the use of fixed resistance thresholds with respect to sustained reduction in gonorrhoea prevalence. Gonorrhoea control is achievable only when core groups are treated, but treatment of core groups maximises dissemination of antimicrobial-resistant strains. This paradox poses a great dilemma to the control and prevention of gonorrhoea and underlines the need for gonococcal vaccines.

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

NASA Astrophysics Data System (ADS)

Maiti, Soumyabrata; Bandyopadhyay, Ritwik; Chatterjee, Anindya

2018-01-01

We study free and harmonically forced vibrations of an Euler-Bernoulli beam with rate-independent hysteretic dissipation. The dissipation follows a model proposed elsewhere for materials with randomly dispersed frictional microcracks. The virtual work of distributed dissipative moments is approximated using Gaussian quadrature, yielding a few discrete internal hysteretic states. Lagrange's equations are obtained for the modal coordinates. Differential equations for the modal coordinates and internal states are integrated together. Free vibrations decay exponentially when a single mode dominates. With multiple modes active, higher modes initially decay rapidly while lower modes decay relatively slowly. Subsequently, lower modes show their own characteristic modal damping, while small amplitude higher modes show more erratic decay. Large dissipation, for the adopted model, leads mathematically to fast and damped oscillations in the limit, unlike viscously overdamped systems. Next, harmonically forced, lightly damped responses of the beam are studied using both a slow frequency sweep and a shooting-method based search for periodic solutions along with numerical continuation. Shooting method and frequency sweep results match for large ranges of frequency. The shooting method struggles near resonances, where internal states collapse into lower dimensional behavior and Newton-Raphson iterations fail. Near the primary resonances, simple numerically-aided harmonic balance gives excellent results. Insights are also obtained into the harmonic content of secondary resonances.

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

Modern astronomical knowledge as component of general education for sustainable development

NASA Astrophysics Data System (ADS)

Nurgaliev, I.

{It is shown that 1) astronomical knowledge was a foundation of emerging modern physics and natural sciences based on mathematics, 2) mathematical basis of the natural sciences serves as an orientation of progress in the true objective of social sciences. The last example for this chain of impacts is the discovery of the fundamental demographic equation (N=aN^2-bN) full of the astronomical analogy [9]. Modern age endorses new imperatives on education. Reckless exploitation of the natural resources will cause irreversible exhaustion of the agro- and bio-potential of the planet during lifetime of a few generations. The adequate respond to the challenge lies in modern technologies and educating responsible (socially oriented) professionals. That is why the importance of teaching modern technologies along with providing the students with the understanding of global long term consequences of the human industrial activities is growing. The course ``Theoretical Foundations of Modern Technologies" at the Moscow State Agricultural University (Timiryazev Academy) taught by the author is discussed. New experimental project ``Space Technologies, Ecology and Safe Energetics in School of the Future" is presented as a project of a new age in the process of implementing at the Moscow city secondary schools by the colleagues and by the author. The new cosmological models in the frame of the Newtonian and general relativistic treatments developed by the author are considered in this report as an example of immediate implementation of new astro-knowledge into the education for modern agrarian students. The centrifugal forces acting between particles rotating randomly around each other are shown to be able to reverse gravitational collapse.

Topics in Core-Collapse Supernova Theory: The Formation of Black Holes and the Transport of Neutrinos

NASA Astrophysics Data System (ADS)

O'Connor, Evan Patrick

Core-Collapse Supernovae are one of the most complex astrophysical systems in the universe. They deeply entwine aspects of physics and astrophysics that are rarely side by side in nature. To accurately model core-collapse supernovae one must self-consistently combine general relativity, nuclear physics, neutrino physics, and magneto-hydrodynamics in a symmetry-free computational environment. This is a challenging task, as each one of these aspects on its own is an area of great study. We take an open approach in an effort to encourage collaboration in the core-collapse supernovae community. In this thesis, we develop a new open-source general-relativistic spherically-symmetric Eulerian hydrodynamics code for studying stellar collapse, protoneutron star formation, and evolution until black hole formation. GR1D includes support for finite temperature equations of state and an efficient and qualitatively accurate treatment of neutrino leakage. GR1D implements spherically-symmetric rotation, allowing for the study of slowly rotating stellar collapse. GR1D is available at http://www.stellarcollapse.org. We use GR1D to perform an extensive study of black hole formation in failing core-collapse supernovae. Over 100 presupernova models from various sources are used in over 700 total simulations. We systematically explore the dependence of black hole formation on the input physics: initial zero-age main sequence (ZAMS) mass and metallicity, nuclear equation of state, rotation, and stellar mass loss rates. Assuming the core-collapse supernova mechanism fails and a black hole forms, we find that the outcome, for a given equation of state, can be estimated, to first order, by a single parameter, the compactness of the stellar core at bounce. By comparing the protoneutron star structure at the onset of gravitational instability with solutions of the Tolman-Oppenheimer-Volkof equations, we find that thermal pressure support in the outer protoneutron star core is responsible for raising the maximum protoneutron star mass by up to 25% above the cold neutron star value. By artificially increasing neutrino heating, we find the critical neutrino heating efficiency required for exploding a given progenitor structure and connect these findings with ZAMS conditions. This establishes, albeit approximately, for the first time based on actual collapse simulations, the mapping between ZAMS parameters and the outcome of core collapse. We also use GR1D to study proposed progenitors of long-duration gamma-ray bursts. We find that many of the proposed progenitors have core structures similar to garden-variety core-collapse supernovae. These are not expected to form black holes, a key ingredient of the collapsar model of long-duration gamma-ray bursts. The small fraction of proposed progenitors that are compact enough to form black holes have fast rotating iron cores, making them prone to a magneto-rotational explosion and the formation of a protomagnetar rather than a black hole. Finally, we present preliminary work on a fully general-relativistic neutrino transport code and neutrino-interaction library. Following along with the trends explored in our black hole formation study, we look at the dependence of the neutrino observables on the bounce compactness. We find clear relationships that will allow us to extract details of the core structure from the next galactic supernova. Following the open approach of GR1D, the neutrino transport code will be made open-source upon completion. The open-source neutrino-interaction library, NuLib, is already available at http://www.nulib.org.

METROPOLITAN-SCALE TRANSPORT AND DISPERSION FROM THE NEW YORK WORLD TRADE CENTER FOLLOWING SEPTEMBER 11, 2001. PART II: AN APPLICATION OF THE CALPUFF PLUME MODEL

EPA Science Inventory

Following the collapse of the New York World Trade Center (WTC) towers on September 11, 2001, Local, State, and Federal agencies initiated numerous air monitoring activities to better understand the ongoing impacts of emissions from the disaster. The collapse of the World Trade C...

Probabilistic hindcasts and projections of the coupled climate, carbon cycle and Atlantic meridional overturning circulation system: a Bayesian fusion of century-scale observations with a simple model

NASA Astrophysics Data System (ADS)

Urban, Nathan M.; Keller, Klaus

2010-10-01

How has the Atlantic Meridional Overturning Circulation (AMOC) varied over the past centuries and what is the risk of an anthropogenic AMOC collapse? We report probabilistic projections of the future climate which improve on previous AMOC projection studies by (i) greatly expanding the considered observational constraints and (ii) carefully sampling the tail areas of the parameter probability distribution function (pdf). We use a Bayesian inversion to constrain a simple model of the coupled climate, carbon cycle and AMOC systems using observations to derive multicentury hindcasts and projections. Our hindcasts show considerable skill in representing the observational constraints. We show that robust AMOC risk estimates can require carefully sampling the parameter pdfs. We find a low probability of experiencing an AMOC collapse within the 21st century for a business-as-usual emissions scenario. The probability of experiencing an AMOC collapse within two centuries is 1/10. The probability of crossing a forcing threshold and triggering a future AMOC collapse (by 2300) is approximately 1/30 in the 21st century and over 1/3 in the 22nd. Given the simplicity of the model structure and uncertainty in the forcing assumptions, our analysis should be considered a proof of concept and the quantitative conclusions subject to severe caveats.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu

We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceedsmore » non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.« less

Economic conditions, hypertension, and cardiovascular disease: analysis of the Icelandic economic collapse.

PubMed

Birgisdóttir, Kristín Helga; Jónsson, Stefán Hrafn; Ásgeirsdóttir, Tinna Laufey

2017-12-01

Previous research has found a positive short-term relationship between the 2008 collapse and hypertension in Icelandic males. With Iceland's economy experiencing a phase of economic recovery, an opportunity to pursue a longer-term analysis of the collapse has emerged. Using data from a nationally representative sample, fixed-effect estimations and mediation analyses were performed to explore the relationship between the Icelandic economic collapse in 2008 and the longer-term impact on hypertension and cardiovascular health. A sensitivity analysis was carried out with pooled logit models estimated as well as an alternative dependent variable. Our attrition analysis revealed that results for cardiovascular diseases were affected by attrition, but not results from estimations on the relationship between the economic crisis and hypertension. When compared to the boom year 2007, our results point to an increased probability of Icelandic women having hypertension in the year 2012, when the Icelandic economy had recovered substantially from the economic collapse in 2008. This represents a deviation from pre-crisis trends, thus suggesting a true economic-recovery impact on hypertension.

Collapse and revival of the Fermi sea in a Bose-Fermi mixture

NASA Astrophysics Data System (ADS)

Iyer, Deepak; Will, Sebastian; Rigol, Marcos

2014-05-01

The collapse and revival of quantum fields is one of the most pristine forms of coherent quantum dynamics far from equilibrium. Until now, it has only been observed in the dynamical evolution of bosonic systems. We report on the first observation of the boson mediated collapse and revival of the Fermi sea in a Bose-Fermi mixture. Specifically, we present a simple model which captures the experimental observations shown in the talk titled Observation of Collapse and Revival Dynamics in the Fermionic Component of a Lattice Bose-Fermi Mixture by Sebastian Will. Our theoretical analysis shows why the results are robust to the presence of harmonic traps during the loading or the time evolution phase. It also makes apparent that the fermionic dynamics is independent of whether the bosonic component consists of a coherent state or localized Fock states with random occupation numbers. Because of the robustness of the experimental results, we argue that this kind of collapse and revival experiment can be used to accurately characterize interactions between bosons and fermions in a lattice.

Collapse of Non-Rectangular Channels in a Soft Elastomer

NASA Astrophysics Data System (ADS)

Tepayotl-Ramirez, Daniel; Park, Yong-Lae; Lu, Tong; Majidi, Carmel

2013-03-01

We examine the collapse of microchannels in a soft elastomer by treating the sidewalls as in- denters that penetrate the channel base. This approach leads to a closed-form algebraic mapping between applied pressure and cross-sectional deformation that are in strong agreement with ex- perimental measurements and Finite Element Analysis (FEA) simulation. Applications of this new approach to modeling soft microchannel collapse range from lab-on-a-chip microfluidics for pressure-controlled protein filtration to soft-matter pressures sensing. We demonstrate the latter by comparing theoretical predictions with experimental measurements of the pressure-controlled electrical resistance of liquid-phase Gallium alloy microchannels embedded in a soft silicone elas- tomer.

Collapse limit states of reinforced earth retaining walls

NASA Astrophysics Data System (ADS)

Bolton, M. D.; Pang, P. L. R.

The use of systems of earth reinforcement or anchorage is gaining in popularity. It therefore becomes important to assess whether the methods of design which were adopted for such constructions represent valid predictions of realistic limit states. Confidence can only be gained with regard to the effectiveness of limit state criteria if a wide variety of representative limit states were observed. Over 80 centrifugal model tests of simple reinforced earth retaining walls were carried out, with the main purpose of clarifying the nature of appropriate collapse criteria. Collapses due to an insufficiency of friction were shown to be repeatable and therefore subject to fairly simple limit state calculations.

Chain Collapse of an Amyloidogenic Intrinsically Disordered Protein

PubMed Central

Jain, Neha; Bhattacharya, Mily; Mukhopadhyay, Samrat

2011-01-01

Natively unfolded or intrinsically disordered proteins (IDPs) are under intense scrutiny due to their involvement in both normal biological functions and abnormal protein misfolding disorders. Polypeptide chain collapse of amyloidogenic IDPs is believed to play a key role in protein misfolding, oligomerization, and aggregation leading to amyloid fibril formation, which is implicated in a number of human diseases. In this work, we used bovine κ-casein, which serves as an archetypal model protein for amyloidogenic IDPs. Using a variety of biophysical tools involving both prediction and spectroscopic techniques, we first established that monomeric κ-casein adopts a collapsed premolten-globule-like conformational ensemble under physiological conditions. Our time-resolved fluorescence and light-scattering data indicate a change in the mean hydrodynamic radius from ∼4.6 nm to ∼1.9 nm upon chain collapse. We then took the advantage of two cysteines separated by 77 amino-acid residues and covalently labeled them using thiol-reactive pyrene maleimide. This dual-labeled protein demonstrated a strong excimer formation upon renaturation from urea- and acid-denatured states under both equilibrium and kinetic conditions, providing compelling evidence of polypeptide chain collapse under physiological conditions. The implication of the IDP chain collapse in protein aggregation and amyloid formation is also discussed. PMID:21961598

A core-halo pattern of entropy creation in gravitational collapse

NASA Astrophysics Data System (ADS)

Wren, Andrew J.

2018-03-01

This paper presents a kinetic theory model of gravitational collapse due to a small perturbation. Solving the relevant equations yields a pattern of entropy destruction in a spherical core around the perturbation, and entropy creation in a surrounding halo. This indicates collisional "de-relaxation" in the core, and collisional relaxation in the halo. Core-halo patterns are ubiquitous in the astrophysics of gravitational collapse, and are found here without any of the prior assumptions of such a pattern usually made in analytical models. Motivated by this analysis, the paper outlines a possible scheme for identifying structure formation in a set of observations or a simulation. This scheme involves a choice of coarse-graining scale appropriate to the structure under consideration, and might aid exploration of hierarchical structure formation, supplementing the usual density-based methods for highlighting astrophysical and cosmological structure at various scales.

A core-halo pattern of entropy creation in gravitational collapse

NASA Astrophysics Data System (ADS)

Wren, Andrew J.

2018-07-01

This paper presents a kinetic theory model of gravitational collapse due to a small perturbation. Solving the relevant equations yields a pattern of entropy destruction in a spherical core around the perturbation, and entropy creation in a surrounding halo. This indicates collisional `de-relaxation' in the core, and collisional relaxation in the halo. Core-halo patterns are ubiquitous in the astrophysics of gravitational collapse and are found here without any of the prior assumptions of such a pattern usually made in analytical models. Motivated by this analysis, the paper outlines a possible scheme for identifying structure formation in a set of observations or a simulation. This scheme involves a choice of coarse-graining scale appropriate to the structure under consideration, and might aid exploration of hierarchical structure formation, supplementing the usual density-based methods for highlighting astrophysical and cosmological structure at various scales.

Airway reopening: Steadily propagating bubbles in buckled elastic tubes

NASA Astrophysics Data System (ADS)

Heil, Matthias; Hazel, Andrew L.

2001-11-01

Many pulmonary diseases result in the collapse and occlusion of parts of the lung by viscous fluid. The subsequent airway reopening is generally assumed to occur via the propagation of an air finger into the collapsed, fluid-filled part of the airway. The problem has some similarity to the scenario of the `first breath' when air has to enter the fluid-filled lungs of a newborn baby for the first time. We have developed the first three-dimensional computational model of airway reopening, based on a finite-element solution of the free-surface Stokes equations, fully coupled to the equations of large-displacement shell theory. Following a brief discussion of the numerical method, we will present results that illustrate the 3D flow field by which the steadily propagating air finger reopens the non-axisymmetrically collapsed airway. Finally, we will contrast the system's behaviour to predictions from earlier two-dimensional models.

Three-Dimensional Integrated Survey for Building Investigations.

PubMed

Costantino, Domenica; Angelini, Maria Giuseppa

2015-11-01

The study shows the results of a survey aimed to represent a building collapse and the feasibility of the modellation as a support of structure analysis. An integrated survey using topographic, photogrammetric, and terrestrial laser techniques was carried out to obtain a three-dimensional (3D) model of the building, plans and prospects, and the particulars of the collapsed area. Authors acquired, by a photogrammetric survey, information about regular parties of the structure; while using laser scanner data they reconstructed a set of more interesting architectural details and areas with higher surface curvature. Specifically, the process of texture provided a detailed 3D structure of the areas under investigation. The analysis of the data acquired resulted to be very useful both in identifying the causes of the disaster and also in helping the reconstruction of the collapsed corner showing the contribution that the integrated surveys can give in preserving architectural and historic heritage. © 2015 American Academy of Forensic Sciences.

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Kobayashi, Hirotada; Morimae, Tomoyuki; Nishimura, Harumichi; Tamate, Shuhei; Tani, Seiichiro

2018-05-01

The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently sampled within a constant multiplicative error unless the polynomial-time hierarchy collapses to the third level [T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014), 10.1103/PhysRevLett.112.130502]. It was open whether we can keep the no-go result while reducing the number of output qubits from three to one. Here, we solve the open problem affirmatively. We also show that the third-level collapse of the polynomial-time hierarchy can be strengthened to the second-level one. The strengthening of the collapse level from the third to the second also holds for other subuniversal models such as the instantaneous quantum polynomial model [M. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011), 10.1098/rspa.2010.0301] and the boson sampling model [S. Aaronson and A. Arkhipov, STOC 2011, p. 333]. We additionally study the classical simulatability of the one-clean-qubit model with further restrictions on the circuit depth or the gate types.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

The Curious Events Leading to the Theory of Shock Waves

NASA Technical Reports Server (NTRS)

Salas, Manuel D.

2006-01-01

We review the history of the development of the modern theory of shock waves. Several attempts at an early-theory quickly collapsed for lack of foundations in mathematics and thermodynamics. It is not until the works of Rankine and later Hugoniot that a full theory is established. Rankine is the first to show that within the shock a non-adiabatic process must occur. Hugoniot showed that in the absence of viscosity and heat conduction conservation of energy implies conservation of entropy in smooth regions and a jump in entropy across a shock. Even after the theory is fully developed, old notions continue to pervade the literature well into the early part of the 20th Century.

Order-of-magnitude physics of neutron stars. Estimating their properties from first principles

NASA Astrophysics Data System (ADS)

Reisenegger, Andreas; Zepeda, Felipe S.

2016-03-01

We use basic physics and simple mathematics accessible to advanced undergraduate students to estimate the main properties of neutron stars. We set the stage and introduce relevant concepts by discussing the properties of "everyday" matter on Earth, degenerate Fermi gases, white dwarfs, and scaling relations of stellar properties with polytropic equations of state. Then, we discuss various physical ingredients relevant for neutron stars and how they can be combined in order to obtain a couple of different simple estimates of their maximum mass, beyond which they would collapse, turning into black holes. Finally, we use the basic structural parameters of neutron stars to briefly discuss their rotational and electromagnetic properties.

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

ERIC Educational Resources Information Center

Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

2016-01-01

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

Interfacial free energy governs single polystyrene chain collapse in water and aqueous solutions.

PubMed

Li, Isaac T S; Walker, Gilbert C

2010-05-12

The hydrophobic interaction is significantly responsible for driving protein folding and self-assembly. To understand it, the thermodynamics, the role of water structure, the dewetting process surrounding hydrophobes, and related aspects have undergone extensive investigations. Here, we examine the hypothesis that polymer-solvent interfacial free energy is adequate to describe the energetics of the collapse of a hydrophobic homopolymer chain at fixed temperature, which serves as a much simplified model for studying the hydrophobic collapse of a protein. This implies that changes in polymer-solvent interfacial free energy should be directly proportional to the force to extend a collapsed polymer into a bad solvent. To test this hypothesis, we undertook single-molecule force spectroscopy on a collapsed, single, polystyrene chain in water-ethanol and water-salt mixtures where we measured the monomer solvation free energy from an ensemble average conformations. Different proportions within the binary mixture were used to create solvents with different interfacial free energies with polystyrene. In these mixed solvents, we observed a linear correlation between the interfacial free energy and the force required to extend the chain into solution, which is a direct measure of the solvation free energy per monomer on a single chain at room temperature. A simple analytical model compares favorably with the experimental results. This knowledge supports a common assumption that explicit water solvent may not be necessary for cases whose primary concerns are hydrophobic interactions and hydrophobic hydration.

Effect of supersonic relative motion between baryons and dark matter on collapsed objects

NASA Astrophysics Data System (ADS)

Asaba, Shinsuke; Ichiki, Kiyotomo; Tashiro, Hiroyuki

2016-01-01

Great attention is given to the first star formation and the epoch of reionization as main targets of planned large radio interferometries (e.g. Square Kilometre Array). Recently, it is claimed that the supersonic relative velocity between baryons and cold dark matter can suppress the abundance of first stars and impact the cosmological reionization process. Therefore, in order to compare observed results with theoretical predictions it is important to examine the effect of the supersonic relative motion on the small-scale structure formation. In this paper, we investigate this effect on the nonlinear structure formation in the context of the spherical collapse model in order to understand the fundamental physics in a simple configuration. We show the evolution of the dark matter sphere with the relative velocity by both using N-body simulations and numerically calculating the equation of motion for the dark matter mass shell. The effects of the relative motion in the spherical collapse model appear as the delay of the collapse time of dark matter halos and the decrease of the baryon mass fraction within the dark matter sphere. Based on these results, we provide the fitting formula of the critical density contrast for collapses with the relative motion effect and calculate the mass function of dark matter halos in the Press-Schechter formalism. As a result, the relative velocity decreases the abundance of dark matter halos whose mass is smaller than 108M⊙/h .

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

NASA Astrophysics Data System (ADS)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

A debris avalanche at Süphan stratovolcano (Turkey) and implications for hazard evaluation

NASA Astrophysics Data System (ADS)

Özdemir, Yavuz; Akkaya, İsmail; Oyan, Vural; Kelfoun, Karim

2016-02-01

The Quaternary Süphan debris avalanche deposit is located in Eastern Anatolia, Turkey. The avalanche formed by the sector collapse of a major stratovolcano towards the north, possibly during a single catastrophic event. The deposit has an estimated volume of 4 km3 and ran out over 25 km to cover an area of approximately 200 km2. Products of the collapse are overlain by younger eruptive units from the Süphan volcano. We have tested the numerical code VolcFlow to first reproduce the emplacement of the Quaternary Süphan debris avalanche and then to develop a hazard assessment for potential future sector collapses and subsequent emplacement of debris avalanches and associated tsunami. The numerical model captures the main features of the propagation process, including travel distance, lateral spread, and run up. The best fit obtained for the existing flow has a constant retarding stress of 50 kPa and a collapse scar volume of 4 km3. Analysis of potential future collapse scenarios reveals that northern sector debris avalanches (up to 6 km3) could affect several towns. In the case of a sector collapse towards the south, a tsunami will reach the city of Van and several of the biggest towns on the southern shoreline of Lake Van. Cities most affected by the larger amplitude waves would be Van, Edremit, Gevaş, Tatvan, and, to a lesser extent, Erciş, with wave amplitudes (first waves after the onset of the collapse) between 8 and 10 m.

Martian tension fractures and the formation of grabens and collapse features at Valles Marineris

NASA Technical Reports Server (NTRS)

Tanaka, K. L.; Golombek, M. P.

1989-01-01

Simple models of the Martian crust are summarized that predict extensional deformation style on the basis of depth, material friction and strength, and hydraulic conditions appropriate to the planet. These models indicate that tension fractures may be common features on Mars, given adequate differential stress conditions. Examples of tension fractures on Mars inferred from morphological criteria are examined based on the probable geologic conditions in which they formed and on model constraints. It is proposed that the grabens and collapse features of Valles Marineris are controlled by tension fractures in intact basement rocks that lie below impact ejecta.

Structural and elastic properties of InX (X = P, As, Sb) at pressure and room temperature

NASA Astrophysics Data System (ADS)

Pawar, Pooja; Singh, Sadhna

2018-06-01

We have investigated the pressure-induced phase transition of InX (X = P, As, Sb) from Zinc-Blende (ZB) to NaCl structure by using realistic interaction potential model involving the effect of temperature. This model consists of Coulomb interaction, three-body interaction and short-range overlap repulsive interaction upto the second nearest neighbor involving temperature. Phase-transition pressure is associated with a sudden collapse in volume, showing the incidence of first-order phase transition. The phase-transition pressure is associated with volume collapses, and the elastic constants obtained from the present model indicate good agreement with the available experimental and theoretical data.

Wrinkling and collapse of mesh reinforced membrane inflated beam under bending

NASA Astrophysics Data System (ADS)

Tao, Qiang; Wang, Changguo; Xue, Zhiming; Xie, Zhimin; Tan, Huifeng

2016-11-01

A novel concept of mesh reinforced membrane (MRM) is proposed in this paper. The tensile collapse mechanism of MRM is elucidated based on three obvious deformed stages. An improved Shell-Membrane model is used to predict the wrinkling and collapse of MRM inflated beam which is verified by a non-contact experiment based on the digital image correlation technique. Further the wrinkling details including the wrinkling evolution, pattern, shape, stress distribution are simulated to evaluate the functions of MRM for loading-carrying capacity of inflated beam. Pressure resistant performance of inflated beam was studied at last. The results revealed that MRM shows a great improvement on the collapse moment of inflated beam. MRM contributes to restrain wrinkling evolution by changing the transfer path of loadings which results from dispersing stress distribution and changing wrinkling pattern. The results show good references to the wrinkling control and the improvement of load-carrying capacity of inflated beam.

Competition between global warming and an abrupt collapse of the AMOC in Earth's energy imbalance.

PubMed

Drijfhout, Sybren

2015-10-06

A collapse of the Atlantic Meridional Overturning Circulation (AMOC) leads to global cooling through fast feedbacks that selectively amplify the response in the Northern Hemisphere (NH). How such cooling competes with global warming has long been a topic for speculation, but was never addressed using a climate model. Here it is shown that global cooling due to a collapsing AMOC obliterates global warming for a period of 15-20 years. Thereafter, the global mean temperature trend is reversed and becomes similar to a simulation without an AMOC collapse. The resulting surface warming hiatus lasts for 40-50 years. Global warming and AMOC-induced NH cooling are governed by similar feedbacks, giving rise to a global net radiative imbalance of similar sign, although the former is associated with surface warming, the latter with cooling. Their footprints in outgoing longwave and absorbed shortwave radiation are very distinct, making attribution possible.

Global force-torque phase diagram for the DNA double helix: structural transitions, triple points and collapsed plectonemes

PubMed Central

Marko, John F.; Neukirch, Sébastien

2014-01-01

We present a free energy model for structural transitions of the DNA double helix driven by tensile and torsional stress. Our model is coarse grained, and is based on semiflexible polymer descriptions of B-DNA, underwound L-DNA, and highly overwound P-DNA. The statistical-mechanical model of plectonemic supercoiling previously developed for B-DNA is applied to semiflexible polymer models of P and L-DNA, to obtain a model of DNA structural transitions in quantitative accord with experiment. We identify two distinct plectonemic states, one “inflated” by electrostatic repulsion and thermal fluctuations, and the other “collapsed”, with the two double helices inside the supercoils driven to close contact. We find that supercoiled B and L are stable only in inflated form, while supercoiled P is always collapsed. We also predict the behavior and experimental signatures of highly underwound “Q”-DNA, the left-handed analog of P-DNA; as for P, supercoiled Q is always collapsed. Overstretched “S”-DNA and strand-separated “stress-melted” DNA are also included in our model, allowing prediction of a global phase diagram for forces up to 1000 pN and torques between ±60 pN nm, or in terms of linking number density, from σ = −5 to +3. PMID:24483501

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Airway Strain during Mechanical Ventilation in an Intact Animal Model

PubMed Central

Sinclair, Scott E.; Molthen, Robert C.; Haworth, Steve T.; Dawson, Christopher A.; Waters, Christopher M.

2007-01-01

Rationale: Mechanical ventilation with large tidal volumes causes ventilator-induced lung injury in animal models. Little direct evidence exists regarding the deformation of airways in vivo during mechanical ventilation, or in the presence of positive end-expiratory pressure (PEEP). Objectives: To measure airway strain and to estimate airway wall tension during mechanical ventilation in an intact animal model. Methods: Sprague-Dawley rats were anesthetized and mechanically ventilated with tidal volumes of 6, 12, and 25 cm3/kg with and without 10–cm H2O PEEP. Real-time tantalum bronchograms were obtained for each condition, using microfocal X-ray imaging. Images were used to calculate circumferential and longitudinal airway strains, and on the basis of a simplified mathematical model we estimated airway wall tensions. Measurements and Main Results: Circumferential and longitudinal airway strains increased with increasing tidal volume. Levels of mechanical strain were heterogeneous throughout the bronchial tree. Circumferential strains were higher in smaller airways (less than 800 μm). Airway size did not influence longitudinal strain. When PEEP was applied, wall tensions increased more rapidly than did strain levels, suggesting that a “strain limit” had been reached. Airway collapse was not observed under any experimental condition. Conclusions: Mechanical ventilation results in significant airway mechanical strain that is heterogeneously distributed in the uninjured lung. The magnitude of circumferential but not axial strain varies with airway diameter. Airways exhibit a “strain limit” above which an abrupt dramatic rise in wall tension is observed. PMID:17626911

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

NASA Astrophysics Data System (ADS)

Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

2013-07-01

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

Collapse and Fragmentation Models of Tidally Interacting Molecular Cloud Cores. IV. Initial Slow Rotation and Magnetic Field Support

NASA Astrophysics Data System (ADS)

Sigalotti, Leonardo Di G.; Klapp, Jaime

2000-03-01

Fragmentation has long been advocated as the primary mechanism for explaining the observed binary frequency among pre-main-sequence stars and, more recently, for explaining the emerging evidence for binary and multiple protostellar systems. The role of magnetic fields and ambipolar diffusion is essential to understand how dense cloud cores begin dynamic collapse and eventually fragment into protostars. Here we consider new numerical models of the gravitational collapse and fragmentation of slowly rotating molecular cloud cores, including the effects of magnetic support and ambipolar diffusion. The starting point of the evolution is provided by a magnetically stable (subcritical) condensation that results from adding a magnetic field pressure, B2/8π [with the field strength given by the scaling relation B=B0(ρ/ρ0)1/2], to a reference state consisting of a thermally supercritical (α~0.36), slowly rotating (β~0.037), Gaussian cloud core of prolate shape and central density ρ0. The effects of ambipolar diffusion are approximated by allowing the reference field strength B0 to gradually decrease over a timescale of 10 free-fall times. The models also include the effects of tidal interaction due to a gravitational encounter with another protostar, and so they may apply to low-mass star formation within a cluster-forming environment. The results indicate that the magnetic forces delay the onset of dynamic collapse, and hence of fragmentation, by an amount of time that depends on the initial central mass-to-flux ratio. Compared with previous magnetic collapse calculations of rapidly rotating (β=0.12) clouds, lower initial rotation (β~0.037) is seen to result in much shorter delay periods, thus anticipating binary fragmentation. In general, the results show that the models are still susceptible to fragment into binary systems. Intermediate magnetic support (η~0.285) and low tidal forces (τ<~0.201) may lead to final triple or quadruple protostellar systems, while increasing the size of η and τ always results in final binary protostellar cores. The formed binary systems have separations of ~200-350 AU, suggesting that the recently observed peaks around ~90 AU and 215 AU for T Tauri stars may be explained by the collapse and fragmentation of initially slowly rotating magnetic cloud cores with β<~0.04.

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Could the collapse of a massive speleothem be the record of a large paleoearthquake?

NASA Astrophysics Data System (ADS)

Valentini, Alessandro; Pace, Bruno; Vasta, Marcello; Ferranti, Luigi; Colella, Abner; Vassallo, Maurizio

2016-04-01

Earthquake forecast and seismic hazard models are generally based on historical and instrumental seismicity. However, in regions characterized by moderate strain rates and by strong earthquakes with recurrence longer than the time span covered by historical catalogues, different approaches are desirable to provide an independent test of seismologically-based models. We used non-conventional methods, such as the so-called "Fragile Geological Features", and in particular cave speleothems, for assessing and improving existing paleoseismological databases and seismic hazard models. In this work we present a detailed study of a massive speleothem found collapsed in the Cola Cave (Abruzzo region, Central Apennines, Italy) that could be considered the record of a large paleoearthquake. Radiometric dating and geotechnical measurements are carried out to characterize the collapse time and the mechanical properties of speleothem. We performed theoretical and numerical modelling in order to estimate the values of the horizontal ground acceleration required to failure the speleothems. In particular we used a finite element method (FEM), with the SAP200 software, starting from the detailed geometry of the speleothem and its mechanical properties. We used several individual seismogenic source geometries and four different ground motion prediction equations to calculate the possible response spectra. We carried out also a seismic noise survey to understand and quantify any ground motion amplification phenomenon. The results suggest two faults located in the Fucino area as the most probable causative sources of the cave speleothem collapses, recorded ~4-5 ka ago, with a Mw=6.8 ± 0.2. Our approach contributes to assess the existence of past earthquakes integrating the classical paleoseismological trenches techniques, and to attribute the retrieved event to geometrically-defined individual seismogenic sources, which represents a key contribution to improve fault-based seismic hazard models.

Three-dimensional flows in a hyperelastic vessel under external pressure.

PubMed

Zhang, Sen; Luo, Xiaoyu; Cai, Zongxi

2018-05-09

We study the collapsible behaviour of a vessel conveying viscous flows subject to external pressure, a scenario that could occur in many physiological applications. The vessel is modelled as a three-dimensional cylindrical tube of nonlinear hyperelastic material. To solve the fully coupled fluid-structure interaction, we have developed a novel approach based on the Arbitrary Lagrangian-Eulerian (ALE) method and the frontal solver. The method of rotating spines is used to enable an automatic mesh adaptation. The numerical code is verified extensively with published results and those obtained using the commercial packages in simpler cases, e.g. ANSYS for the structure with the prescribed flow, and FLUENT for the fluid flow with prescribed structure deformation. We examine three different hyperelastic material models for the tube for the first time in this context and show that at the small strain, all three material models give similar results. However, for the large strain, results differ depending on the material model used. We further study the behaviour of the tube under a mode-3 buckling and reveal its complex flow patterns under various external pressures. To understand these flow patterns, we show how energy dissipation is associated with the boundary layers created at the narrowest collapsed section of the tube, and how the transverse flow forms a virtual sink to feed a strong axial jet. We found that the energy dissipation associated with the recirculation does not coincide with the flow separation zone itself, but overlaps with the streamlines that divide the three recirculation zones. Finally, we examine the bifurcation diagrams for both mode-3 and mode-2 collapses and reveal that multiple solutions exist for a range of the Reynolds number. Our work is a step towards modelling more realistic physiological flows in collapsible arteries and veins.

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

Brine Migration from a Flooded Salt Mine in the Genesee Valley, Livingston County, New York: Geochemical Modeling and Simulation of Variable-Density Flow

USGS Publications Warehouse

Yager, Richard M.; Misut, Paul E.; Langevin, Christian D.; Parkhurst, David L.

2009-01-01

The Retsof salt mine in upstate New York was flooded from 1994 to 1996 after two roof collapses created rubble chimneys in overlying bedrock that intersected a confined aquifer in glacial sediments. The mine now contains about 60 billion liters of saturated halite brine that is slowly being displaced as the weight of overlying sediments causes the mine cavity to close, a process that could last several hundred years. Saline water was detected in the confined aquifer in 2002, and a brine-mitigation project that includes pumping followed by onsite desalination was implemented in 2006 to prevent further migration of saline water from the collapse area. A study was conducted by the U.S. Geological Survey using geochemical and variable-density flow modeling to determine sources of salinity in the confined aquifer and to assess (1) processes that control movement and mixing of waters in the collapse area, (2) the effect of pumping on salinity, and (3) the potential for anhydrite dissolution and subsequent land subsidence resulting from mixing of waters induced by pumping. The primary source of salinity in the collapse area is halite brine that was displaced from the flooded mine and transported upward by advection and dispersion through the rubble chimneys and surrounding deformation zone. Geochemical and variable-density modeling indicate that salinity in the upper part of the collapse area is partly derived from inflow of saline water from bedrock fracture zones during water-level recovery (January 1996 through August 2006). The lateral diversion of brine into bedrock fracture zones promoted the upward migration of mine water through mixing with lower density waters. The relative contributions of mine water, bedrock water, and aquifer water to the observed salinity profile within the collapse area are controlled by the rates of flow to and from bedrock fracture zones. Variable-density simulations of water-level recovery indicate that saline water has probably not migrated beyond the collapse area, while simulations of pumping indicate that further upward migration of brine and saline water is now prevented by groundwater withdrawals under the brine-mitigation project. Geochemical modeling indicates that additional land subsidence as a result of anhydrite dissolution in the collapse area is not a concern, as long as the rate of brine pumping is less than the rate of upward flow of brine from the flooded mine. The collapse area above the flooded salt mine is within a glacially scoured bedrock valley that is filled with more than 150 meters of glacial drift. A confined aquifer at the bottom of the glacial sediments (referred to as the lower confined aquifer, or LCA) was the source of most of the water that flooded the mine. Two rubble chimneys that formed above the roof collapses in 1994 hydraulically connect the flooded mine to the LCA through 180 meters of sedimentary rock. From 1996 through 2006, water levels in the aquifer system recovered and the brine-displacement rate ranged from 4.4 to 1.6 liters per second, as estimated from land-surface subsidence above the mine. A zone of fracturing within the bedrock (the deformation zone) formed around the rubble chimneys as rock layers sagged toward the mine cavity after the roof collapses. Borehole geophysical surveys have identified three saline-water-bearing fracture zones in the bedrock: at stratigraphic contacts between the Onondaga and Bertie Limestones (O/B-FZ) and the Bertie Limestone and the Camillus Shale (B/C-FZ), and in the Syracuse Formation (Syr-FZ). The only outlets for brine displaced from the mine are through the rubble chimneys, but some of the brine could be diverted laterally into fracture zones in the rocks that lie between the mine and the LCA. Inverse geochemical models developed using PHREEQC indicate that halite brine in the flooded mine is derived from a mixture of freshwater from the LCA (81 percent), saline water from bedrock fracture zones (16 per

Calderas and caldera structures: a review

NASA Astrophysics Data System (ADS)

Cole, J. W.; Milner, D. M.; Spinks, K. D.

2005-02-01

Calderas are important features in all volcanic environments and are commonly the sites of geothermal activity and mineralisation. Yet, it is only in the last 25 years that a thorough three-dimensional study of calderas has been carried out, utilising studies of eroded calderas, geophysical analysis of their structures and analogue modelling of caldera formation. As more data has become available on calderas, their individuality has become apparent. A distinction between 'caldera', 'caldera complex', 'cauldron', and 'ring structure' is necessary, and new definitions are given in this paper. Descriptions of calderas, based on dominant composition of eruptives (basaltic, peralkaline, andesitic-dacitic, rhyolitic) can be used, and characteristics of each broad group are given. Styles of eruption may be effusive or explosive, with the former dominant in basaltic calderas, and the latter dominant in andesitic-dacitic, rhyolitic and peralkaline calderas. Four 'end-member' collapse styles occur—plate or piston, piecemeal, trapdoor, and downsag—but many calderas have multiple styles. Features of so-called 'funnel' and 'chaotic' calderas proposed in the literature can be explained by other collapse styles and the terms are considered unnecessary. Ground deformation comprises subsidence or collapse (essential characteristics of a caldera) and uplifting/doming and fracturing due to tumescence and/or resurgence (frequent, but not essential). Collapse may occur on pre-existing structures, such as regional faults or on faults created during the caldera formation, and the shape of the collapse area will be influenced by depth, size and shape of the magma chamber. The final morphology of a caldera will depend on how the caldera floor breaks up; whether collapse takes place in one event or multiple events, whether vertical movement is spasmodic or continuous throughout the eruptive sequence, and whether blocks subside uniformly or chaotically at one or more collapse centres. A meaningful description of any caldera should therefore include; number of collapse events, presence or absence of resurgence, caldera-floor coherency, caldera-floor collapse geometry, and dominant composition of eruptives.

Sub-surface structures and collapse mechanisms of summit pit craters

NASA Astrophysics Data System (ADS)

Roche, O.; van Wyk de Vries, B.; Druitt, T. H.

2001-01-01

Summit pit craters are found in many types of volcanoes and are generally thought to be the product of collapse into an underpressured reservoir caused by magma withdrawal. We investigate the mechanisms and structures associated with summit pit crater formation by scaled analogue experiments and make comparisons with natural examples. Models use a sand plaster mixture as analogue rock over a cylinder of silicone simulating an underpressured magma reservoir. Experiments are carried out using different roof aspect ratios (roof thickness/roof width) of 0.2-2. They reveal two basic collapse mechanisms, dependant on the roof aspect ratio. One occurs at low aspect ratios (≤1), as illustrated by aspect ratios of 0.2 and 1. Outward dipping reverse faults initiated at the silicone margins propagates through the entire roof thickness and cause subsidence of a coherent block. Collapse along the reverse faults is accommodated by marginal flexure of the block and tension fractures at the surface (aspect ratio of 0.2) or by the creation of inward dipping normal faults delimiting a terrace (aspect ratio of 1). At an aspect ratio of 1, overhanging pit walls are the surface expressions of the reverse faults. Experiments at high aspect ratio (>1.2) reveal a second mechanism. In this case, collapse occurs by stopping, which propagates upwards by a complex pattern of both reverse faults and tension fractures. The initial underground collapse is restricted to a zone above the reservoir and creates a cavity with a stable roof above it. An intermediate mechanism occurs at aspect ratios of 1.1-1.2. In this case, stopping leads to the formation of a cavity with a thin and unstable roof, which collapses suddenly. The newly formed depression then exhibits overhanging walls. Surface morphology and structure of natural examples, such as the summit pit craters at Masaya Volcano, Nicaragua, have many of the features created in the models, indicating that the internal structural geometry of experiments can be applied to real examples. In particular, the surface area and depth of the underpressured reservoir can be roughly estimated. We present a morphological analysis of summit pit craters at volcanoes such as Kilimanjaro (Tanzania), San Cristobal, Telica and Masaya (Nicaragua), and Ubinas (Peru), and indicate a likely type of subsidence and possible position of the former magma reservoir responsible for collapse in each case.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

Approaches to Numerical Relativity

NASA Astrophysics Data System (ADS)

d'Inverno, Ray

2005-07-01

Introduction Ray d'Inverno; Preface C. J. S. Clarke; Part I. Theoretical Approaches: 1. Numerical relativity on a transputer array Ray d'Inverno; 2. Some aspects of the characteristic initial value problem in numerical relativity Nigel Bishop; 3. The characteristic initial value problem in general relativity J. M. Stewart; 4. Algebraic approachs to the characteristic initial value problem in general relativity Jõrg Frauendiener; 5. On hyperboidal hypersurfaces Helmut Friedrich; 6. The initial value problem on null cones J. A. Vickers; 7. Introduction to dual-null dynamics S. A. Hayward; 8. On colliding plane wave space-times J. B. Griffiths; 9. Boundary conditions for the momentum constraint Niall O Murchadha; 10. On the choice of matter model in general relativity A. D. Rendall; 11. A mathematical approach to numerical relativity J. W. Barrett; 12. Making sense of the effects of rotation in general relativity J. C. Miller; 13. Stability of charged boson stars and catastrophe theory Franz E. Schunck, Fjodor V. Kusmartsev and Eckehard W. Mielke; Part II. Practical Approaches: 14. Numerical asymptotics R. Gómez and J. Winicour; 15. Instabilities in rapidly rotating polytropes Scott C. Smith and Joan M. Centrella; 16. Gravitational radiation from coalescing binary neutron stars Ken-Ichi Oohara and Takashi Nakamura; 17. 'Critical' behaviour in massless scalar field collapse M. W. Choptuik; 18. Goudunov-type methods applied to general relativistic gravitational collapse José Ma. Ibánez, José Ma. Martí, Juan A. Miralles and J. V. Romero; 19. Astrophysical sources of gravitational waves and neutrinos Silvano Bonazzola, Eric Gourgoulhon, Pawel Haensel and Jean-Alain Marck; 20. Gravitational radiation from triaxial core collapse Jean-Alain Marck and Silvano Bonazzola; 21. A vacuum fully relativistic 3D numerical code C. Bona and J. Massó; 22. Solution of elliptic equations in numerical relativity using multiquadrics M. R. Dubal, S. R. Oliveira and R. A. Matzner; 23. Self-gravitating thin disks around rotating black holes A. Lanza; 24. An ADI and causal reconnection Gabrielle D. Allen and Bernard F. Schutz; 25. Time-symmetric ADI and causal reconnection Miguel Alcubierre and Bernard F. Schutz; 26. The numerical study of topological defects E. P. S. Shellard; 27. Computations of bubble growth during the cosmological quark-hadron transition J. C. Miller and O. Pantano; 28. Initial data of axisymmetric gravitational waves with a cosmological constant Ken-Ichi Nakao, Kei-Ichi Maeda, Takashi Nakamura and Ken-Ichi Oohara.

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Updating the debate on model complexity

USGS Publications Warehouse

Simmons, Craig T.; Hunt, Randall J.

2012-01-01

As scientists who are trying to understand a complex natural world that cannot be fully characterized in the field, how can we best inform the society in which we live? This founding context was addressed in a special session, “Complexity in Modeling: How Much is Too Much?” convened at the 2011 Geological Society of America Annual Meeting. The session had a variety of thought-provoking presentations—ranging from philosophy to cost-benefit analyses—and provided some areas of broad agreement that were not evident in discussions of the topic in 1998 (Hunt and Zheng, 1999). The session began with a short introduction during which model complexity was framed borrowing from an economic concept, the Law of Diminishing Returns, and an example of enjoyment derived by eating ice cream. Initially, there is increasing satisfaction gained from eating more ice cream, to a point where the gain in satisfaction starts to decrease, ending at a point when the eater sees no value in eating more ice cream. A traditional view of model complexity is similar—understanding gained from modeling can actually decrease if models become unnecessarily complex. However, oversimplified models—those that omit important aspects of the problem needed to make a good prediction—can also limit and confound our understanding. Thus, the goal of all modeling is to find the “sweet spot” of model sophistication—regardless of whether complexity was added sequentially to an overly simple model or collapsed from an initial highly parameterized framework that uses mathematics and statistics to attain an optimum (e.g., Hunt et al., 2007). Thus, holistic parsimony is attained, incorporating “as simple as possible,” as well as the equally important corollary “but no simpler.”

Spherical collapse and virialization in f ( T ) gravities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Rui-Hui; Zhai, Xiang-Hua; Li, Xin-Zhou, E-mail: 1000379711@smail.shnu.edu.cn, E-mail: zhaixh@shnu.edu.cn, E-mail: kychz@shnu.edu.cn

2017-03-01

Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in f ( T ) gravities. In particular, three concrete models, which have been tested against the observation of large-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of f ( T ) gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in themore » magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in f ( T ) gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.« less

Tsunamis caused by submarine slope failures along western Great Bahama Bank

PubMed Central

Schnyder, Jara S.D.; Eberli, Gregor P.; Kirby, James T.; Shi, Fengyan; Tehranirad, Babak; Mulder, Thierry; Ducassou, Emmanuelle; Hebbeln, Dierk; Wintersteller, Paul

2016-01-01

Submarine slope failures are a likely cause for tsunami generation along the East Coast of the United States. Among potential source areas for such tsunamis are submarine landslides and margin collapses of Bahamian platforms. Numerical models of past events, which have been identified using high-resolution multibeam bathymetric data, reveal possible tsunami impact on Bimini, the Florida Keys, and northern Cuba. Tsunamis caused by slope failures with terminal landslide velocity of 20 ms−1 will either dissipate while traveling through the Straits of Florida, or generate a maximum wave of 1.5 m at the Florida coast. Modeling a worst-case scenario with a calculated terminal landslide velocity generates a wave of 4.5 m height. The modeled margin collapse in southwestern Great Bahama Bank potentially has a high impact on northern Cuba, with wave heights between 3.3 to 9.5 m depending on the collapse velocity. The short distance and travel time from the source areas to densely populated coastal areas would make the Florida Keys and Miami vulnerable to such low-probability but high-impact events. PMID:27811961

Characteristic Structure of Star-forming Clouds

NASA Astrophysics Data System (ADS)

Myers, Philip C.

2015-06-01

This paper presents a new method to diagnose the star-forming potential of a molecular cloud region from the probability density function of its column density (N-pdf). This method provides expressions for the column density and mass profiles of a symmetric filament having the same N-pdf as a filamentary region. The central concentration of this characteristic filament can distinguish regions and can quantify their fertility for star formation. Profiles are calculated for N-pdfs which are pure lognormal, pure power law, or a combination. In relation to models of singular polytropic cylinders, characteristic filaments can be unbound, bound, or collapsing depending on their central concentration. Such filamentary models of the dynamical state of N-pdf gas are more relevant to star-forming regions than are spherical collapse models. The star formation fertility of a bound or collapsing filament is quantified by its mean mass accretion rate when in radial free fall. For a given mass per length, the fertility increases with the filament mean column density and with its initial concentration. In selected regions the fertility of their characteristic filaments increases with the level of star formation.

Tsunamis caused by submarine slope failures along western Great Bahama Bank

NASA Astrophysics Data System (ADS)

Schnyder, Jara S. D.; Eberli, Gregor P.; Kirby, James T.; Shi, Fengyan; Tehranirad, Babak; Mulder, Thierry; Ducassou, Emmanuelle; Hebbeln, Dierk; Wintersteller, Paul

2016-11-01

Submarine slope failures are a likely cause for tsunami generation along the East Coast of the United States. Among potential source areas for such tsunamis are submarine landslides and margin collapses of Bahamian platforms. Numerical models of past events, which have been identified using high-resolution multibeam bathymetric data, reveal possible tsunami impact on Bimini, the Florida Keys, and northern Cuba. Tsunamis caused by slope failures with terminal landslide velocity of 20 ms-1 will either dissipate while traveling through the Straits of Florida, or generate a maximum wave of 1.5 m at the Florida coast. Modeling a worst-case scenario with a calculated terminal landslide velocity generates a wave of 4.5 m height. The modeled margin collapse in southwestern Great Bahama Bank potentially has a high impact on northern Cuba, with wave heights between 3.3 to 9.5 m depending on the collapse velocity. The short distance and travel time from the source areas to densely populated coastal areas would make the Florida Keys and Miami vulnerable to such low-probability but high-impact events.

Tsunamis caused by submarine slope failures along western Great Bahama Bank.

PubMed

Schnyder, Jara S D; Eberli, Gregor P; Kirby, James T; Shi, Fengyan; Tehranirad, Babak; Mulder, Thierry; Ducassou, Emmanuelle; Hebbeln, Dierk; Wintersteller, Paul

2016-11-04

Submarine slope failures are a likely cause for tsunami generation along the East Coast of the United States. Among potential source areas for such tsunamis are submarine landslides and margin collapses of Bahamian platforms. Numerical models of past events, which have been identified using high-resolution multibeam bathymetric data, reveal possible tsunami impact on Bimini, the Florida Keys, and northern Cuba. Tsunamis caused by slope failures with terminal landslide velocity of 20 ms -1 will either dissipate while traveling through the Straits of Florida, or generate a maximum wave of 1.5 m at the Florida coast. Modeling a worst-case scenario with a calculated terminal landslide velocity generates a wave of 4.5 m height. The modeled margin collapse in southwestern Great Bahama Bank potentially has a high impact on northern Cuba, with wave heights between 3.3 to 9.5 m depending on the collapse velocity. The short distance and travel time from the source areas to densely populated coastal areas would make the Florida Keys and Miami vulnerable to such low-probability but high-impact events.

Basic processes and factors determining the evolution of collapse sinkholes: a sensitivity study

NASA Astrophysics Data System (ADS)

Romanov, Douchko; Kaufmann, Georg

2017-04-01

Collapse sinkholes appear as closed depressions at the surface. The origin of these karst features is related to the continuous dissolution of the soluble rock caused by a focussed sub-surface flow. Water flowing along a preferential pathway through fissures and fractures within the phreatic part of a karst aquifer is able to dissolve the rock (limestone, gypsum, anhydrite). With time, the dissolved void volume increases and part of the ceiling above the stream can become unstable, collapses, and accumulates as debris in the flow path. The debris partially blocks the flow and thus activates new pathways. Because of the low compaction of the debris (high hydraulic conductivity), the flow and the dissolution rates within this crushed zone remain high. This allows a relatively fast dissolutional and erosional removal of the crushed material and the development of new empty voids. The void volume expands upwards towards the surface until a collapse sinkhole is formed. The collapse sinkholes exhibit a large variety of shapes (cylindrical, cone-, bowl-shaped), depths (from few to few hundred meters) and diameters (meters up to hundreds of meters). Two major processes are responsible for this diversity: a) the karst evolution of the aquifer - responsible for the dissolutional and erosional removal of material; b) the mechanical evolution of the host rock and the existence of structural features, faults for example, which determine the stability and the magnitude of the subsequent collapses. In this work we demonstrate the influence of the host rock type, the hydrological and geological boundary conditions, the chemical composition of the flowing water, and the geometry and the scale of the crushed zone, on the location and the evolution of the growing sinkhole. We demonstrate the ability of the karst evolution models to explain, at least qualitatively, the growth and the morphology of the collapse sinkholes and to roughly predict their shape and location. Implementing simple rules that describe the mechanical collapse, we come to the conclusion that a complete quantitative and qualitative description of a collapse sinkhole is possible, but for this it is necessary to take into account also the mechanical properties of the rock and the processes determining the mechanics of the collapses.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

ERIC Educational Resources Information Center

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

ERIC Educational Resources Information Center

Charpin, J. P. F.; O'Hara, S.; Mackey, D.

2013-01-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Comparison of learning models based on mathematics logical intelligence in affective domain

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Constructing a patient-specific computer model of the upper airway in sleep apnea patients.

PubMed

Dhaliwal, Sandeep S; Hesabgar, Seyyed M; Haddad, Seyyed M H; Ladak, Hanif; Samani, Abbas; Rotenberg, Brian W

2018-01-01

The use of computer simulation to develop a high-fidelity model has been proposed as a novel and cost-effective alternative to help guide therapeutic intervention in sleep apnea surgery. We describe a computer model based on patient-specific anatomy of obstructive sleep apnea (OSA) subjects wherein the percentage and sites of upper airway collapse are compared to findings on drug-induced sleep endoscopy (DISE). Basic science computer model generation. Three-dimensional finite element techniques were undertaken for model development in a pilot study of four OSA patients. Magnetic resonance imaging was used to capture patient anatomy and software employed to outline critical anatomical structures. A finite-element mesh was applied to the volume enclosed by each structure. Linear and hyperelastic soft-tissue properties for various subsites (tonsils, uvula, soft palate, and tongue base) were derived using an inverse finite-element technique from surgical specimens. Each model underwent computer simulation to determine the degree of displacement on various structures within the upper airway, and these findings were compared to DISE exams performed on the four study patients. Computer simulation predictions for percentage of airway collapse and site of maximal collapse show agreement with observed results seen on endoscopic visualization. Modeling the upper airway in OSA patients is feasible and holds promise in aiding patient-specific surgical treatment. NA. Laryngoscope, 128:277-282, 2018. © 2017 The American Laryngological, Rhinological and Otological Society, Inc.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Use of Structure-from-Motion Photogrammetry Technique to model Danxia red bed landform slope stability by discrete element modeling - case study at Mt. Langshan, Hunan Province, China

NASA Astrophysics Data System (ADS)

Simonson, Scott; Hua, Peng; Luobin, Yan; Zhi, Chen

2016-04-01

Important to the evolution of Danxia landforms is how the rock cliffs are in large part shaped by rock collapse events, ranging from small break offs to large collapses. Quantitative research of Danxia landform evolution is still relatively young. In 2013-2014, Chinese and Slovak researchers conducted joint research to measure deformation of two large rock walls. In situ measurements of one rock wall found it to be stable, and Ps-InSAR measurements of the other were too few to be validated. Research conducted this year by Chinese researchers modeled the stress states of a stone pillar at Mt. Langshan, in Hunan Province, that toppled over in 2009. The model was able to demonstrate how stress states within the pillar changed as the soft basal layer retreated, but was not able to show the stress states at the point of complete collapse. According to field observations, the back side of the pillar fell away from the entire cliff mass before the complete collapse, and no models have been able to demonstrate the mechanisms behind this behavior. A further understanding of the mechanisms controlling rockfall events in Danxia landforms is extremely important because these stunning sceneries draw millions of tourists each year. Protecting the tourists and the infrastructure constructed to accommodate tourism is of utmost concern. This research will employ a UAV to as universally as possible photograph a stone pillar at Mt. Langshan that stands next to where the stone pillar collapsed in 2009. Using the recently developed structure-from-motion technique, a 3D model of the pillar will be constructed in order to extract geometrical data of the entire slope and its structural fabric. Also in situ measurements will be taken of the slope's toe during the field work exercises. These data are essential to constructing a realistic discrete element model using the 3DEC code and perform a kinematic analysis of the rock mass. Intact rock behavior will be based on the Mohr Coulomb Plasticity Model. Physical and mechanical parameters of the continuum and discontinuum elements will be gathered from laboratory experiments and used as constitutive criteria parameters within the 3DEC model. This research hopes to show how easily and relatively cheaply previously unaccessible Danxia landform geometrical data can be obtained using readily available photographic and software technologies. Also, obtaining a clearer quantitative understanding of the mechanisms controlling slope failure in Danxia landscapes will help future land planners appropriately take advantage of these outstanding scenic sites.

Axisymmetric simulations of magnetorotational core collapse: approximate inclusion of general relativistic effects

NASA Astrophysics Data System (ADS)

Obergaulinger, M.; Aloy, M. A.; Dimmelmeier, H.; Müller, E.

2006-10-01

We continue our investigations of the magnetorotational collapse of stellar cores by discussing simulations performed with a modified Newtonian gravitational potential that mimics general relativistic effects. The approximate TOV gravitational potential used in our simulations captures several basic features of fully relativistic simulations quite well. In particular, it is able to correctly reproduce the behavior of models that show a qualitative change both of the dynamics and the gravitational wave signal when switching from Newtonian to fully relativistic simulations. For models where the dynamics and gravitational wave signals are already captured qualitatively correctly by a Newtonian potential, the results of the Newtonian and the approximate TOV models differ quantitatively. The collapse proceeds to higher densities with the approximate TOV potential, allowing for a more efficient amplification of the magnetic field by differential rotation. The strength of the saturation fields (˜ 1015 ~ G at the surface of the inner core) is a factor of two to three higher than in Newtonian gravity. Due to the more efficient field amplification, the influence of magnetic fields is considerably more pronounced than in the Newtonian case for some of the models. As in the Newtonian case, sufficiently strong magnetic fields slow down the core's rotation and trigger a secular contraction phase to higher densities. More clearly than in Newtonian models, the collapsed cores of these models exhibit two different kinds of shock generation. Due to magnetic braking, a first shock wave created during the initial centrifugal bounce at subnuclear densities does not suffice for ejecting any mass, and the temporarily stabilized core continues to collapse to supranuclear densities. Another stronger shock wave is generated during the second bounce as the core exceeds nuclear matter density. The gravitational wave signal of these models does not fit into the standard classification. Therefore, in the first paper of this series we introduced a new type of gravitational wave signal, which we call type IV or “magnetic type”. This signal type is more frequent for the approximate relativistic potential than for the Newtonian one. Most of our weak-field models are marginally detectable with the current LIGO interferometer for a source located at a distance of 10 kpc. Strongly magnetized models emit a substantial fraction of their GW power at very low frequencies. A flat spectrum between 10 Hz and ⪉ 100 kHz denotes the generation of a jet-like hydromagnetic outflow.

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

PubMed

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Automatic mathematical modeling for real time simulation program (AI application)

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

The Explosion Mechanism of Core-Collapse Supernovae: Progress in Supernova Theory and Experiments

DOE PAGES

Foglizzo, Thierry; Kazeroni, Rémi; Guilet, Jérôme; ...

2015-01-01

The explosion of core-collapse supernova depends on a sequence of events taking place in less than a second in a region of a few hundred kilometers at the center of a supergiant star, after the stellar core approaches the Chandrasekhar mass and collapses into a proto-neutron star, and before a shock wave is launched across the stellar envelope. Theoretical efforts to understand stellar death focus on the mechanism which transforms the collapse into an explosion. Progress in understanding this mechanism is reviewed with particular attention to its asymmetric character. We highlight a series of successful studies connecting observations of supernovamore » remnants and pulsars properties to the theory of core-collapse using numerical simulations. The encouraging results from first principles models in axisymmetric simulations is tempered by new puzzles in 3D. The diversity of explosion paths and the dependence on the pre-collapse stellar structure is stressed, as well as the need to gain a better understanding of hydrodynamical and MHD instabilities such as SASI and neutrino-driven convection. The shallow water analogy of shock dynamics is presented as a comparative system where buoyancy effects are absent. This dynamical system can be studied numerically and also experimentally with a water fountain. Lastly, we analyse the potential of this complementary research tool for supernova theory. We also review its potential for public outreach in science museums.« less

THE THREE-DIMENSIONAL EVOLUTION TO CORE COLLAPSE OF A MASSIVE STAR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Couch, Sean M.; Chatzopoulos, Emmanouil; Arnett, W. David

2015-07-20

We present the first three-dimensional (3D) simulation of the final minutes of iron core growth in a massive star, up to and including the point of core gravitational instability and collapse. We capture the development of strong convection driven by violent Si burning in the shell surrounding the iron core. This convective burning builds the iron core to its critical mass and collapse ensues, driven by electron capture and photodisintegration. The non-spherical structure and motion generated by 3D convection is substantial at the point of collapse, with convective speeds of several hundreds of km s{sup −1}. We examine the impactmore » of such physically realistic 3D initial conditions on the core-collapse supernova mechanism using 3D simulations including multispecies neutrino leakage and find that the enhanced post-shock turbulence resulting from 3D progenitor structure aids successful explosions. We conclude that non-spherical progenitor structure should not be ignored, and should have a significant and favorable impact on the likelihood for neutrino-driven explosions. In order to make simulating the 3D collapse of an iron core feasible, we were forced to make approximations to the nuclear network making this effort only a first step toward accurate, self-consistent 3D stellar evolution models of the end states of massive stars.« less

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

USGS Publications Warehouse

Raghunandan, Meera; Liel, Abbie B.; Luco, Nicolas

2015-01-01

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock-damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post-earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures.

The Explosion Mechanism of Core-Collapse Supernovae: Progress in Supernova Theory and Experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Foglizzo, Thierry; Kazeroni, Rémi; Guilet, Jérôme

The explosion of core-collapse supernova depends on a sequence of events taking place in less than a second in a region of a few hundred kilometers at the center of a supergiant star, after the stellar core approaches the Chandrasekhar mass and collapses into a proto-neutron star, and before a shock wave is launched across the stellar envelope. Theoretical efforts to understand stellar death focus on the mechanism which transforms the collapse into an explosion. Progress in understanding this mechanism is reviewed with particular attention to its asymmetric character. We highlight a series of successful studies connecting observations of supernovamore » remnants and pulsars properties to the theory of core-collapse using numerical simulations. The encouraging results from first principles models in axisymmetric simulations is tempered by new puzzles in 3D. The diversity of explosion paths and the dependence on the pre-collapse stellar structure is stressed, as well as the need to gain a better understanding of hydrodynamical and MHD instabilities such as SASI and neutrino-driven convection. The shallow water analogy of shock dynamics is presented as a comparative system where buoyancy effects are absent. This dynamical system can be studied numerically and also experimentally with a water fountain. Lastly, we analyse the potential of this complementary research tool for supernova theory. We also review its potential for public outreach in science museums.« less

The heart works against gravity

NASA Technical Reports Server (NTRS)

Seymour, R. S.; Hargens, A. R.; Pedley, T. J.

1993-01-01

The circulatory systems of vertebrate animals are closed, and blood leaves and returns to the heart at the same level. It is often concluded, therefore, that the heart works only against the viscous resistance of the system, not against gravity, even in vascular loops above the heart in which the siphon principle operates. However, we argue that the siphon principle does not assist blood flow in superior vascular loops if any of the descending vasculature is collapsible. If central arterial blood pressure is insufficient to support a blood column between the heart and the head, blood flow ceases because of vascular collapse. Furthermore, the siphon principle does not assist the heart even when a continuous stream of blood is flowing in a superior loop. The potential energy gained by blood as it is pumped to the head is lost to friction in partially collapsed descending vessels and thus is not regained. Application of the Poiseuille equation to flow in collapsible vessels is limited; resistance depends on flow rate in partially collapsed vessels with no transmural pressure difference, but flow rate is independent of resistance. Thus the pressure developed by the heart to establish a given flow rate is independent of the resistance occurring in the partially collapsed vessels. The pressure depends only on the height of the blood column and the resistance in the noncollapsed parts of the system. Simple laboratory models, involving water flow in collapsible tubing, dispel the idea that the siphon principle facilitates blood flow and suggest that previously published results may have been affected by experimental artifact.

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

How stands collapse I

NASA Astrophysics Data System (ADS)

Pearle, Philip

2007-03-01

In this volume in honour of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. Ten problems are introduced, nine of which were seen following my initial work. Four of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's spontaneous localization (SL) model (which added one more problem). This stimulated a (somewhat different) resolution of these five problems in the continuous spontaneous localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honour of Abner Shimony, I shall discuss the status of the remaining five post-CSL problems.

Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials

DOE PAGES

Sun, WaiChing; Chen, Qiushi; Ostien, Jakob T.

2013-11-22

A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses.

Improved models of stellar core collapse and still no explosions: what is missing?

PubMed

Buras, R; Rampp, M; Janka, H-Th; Kifonidis, K

2003-06-20

Two-dimensional hydrodynamic simulations of stellar core collapse are presented which for the first time were performed by solving the Boltzmann equation for the neutrino transport including a state-of-the-art description of neutrino interactions. Stellar rotation is also taken into account. Although convection develops below the neutrinosphere and in the neutrino-heated region behind the supernova shock, the models do not explode. This suggests missing physics, possibly with respect to the nuclear equation of state and weak interactions in the subnuclear regime. However, it might also indicate a fundamental problem with the neutrino-driven explosion mechanism.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Understand rotating isothermal collapses yet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tohline, J.E.

1985-01-01

A scalar virial equation is used to describe the dynamic properties of equilibrium gas clouds, taking into account the relative effects of surface pressure, rotation, self gravity and internal isothermal pressure. Details concerning the internal structure of the clouds are ignored in order to obtain a globalized analytical expression. The obtained solution to the equation is found to agree with the surface-pressure-dominated model of Stahler (1983), and the rotation-dominated model of Hayashi, Narita, and Miyama (1982). On the basis of the analytical expression of virial equilibrium in the clouds, some of the limiting properties of isothermal clouds are described, andmore » a realistic starting model for cloud collapse is proposed. 18 references.« less

Equations of state for neutron stars and core-collapse supernovae

NASA Astrophysics Data System (ADS)

Oertel, Micaela; Providência, Constança

2018-04-01

Modelling compact stars is a complex task which depends on many ingredients, among others the properties of dense matter. In this contribution models for the equation of state (EoS) of dense matter will be discussed, relevant for the description of core-collapse supernovae, compact stars and compact star mergers. Such EoS models have to cover large ranges in baryon number density, temperature and isospin asymmetry. The characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or quarks. Some implications for compact star astrophysics will be highlighted, too.

A Systematic Study of Explosions in Core Collapse Supernovae

NASA Technical Reports Server (NTRS)

Swesty, F. Douglas; Mihalas, Dimitri; Norman, Michael

1997-01-01

This report covers the research conducted from September 1996 to August 1997 (eighteen months into the three year grant). We have obtained a number of significant findings based on the on the work that we have conducted under this grant during the past year. As we stated in our original proposal the work has focused on multi-dimensional models of the convective epoch in core collapse supernovae. During the past year we have developed a large number of models of the convective epoch in 2-D under two levels of neutrino transport approximation and we are currently working on 3-D models. In the following pages will endeavor to give brief descriptions of our results.

Characterizing SRAM Single Event Upset in Terms of Single and Double Node Charge Collection

NASA Technical Reports Server (NTRS)

Black, J. D.; Ball, D. R., II; Robinson, W. H.; Fleetwood, D. M.; Schrimpf, R. D.; Reed, R. A.; Black, D. A.; Warren, K. M.; Tipton, A. D.; Dodd, P. E.;