Entanglement dynamics in short- and long-range harmonic oscillators

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, M. Ghasemi; Rajabpour, M. A.

2014-11-01

We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as 1 /rd +α with the distance r . After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and Rényi entropies. We show that for 1 <α <2 we have a linear growth of entanglement and then saturation independent of the initial state. For 0 <α <1 depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

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

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Local reduction of certain wave operators to one-dimensional form

NASA Technical Reports Server (NTRS)

Roe, Philip

1994-01-01

It is noted that certain common linear wave operators have the property that linear variation of the initial data gives rise to one-dimensional evolution in a plane defined by time and some direction in space. The analysis is given For operators arising in acoustics, electromagnetics, elastodynamics, and an abstract system.

Stabilization and control of distributed systems with time-dependent spatial domains

NASA Technical Reports Server (NTRS)

Wang, P. K. C.

1990-01-01

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

Complexity and health professions education: a basic glossary.

PubMed

Mennin, Stewart

2010-08-01

The study of health professions education in the context of complexity science and complex adaptive systems involves different concepts and terminology that are likely to be unfamiliar to many health professions educators. A list of selected key terms and definitions from the literature of complexity science is provided to assist readers to navigate familiar territory from a different perspective. include agent, attractor, bifurcation, chaos, co-evolution, collective variable, complex adaptive systems, complexity science, deterministic systems, dynamical system, edge of chaos, emergence, equilibrium, far from equilibrium, fuzzy boundaries, linear system, non-linear system, random, self-organization and self-similarity.

Decoherence in quantum systems in a static gravitational field

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Loran, Farhang

2016-09-01

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Evolution of complex dynamics

NASA Astrophysics Data System (ADS)

Wilds, Roy; Kauffman, Stuart A.; Glass, Leon

2008-09-01

We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.

Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces

NASA Astrophysics Data System (ADS)

Licht, Christian; Tran Thu Ha

2005-02-01

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).

Dynamics of one-dimensional self-gravitating systems using Hermite-Legendre polynomials

NASA Astrophysics Data System (ADS)

Barnes, Eric I.; Ragan, Robert J.

2014-01-01

The current paradigm for understanding galaxy formation in the Universe depends on the existence of self-gravitating collisionless dark matter. Modelling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective non-linear dynamics of many particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyse the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase-space distribution functions f(x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.

Convergent evolution and mimicry of protein linear motifs in host-pathogen interactions.

PubMed

Chemes, Lucía Beatriz; de Prat-Gay, Gonzalo; Sánchez, Ignacio Enrique

2015-06-01

Pathogen linear motif mimics are highly evolvable elements that facilitate rewiring of host protein interaction networks. Host linear motifs and pathogen mimics differ in sequence, leading to thermodynamic and structural differences in the resulting protein-protein interactions. Moreover, the functional output of a mimic depends on the motif and domain repertoire of the pathogen protein. Regulatory evolution mediated by linear motifs can be understood by measuring evolutionary rates, quantifying positive and negative selection and performing phylogenetic reconstructions of linear motif natural history. Convergent evolution of linear motif mimics is widespread among unrelated proteins from viral, prokaryotic and eukaryotic pathogens and can also take place within individual protein phylogenies. Statistics, biochemistry and laboratory models of infection link pathogen linear motifs to phenotypic traits such as tropism, virulence and oncogenicity. In vitro evolution experiments and analysis of natural sequences suggest that changes in linear motif composition underlie pathogen adaptation to a changing environment. Copyright © 2015 Elsevier Ltd. All rights reserved.

Unscrambling the lead model ages

NASA Astrophysics Data System (ADS)

Albarede, Francis; Martine, Juteau

1984-01-01

A linear relation is derived for the secular evolution of 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb ratios, that permits tests to be made for open system evolution on each system independently. Application of the method to conformable ore bodies of various geological age indicates that the available data do not demand an open system evolution for the last 3.8 b.y. 238U/204Pb and 232Th/204Pb of 9.66 ± 0.15 and 37.65 ± 1.14 respectively fit best the data for this time interval. A single stage evolution since 4.5 b.y. is unlikely, however, and the major events of continent formation postdate the Earth accretion by at least 400 m.y. The larger scatter of 207Pb/204Pb data about the evolution line relative to the other isotopic ratios is also interpreted as resulting from a series of continental differentiation events taking place at 3.85 ± 0.15 b.y.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

A Sequential Ensemble Prediction System at Convection Permitting Scales

NASA Astrophysics Data System (ADS)

Milan, M.; Simmer, C.

2012-04-01

A Sequential Assimilation Method (SAM) following some aspects of particle filtering with resampling, also called SIR (Sequential Importance Resampling), is introduced and applied in the framework of an Ensemble Prediction System (EPS) for weather forecasting on convection permitting scales, with focus to precipitation forecast. At this scale and beyond, the atmosphere increasingly exhibits chaotic behaviour and non linear state space evolution due to convectively driven processes. One way to take full account of non linear state developments are particle filter methods, their basic idea is the representation of the model probability density function by a number of ensemble members weighted by their likelihood with the observations. In particular particle filter with resampling abandons ensemble members (particles) with low weights restoring the original number of particles adding multiple copies of the members with high weights. In our SIR-like implementation we substitute the likelihood way to define weights and introduce a metric which quantifies the "distance" between the observed atmospheric state and the states simulated by the ensemble members. We also introduce a methodology to counteract filter degeneracy, i.e. the collapse of the simulated state space. To this goal we propose a combination of resampling taking account of simulated state space clustering and nudging. By keeping cluster representatives during resampling and filtering, the method maintains the potential for non linear system state development. We assume that a particle cluster with initially low likelihood may evolve in a state space with higher likelihood in a subsequent filter time thus mimicking non linear system state developments (e.g. sudden convection initiation) and remedies timing errors for convection due to model errors and/or imperfect initial condition. We apply a simplified version of the resampling, the particles with highest weights in each cluster are duplicated; for the model evolution for each particle pair one particle evolves using the forward model; the second particle, however, is nudged to the radar and satellite observation during its evolution based on the forward model.

The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

DTIC Science & Technology

1984-01-01

5.5) respectively (5.3) and (5.8) which means that u(t) - 0 respectively v(t) - 0 for t > o. The evolution of the systems (5.1) and (5.3) in terms ...input/output delays; and b) the general theory is presented in such a way that it applies to both . . ... ..- Lr parabolic and hyperbolic I P9es as...particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Linear entropy and collapse–revival phenomenon for a general formalism N-type four-level atom interacting with a single-mode field

NASA Astrophysics Data System (ADS)

Eied, A. A.

2018-05-01

In this paper, the linear entropy and collapse-revival phenomenon through the relation (< {\\hat{a}}+{\\hat{a}} > -{\\bar{n}}) in a system of N-configuration four-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling functional are investigated. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent states and the atom initially in its most upper excited state. The dynamical behavior of the linear entropy and the time evolution of (< {\\hat{a}}+ {\\hat{a}} > -{\\bar{n}}) are analyzed. In particular, the effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy and the evolution of (< {\\hat{a}}+ {\\hat{a}} > -{\\bar{n}}) are examined.

Linear Optics Simulation of Quantum Non-Markovian Dynamics

PubMed Central

Chiuri, Andrea; Greganti, Chiara; Mazzola, Laura; Paternostro, Mauro; Mataloni, Paolo

2012-01-01

The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects. PMID:23236588

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO{sub 2} dissolution in water

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

Outeda, R.; D'Onofrio, A.; El Hasi, C.

Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a colormore » indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.« less

Optimum Damping in a Non-Linear Base Isolation System

NASA Astrophysics Data System (ADS)

Jangid, R. S.

1996-02-01

Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.

Electronic Nose For Measuring Wine Evolution In Wine Cellars

NASA Astrophysics Data System (ADS)

Lozano, J.; Santos, J. P.; Horrillo, M. C.; Cabellos, J. M.; Arroyo, T.

2009-05-01

An electronic nose installed in a wine cellar for measuring the wine evolution is presented in this paper. The system extract the aroma directly from the tanks where wine is stored and carry the volatile compounds to the sensors cell. A tin oxide multisensor, prepared with RF sputtering onto an alumina substrate and doped with chromium and indium, is used. The whole system is fully automated and controlled by computer and can be supervised by internet. Linear techniques like principal component analysis (PCA) and nonlinear ones like probabilistic neural networks (PNN) are used for pattern recognition. Results show that system can detect the evolution of two different wines along 9 months stored in tanks. This system could be trained to detect off-odours of wine and warn the wine expert to correct it as soon as possible, improving the final quality of wine.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Evolution of Linux operating system network

NASA Astrophysics Data System (ADS)

Xiao, Guanping; Zheng, Zheng; Wang, Haoqin

2017-01-01

Linux operating system (LOS) is a sophisticated man-made system and one of the most ubiquitous operating systems. However, there is little research on the structure and functionality evolution of LOS from the prospective of networks. In this paper, we investigate the evolution of the LOS network. 62 major releases of LOS ranging from versions 1.0 to 4.1 are modeled as directed networks in which functions are denoted by nodes and function calls are denoted by edges. It is found that the size of the LOS network grows almost linearly, while clustering coefficient monotonically decays. The degree distributions are almost the same: the out-degree follows an exponential distribution while both in-degree and undirected degree follow power-law distributions. We further explore the functionality evolution of the LOS network. It is observed that the evolution of functional modules is shown as a sequence of seven events (changes) succeeding each other, including continuing, growth, contraction, birth, splitting, death and merging events. By means of a statistical analysis of these events in the top 4 largest components (i.e., arch, drivers, fs and net), it is shown that continuing, growth and contraction events occupy more than 95% events. Our work exemplifies a better understanding and describing of the dynamics of LOS evolution.

Towards a non-linear theory for fluid pressure and osmosis in shales

NASA Astrophysics Data System (ADS)

Droghei, Riccardo; Salusti, Ettore

2015-04-01

In exploiting deep hydrocarbon reservoirs, often injections of fluid and/or solute are used. To control and avoid troubles as fluid and gas unexpected diffusions, a reservoir characterization can be obtained also from observations of space and time evolution of micro-earthquake clouds resulting from such injections. This is important since several among the processes caused by fluid injections can modify the deep matrix. Information about the evolution of such micro-seismicity clouds therefore plays a realistic role in the reservoir analyses. To reach a better insight about such processes, and obtain a better system control, we here analyze the initial stress necessary to originate strong non linear transients of combined fluid pressure and solute density (osmosis) in a porous matrix. All this can indeed perturb in a mild (i.e. a linear diffusion) or dramatic non linear way the rock structure, till inducing rock deformations, micro-earthquakes or fractures. I more detail we here assume first a linear Hooke law relating strain, stress, solute density and fluid pressure, and analyze their effect in the porous rock dynamics. Then we analyze its generalization, i.e. the further non linear effect of a stronger external pressure, also in presence of a trend of pressure or solute in the whole region. We moreover characterize the zones where a sudden arrival of such a front can cause micro-earthquakes or fractures. All this allows to reach a novel, more realistic insight about the control of rock evolution in presence of strong pressure fronts. We thus obtain a more efficient reservoir control to avoid large geological perturbations. It is of interest that our results are very similar to those found by Shapiro et al.(2013) with a different approach.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

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

Asplund, Curtis T., E-mail: ca2621@columbia.edu; Berenstein, David, E-mail: dberens@physics.ucsb.edu

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate themore » dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.« less

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Age constraints on the evolution of the Quetico belt, Superior Province, Ontario

NASA Technical Reports Server (NTRS)

Percival, J. A.; Sullivan, R. W.

1986-01-01

Much attention has been focused on the nature of Archean tectonic processes and the extent to which they were different from modern rigid-plate tectonics. The Archean Superior Province has linear metavolcanic and metasediment-dominated subprovinces of similar scale to cenozoic island arc-trench systems of the western Pacific, suggesting an origin by accreting arcs. Models of the evolution of metavolcanic belts in parts of the Superior Province suggest an arc setting but the tectonic environment and evolution of the intervening metasedimentary belts are poorly understood. In addition to explaining the setting giving rise to a linear sedimentary basin, models must account for subsequent shortening and high-temperature, low-pressure metamorphism. Correlation of rock units and events in adjacent metavolcanic and metasedimentary belts is a first step toward understanding large-scale crustal interactions. To this end, zircon geochronology has been applied to metavolcanic belts of the western Superior Province; new age data for the Quetico metasedimentary belt is reported, permitting correlation with the adjacent Wabigoon and Wawa metavolcanic subprovinces.

Comparing TCV experimental VDE responses with DINA code simulations

NASA Astrophysics Data System (ADS)

Favez, J.-Y.; Khayrutdinov, R. R.; Lister, J. B.; Lukash, V. E.

2002-02-01

The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current Ip, the elongation κ, the triangularity δ, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma βp, and the internal self inductance li also show acceptable agreement. The evolution of the growth rate γ is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.

[Scale Relativity Theory in living beings morphogenesis: fratal, determinism and chance].

PubMed

Chaline, J

2012-10-01

The Scale Relativity Theory has many biological applications from linear to non-linear and, from classical mechanics to quantum mechanics. Self-similar laws have been used as model for the description of a huge number of biological systems. Theses laws may explain the origin of basal life structures. Log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps. The existence of such a law does not mean that the role of chance in evolution is reduced, but instead that randomness and contingency may occur within a framework which may itself be structured in a partly statistical way. The scale relativity theory can open new perspectives in evolution. Copyright © 2012 Elsevier Masson SAS. All rights reserved.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system

NASA Astrophysics Data System (ADS)

Jonsson, Thorsteinn H.; Manolescu, Andrei; Goan, Hsi-Sheng; Abdullah, Nzar Rauf; Sitek, Anna; Tang, Chi-Shung; Gudmundsson, Vidar

2017-11-01

Master equations are commonly used to describe time evolution of open systems. We introduce a general computationally efficient method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time-dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The efficiency of the approach allows us to place the bias window defined by the external leads high into the many-body spectrum of the cavity photon-dressed states of the central system revealing a cascade of intermediate transitions as the system relaxes to a steady state. The very diverse relaxation times present in the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many orders of magnitude. In our approach, the generalized master equation is mapped from a many-body Fock space of states to a Liouville space of transitions. We show that this results in a linear equation which is solved exactly through an eigenvalue analysis, which supplies information on the steady state and the time evolution of the system.

Experimental evidence for an effect of early-diagenetic interaction between labile and refractory marine sedimentary organic matter on nitrogen dynamics

NASA Astrophysics Data System (ADS)

Turnewitsch, Robert; Domeyer, Bettina; Graf, Gerhard

2007-05-01

In most natural sedimentary systems labile and refractory organic material (OM) occur concomitantly. Little, however, is known on how different kinds of OM interact and how such interactions affect early diagenesis in sediments. In a simple sediment experiment, we investigated how interactions of OM substrates of different degradability affect benthic nitrogen (N) dynamics. Temporal evolution of a set of selected biogeochemical parameters was monitored in sandy sediment over 116 days in three experimental set-ups spiked with labile OM (tissue of Mytilus edulis), refractory OM (mostly aged Zostera marina and macroalgae), and a 1:1 mixture of labile and refractory OM. The initial amounts of particulate organic carbon (POC) were identical in the three set-ups. To check for non-linear interactions between labile and refractory OM, the evolution of the mixture system was compared with the evolution of the simple sum of the labile and refractory systems, divided by two. The sum system is the experimental control where labile and refractory OM are virtually combined but not allowed to interact. During the first 30 days there was evidence for net dissolved-inorganic-nitrogen (DIN) production followed by net DIN consumption. (Here 'DIN' is the sum of ammonium, nitrite and nitrate.) After ˜ 30 days a quasi steady state was reached. Non-linear interactions between the two types of OM were reflected by three main differences between the early-diagenetic evolutions of nitrogen dynamics of the mixture and sum (control) systems: (1) In the mixture system the phases of net DIN production and consumption commenced more rapidly and were more intense. (2) The mixture system was shifted towards a more oxidised state of DIN products [as indicated by increased (nitrite + nitrate)/(ammonium) ratios]. (3) There was some evidence that more OM, POC and particulate nitrogen were preserved in the mixture system. That is, in the mixture system more particulate OM was preserved while a higher proportion of the decomposed particulate N was converted into inorganic N. It can be concluded that during the first days and weeks of early diagenesis the magnitude and composition of the flux of decompositional dissolved N-compounds from sediments into the overlying water was influenced by non-linear interactions of OM substrates of different degradability. Given these experimental results it is likely that the relative spatial distributions of OM of differing degradability in sediments control the magnitude and composition of the return flux of dissolved N-bearing compounds from sediments into the overlying water column.

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

Model predictive control of P-time event graphs

NASA Astrophysics Data System (ADS)

Hamri, H.; Kara, R.; Amari, S.

2016-12-01

This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.

Emergent properties of gene evolution: Species as attractors in phenotypic space

NASA Astrophysics Data System (ADS)

Reuveni, Eli; Giuliani, Alessandro

2012-02-01

The question how the observed discrete character of the phenotype emerges from a continuous genetic distance metrics is the core argument of two contrasted evolutionary theories: punctuated equilibrium (stable evolution scattered with saltations in the phenotype) and phyletic gradualism (smooth and linear evolution of the phenotype). Identifying phenotypic saltation on the molecular levels is critical to support the first model of evolution. We have used DNA sequences of ∼1300 genes from 6 isolated populations of the budding yeast Saccharomyces cerevisiae. We demonstrate that while the equivalent measure of the genetic distance show a continuum between lineage distance with no evidence of discrete states, the phenotypic space illustrates only two (discrete) possible states that can be associated with a saltation of the species phenotype. The fact that such saltation spans large fraction of the genome and follows by continuous genetic distance is a proof of the concept that the genotype-phenotype relation is not univocal and may have severe implication when looking for disease related genes and mutations. We used this finding with analogy to attractor-like dynamics and show that punctuated equilibrium could be explained in the framework of non-linear dynamics systems.

An idealised study for the long term evolution of crescentic bars

NASA Astrophysics Data System (ADS)

Chen, W. L.; Dodd, N.; Tiessen, M. C. H.; Calvete, D.

2018-01-01

An idealised study that identifies the mechanisms in the long term evolution of crescentic bar systems in nature is presented. Growth to finite amplitude (i.e., equilibration, sometimes referred to as saturation) and higher harmonic interaction are hypothesised to be the leading nonlinear effects in long-term evolution of these systems. These nonlinear effects are added to a linear stability model and used to predict crescentic bar development along a beach in Duck, North Carolina (USA) over a 2-month period. The equilibration prolongs the development of bed patterns, thus allowing the long term evolution. Higher harmonic interaction enables the amplitude to be transferred from longer to shorter lengthscales, which leads to the dominance of shorter lengthscales in latter post-storm stages, as observed at Duck. The comparison with observations indicates the importance of higher harmonic interaction in the development of nearshore crescentic bar systems in nature. Additionally, it is concluded that these nonlinear effects should be included in models simulating the development of different bed patterns, and that this points a way forward for long-term morphodynamical modelling in general.

Experimental tests of coherence and entanglement conservation under unitary evolutions

NASA Astrophysics Data System (ADS)

Černoch, Antonín; Bartkiewicz, Karol; Lemr, Karel; Soubusta, Jan

2018-04-01

We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based on a linear optical controlled-phase quantum gate and the second scheme utilizes effects of nonlinear optics. Our experiment allows one to verify the relation between correlations of the subsystems and the coherence of the composite system, which was given in terms of a conservation law for maximal accessible coherence by Svozilík et al. [J. Svozilík et al., Phys. Rev. Lett. 115, 220501 (2015), 10.1103/PhysRevLett.115.220501]. We observe that the maximal accessible coherence is conserved for the implemented class of global evolutions of the composite system.

Stability of the IMEX Methods, CNLF and BDF2-AB2, for Uncoupling Systems of Evolution Equations

DTIC Science & Technology

2011-02-01

Implicit-Explicit linear multistep methods, Tech. rep., Centrum Wiskunde and Informatica (CWI) (1996). [14] W. Hundsdorfer, J. Verwer, Numerical...component splitting for the Crank-Nicolson Leap- Frog integration method, Tech. rep., Centrum Wiskunde and Informatica (CWI) (2009). [23] J. Verwer

Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

NASA Astrophysics Data System (ADS)

Sander, Tobias; Kresse, Georg

2017-02-01

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Modeling elastic anisotropy in strained heteroepitaxy

NASA Astrophysics Data System (ADS)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to < 1 0 5 > facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Evolution of branched regulatory genetic pathways: directional selection on pleiotropic loci accelerates developmental system drift.

PubMed

Johnson, Norman A; Porter, Adam H

2007-01-01

Developmental systems are regulated by a web of interacting loci. One common and useful approach in studying the evolution of development is to focus on classes of interacting elements within these systems. Here, we use individual-based simulations to study the evolution of traits controlled by branched developmental pathways involving three loci, where one locus regulates two different traits. We examined the system under a variety of selective regimes. In the case where one branch was under stabilizing selection and the other under directional selection, we observed "developmental system drift": the trait under stabilizing selection showed little phenotypic change even though the loci underlying that trait showed considerable evolutionary divergence. This occurs because the pleiotropic locus responds to directional selection and compensatory mutants are then favored in the pathway under stabilizing selection. Though developmental system drift may be caused by other mechanisms, it seems likely that it is accelerated by the same underlying genetic mechanism as that producing the Dobzhansky-Muller incompatibilities that lead to speciation in both linear and branched pathways. We also discuss predictions of our model for developmental system drift and how different selective regimes affect probabilities of speciation in the branched pathway system.

Instability of isolated planar shock waves

DTIC Science & Technology

2007-06-07

Note that multi-mode perturbations can be treated by the inclusion of additional terms in Eq. (4), but owing to the linear independence of the... Volterra equation Figure 4 shows five examples of the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by...showing the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by numerically solving the Volterra equation in

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

NASA Astrophysics Data System (ADS)

Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko

2018-03-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Many-to-one form-to-function mapping weakens parallel morphological evolution.

PubMed

Thompson, Cole J; Ahmed, Newaz I; Veen, Thor; Peichel, Catherine L; Hendry, Andrew P; Bolnick, Daniel I; Stuart, Yoel E

2017-11-01

Evolutionary ecologists aim to explain and predict evolutionary change under different selective regimes. Theory suggests that such evolutionary prediction should be more difficult for biomechanical systems in which different trait combinations generate the same functional output: "many-to-one mapping." Many-to-one mapping of phenotype to function enables multiple morphological solutions to meet the same adaptive challenges. Therefore, many-to-one mapping should undermine parallel morphological evolution, and hence evolutionary predictability, even when selection pressures are shared among populations. Studying 16 replicate pairs of lake- and stream-adapted threespine stickleback (Gasterosteus aculeatus), we quantified three parts of the teleost feeding apparatus and used biomechanical models to calculate their expected functional outputs. The three feeding structures differed in their form-to-function relationship from one-to-one (lower jaw lever ratio) to increasingly many-to-one (buccal suction index, opercular 4-bar linkage). We tested for (1) weaker linear correlations between phenotype and calculated function, and (2) less parallel evolution across lake-stream pairs, in the many-to-one systems relative to the one-to-one system. We confirm both predictions, thus supporting the theoretical expectation that increasing many-to-one mapping undermines parallel evolution. Therefore, sole consideration of morphological variation within and among populations might not serve as a proxy for functional variation when multiple adaptive trait combinations exist. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Entanglement tsunami: universal scaling in holographic thermalization.

PubMed

Liu, Hong; Suh, S Josephine

2014-01-10

We consider the time evolution of entanglement entropy after a global quench in a strongly coupled holographic system, whose subsequent equilibration is described in the gravity dual by the gravitational collapse of a thin shell of matter resulting in a black hole. In the limit of large regions of entanglement, the evolution of entanglement entropy is controlled by the geometry around and inside the event horizon of the black hole, resulting in regimes of pre-local-equilibration quadratic growth (in time), post-local-equilibration linear growth, a late-time regime in which the evolution does not carry memory of the size and shape of the entangled region, and a saturation regime with critical behavior resembling those in continuous phase transitions. Collectively, these regimes suggest a picture of entanglement growth in which an "entanglement tsunami" carries entanglement inward from the boundary. We also make a conjecture on the maximal rate of entanglement growth in relativistic systems.

Evolution of wetting layer in InAs/GaAs quantum dot system

PubMed Central

Ye, XL; Wang, ZG

2006-01-01

For InAs/GaAs quantum dot system, the evolution of the wetting layer (WL) with the InAs deposition thickness has been studied by reflectance difference spectroscopy (RDS). Two transitions related to the heavy- and light-hole in the WL have been distinguished in RD spectra. Taking into account the strain and segregation effects, a model has been presented to deduce the InAs amount in the WL and the segregation coefficient of the indium atoms from the transition energies of heavy- and light-holes. The variation of the InAs amount in the WL and the segregation coefficient are found to rely closely on the growth modes. In addition, the huge dots also exhibits a strong effect on the evolution of the WL. The observed linear dependence of In segregation coefficient upon the InAs amount in the WL demonstrates that the segregation is enhanced by the strain in the WL.

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Tauber, Uwe C.

2012-02-01

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.

Solar System Dynamics

NASA Technical Reports Server (NTRS)

Wisdom, Jack

2002-01-01

In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.

Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems.

PubMed

Ait Ouarabi, Mohand; Antonaci, Paola; Boubenider, Fouad; Gliozzi, Antonio S; Scalerandi, Marco

2017-01-07

Alkaline solutions, such as sodium, potassium or lithium silicates, appear to be very promising as healing agents for the development of encapsulated self-healing concretes. However, the evolution of their mechanical and acoustic properties in time has not yet been completely clarified, especially regarding their behavior and related kinetics when they are used in the form of a thin layer in contact with a hardened cement matrix. This study aims to monitor, using linear and nonlinear ultrasonic methods, the evolution of a sodium silicate solution interacting with a cement matrix in the presence of localized cracks. The ultrasonic inspection via linear methods revealed that an almost complete recovery of the elastic and acoustic properties occurred within a few days of healing. The nonlinear ultrasonic measurements contributed to provide further insight into the kinetics of the recovery due to the presence of the healing agent. A good regain of mechanical performance was ascertained through flexural tests at the end of the healing process, confirming the suitability of sodium silicate as a healing agent for self-healing cementitious systems.

A physically based connection between fractional calculus and fractal geometry

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

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Microbial detection method based on sensing molecular hydrogen

NASA Technical Reports Server (NTRS)

Wilkins, J. R.; Stoner, G. E.; Boykin, E. H.

1974-01-01

A simple method for detecting bacteria, based on the time of hydrogen evolution, was developed and tested against various members of the Enterobacteriaceae group. The test system consisted of (1) two electrodes, platinum and a reference electrode, (2) a buffer amplifier, and (3) a strip-chart recorder. Hydrogen evolution was measured by an increase in voltage in the negative (cathodic) direction. A linear relationship was established between inoculum size and the time hydrogen was detected (lag period). Lag times ranged from 1 h for 1 million cells/ml to 7 h for 1 cell/ml. For each 10-fold decrease in inoculum, length of the lag period increased 60 to 70 min. Based on the linear relationship between inoculum and lag period, these results indicate the potential application of the hydrogen-sensing method for rapidly detecting coliforms and other gas-producing microorganisms in a variety of clinical, food, and other samples.

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

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

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

Signatures of Pleiotropy, Economy and Convergent Evolution in a Domain-Resolved Map of Human–Virus Protein–Protein Interaction Networks

PubMed Central

Garamszegi, Sara; Franzosa, Eric A.; Xia, Yu

2013-01-01

A central challenge in host-pathogen systems biology is the elucidation of general, systems-level principles that distinguish host-pathogen interactions from within-host interactions. Current analyses of host-pathogen and within-host protein-protein interaction networks are largely limited by their resolution, treating proteins as nodes and interactions as edges. Here, we construct a domain-resolved map of human-virus and within-human protein-protein interaction networks by annotating protein interactions with high-coverage, high-accuracy, domain-centric interaction mechanisms: (1) domain-domain interactions, in which a domain in one protein binds to a domain in a second protein, and (2) domain-motif interactions, in which a domain in one protein binds to a short, linear peptide motif in a second protein. Analysis of these domain-resolved networks reveals, for the first time, significant mechanistic differences between virus-human and within-human interactions at the resolution of single domains. While human proteins tend to compete with each other for domain binding sites by means of sequence similarity, viral proteins tend to compete with human proteins for domain binding sites in the absence of sequence similarity. Independent of their previously established preference for targeting human protein hubs, viral proteins also preferentially target human proteins containing linear motif-binding domains. Compared to human proteins, viral proteins participate in more domain-motif interactions, target more unique linear motif-binding domains per residue, and contain more unique linear motifs per residue. Together, these results suggest that viruses surmount genome size constraints by convergently evolving multiple short linear motifs in order to effectively mimic, hijack, and manipulate complex host processes for their survival. Our domain-resolved analyses reveal unique signatures of pleiotropy, economy, and convergent evolution in viral-host interactions that are otherwise hidden in the traditional binary network, highlighting the power and necessity of high-resolution approaches in host-pathogen systems biology. PMID:24339775

Flight control optimization from design to assessment application on the Cessna Citation X business aircraft =

NASA Astrophysics Data System (ADS)

Boughari, Yamina

New methodologies have been developed to optimize the integration, testing and certification of flight control systems, an expensive process in the aerospace industry. This thesis investigates the stability of the Cessna Citation X aircraft without control, and then optimizes two different flight controllers from design to validation. The aircraft's model was obtained from the data provided by the Research Aircraft Flight Simulator (RAFS) of the Cessna Citation business aircraft. To increase the stability and control of aircraft systems, optimizations of two different flight control designs were performed: 1) the Linear Quadratic Regulation and the Proportional Integral controllers were optimized using the Differential Evolution algorithm and the level 1 handling qualities as the objective function. The results were validated for the linear and nonlinear aircraft models, and some of the clearance criteria were investigated; and 2) the Hinfinity control method was applied on the stability and control augmentation systems. To minimize the time required for flight control design and its validation, an optimization of the controllers design was performed using the Differential Evolution (DE), and the Genetic algorithms (GA). The DE algorithm proved to be more efficient than the GA. New tools for visualization of the linear validation process were also developed to reduce the time required for the flight controller assessment. Matlab software was used to validate the different optimization algorithms' results. Research platforms of the aircraft's linear and nonlinear models were developed, and compared with the results of flight tests performed on the Research Aircraft Flight Simulator. Some of the clearance criteria of the optimized H-infinity flight controller were evaluated, including its linear stability, eigenvalues, and handling qualities criteria. Nonlinear simulations of the maneuvers criteria were also investigated during this research to assess the Cessna Citation X's flight controller clearance, and therefore, for its anticipated certification.

Signatures of pleiotropy, economy and convergent evolution in a domain-resolved map of human-virus protein-protein interaction networks.

PubMed

Garamszegi, Sara; Franzosa, Eric A; Xia, Yu

2013-01-01

A central challenge in host-pathogen systems biology is the elucidation of general, systems-level principles that distinguish host-pathogen interactions from within-host interactions. Current analyses of host-pathogen and within-host protein-protein interaction networks are largely limited by their resolution, treating proteins as nodes and interactions as edges. Here, we construct a domain-resolved map of human-virus and within-human protein-protein interaction networks by annotating protein interactions with high-coverage, high-accuracy, domain-centric interaction mechanisms: (1) domain-domain interactions, in which a domain in one protein binds to a domain in a second protein, and (2) domain-motif interactions, in which a domain in one protein binds to a short, linear peptide motif in a second protein. Analysis of these domain-resolved networks reveals, for the first time, significant mechanistic differences between virus-human and within-human interactions at the resolution of single domains. While human proteins tend to compete with each other for domain binding sites by means of sequence similarity, viral proteins tend to compete with human proteins for domain binding sites in the absence of sequence similarity. Independent of their previously established preference for targeting human protein hubs, viral proteins also preferentially target human proteins containing linear motif-binding domains. Compared to human proteins, viral proteins participate in more domain-motif interactions, target more unique linear motif-binding domains per residue, and contain more unique linear motifs per residue. Together, these results suggest that viruses surmount genome size constraints by convergently evolving multiple short linear motifs in order to effectively mimic, hijack, and manipulate complex host processes for their survival. Our domain-resolved analyses reveal unique signatures of pleiotropy, economy, and convergent evolution in viral-host interactions that are otherwise hidden in the traditional binary network, highlighting the power and necessity of high-resolution approaches in host-pathogen systems biology.

Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Manipulation of a photonic quantum memory

NASA Astrophysics Data System (ADS)

Reagor, Matthew; Pfaff, Wolfgang; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Albert, Victor V.; Frunzio, Luigi; Devoret, Michel H.; Jiang, Liang; Schoelkopf, Robert J.

2015-03-01

Recent advances in circuit QED have shown great potential for using microwave resonators as quantum memories. In particular, it is possible to encode the state of a quantum bit in non-classical photonic states inside a high-Q linear resonator. An outstanding challenge is to perform controlled operations on such a photonic state. We demonstrate experimentally how a continuous drive on a transmon qubit coupled to a high-Q storage resonator can be used to induce non-linear dynamics of the resonator. Tailoring the drive properties allows us to cancel or enhance non-linearities in the system such that we can manipulate the state stored in the cavity. This approach can be used to either counteract undesirable evolution due to the bare Hamiltonian of the system or, ultimately, to perform logical operations on the state encoded in the cavity field. Our method provides a promising pathway towards performing universal control for quantum states stored in high-coherence resonators in the circuit QED platform.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Modeling mutual feedback between users and recommender systems

NASA Astrophysics Data System (ADS)

Zeng, An; Yeung, Chi Ho; Medo, Matúš; Zhang, Yi-Cheng

2015-07-01

Recommender systems daily influence our decisions on the Internet. While considerable attention has been given to issues such as recommendation accuracy and user privacy, the long-term mutual feedback between a recommender system and the decisions of its users has been neglected so far. We propose here a model of network evolution which allows us to study the complex dynamics induced by this feedback, including the hysteresis effect which is typical for systems with non-linear dynamics. Despite the popular belief that recommendation helps users to discover new things, we find that the long-term use of recommendation can contribute to the rise of extremely popular items and thus ultimately narrow the user choice. These results are supported by measurements of the time evolution of item popularity inequality in real systems. We show that this adverse effect of recommendation can be tamed by sacrificing part of short-term recommendation accuracy.

How does non-linear dynamics affect the baryon acoustic oscillation?

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

Sugiyama, Naonori S.; Spergel, David N., E-mail: nao.s.sugiyama@gmail.com, E-mail: dns@astro.princeton.edu

2014-02-01

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do notmore » guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.« less

Wind-accelerated orbital evolution in binary systems with giant stars

NASA Astrophysics Data System (ADS)

Chen, Zhuo; Blackman, Eric G.; Nordhaus, Jason; Frank, Adam; Carroll-Nellenback, Jonathan

2018-01-01

Using 3D radiation-hydrodynamic simulations and analytic theory, we study the orbital evolution of asymptotic giant branch (AGB) binary systems for various initial orbital separations and mass ratios, and thus different initial accretion modes. The time evolution of binary separations and orbital periods are calculated directly from the averaged mass-loss rate, accretion rate and angular momentum loss rate. We separately consider spin-orbit synchronized and zero-spin AGB cases. We find that the angular momentum carried away by the mass loss together with the mass transfer can effectively shrink the orbit when accretion occurs via wind-Roche lobe overflow. In contrast, the larger fraction of mass lost in Bondi-Hoyle-Lyttleton accreting systems acts to enlarge the orbit. Synchronized binaries tend to experience stronger orbital period decay in close binaries. We also find that orbital period decay is faster when we account for the non-linear evolution of the accretion mode as the binary starts to tighten. This can increase the fraction of binaries that result in common envelope, luminous red novae, Type Ia supernovae and planetary nebulae with tight central binaries. The results also imply that planets in the habitable zone around white dwarfs are unlikely to be found.

Rapidity evolution of gluon TMD from low to moderate x

DOE PAGES

Balitsky, Ian; Tarasov, A.

2015-10-05

In this article, we study how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at smallmore » $$x \\ll 1$$ to linear evolution at moderate $$x \\sim 1$$.« less

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

Evolution of Advection Upstream Splitting Method Schemes

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2010-01-01

This paper focuses on the evolution of advection upstream splitting method(AUSM) schemes. The main ingredients that have led to the development of modern computational fluid dynamics (CFD) methods have been reviewed, thus the ideas behind AUSM. First and foremost is the concept of upwinding. Second, the use of Riemann problem in constructing the numerical flux in the finite-volume setting. Third, the necessity of including all physical processes, as characterised by the linear (convection) and nonlinear (acoustic) fields. Fourth, the realisation of separating the flux into convection and pressure fluxes. The rest of this review briefly outlines the technical evolution of AUSM and more details can be found in the cited references. Keywords: Computational fluid dynamics methods, hyperbolic systems, advection upstream splitting method, conservation laws, upwinding, CFD

Analytical optimal pulse shapes obtained with the aid of genetic algorithms

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

Guerrero, Rubén D., E-mail: rdguerrerom@unal.edu.co; Arango, Carlos A.; Reyes, Andrés

2015-09-28

We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding themore » interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions.« less

Race, Culture, and Pluralism: The Evolution of Dewey's Vision for a Democratic Curriculum

ERIC Educational Resources Information Center

Fallace, Thomas

2012-01-01

In this historical study, the author traces the evolution of Dewey's vision for a democratic curriculum. Prior to 1916, Dewey was a linear historicist, meaning that he conceptualized culture as moving linearly through three distinct stages--savagery, barbarianism, civilization--that corresponded with stages of child development. Dewey's suggested…

The Seismic Tool-Kit (STK): an open source software for seismology and signal processing.

NASA Astrophysics Data System (ADS)

Reymond, Dominique

2016-04-01

We present an open source software project (GNU public license), named STK: Seismic ToolKit, that is dedicated mainly for seismology and signal processing. The STK project that started in 2007, is hosted by SourceForge.net, and count more than 19 500 downloads at the date of writing. The STK project is composed of two main branches: First, a graphical interface dedicated to signal processing (in the SAC format (SAC_ASCII and SAC_BIN): where the signal can be plotted, zoomed, filtered, integrated, derivated, ... etc. (a large variety of IFR and FIR filter is proposed). The estimation of spectral density of the signal are performed via the Fourier transform, with visualization of the Power Spectral Density (PSD) in linear or log scale, and also the evolutive time-frequency representation (or sonagram). The 3-components signals can be also processed for estimating their polarization properties, either for a given window, or either for evolutive windows along the time. This polarization analysis is useful for extracting the polarized noises, differentiating P waves, Rayleigh waves, Love waves, ... etc. Secondly, a panel of Utilities-Program are proposed for working in a terminal mode, with basic programs for computing azimuth and distance in spherical geometry, inter/auto-correlation, spectral density, time-frequency for an entire directory of signals, focal planes, and main components axis, radiation pattern of P waves, Polarization analysis of different waves (including noize), under/over-sampling the signals, cubic-spline smoothing, and linear/non linear regression analysis of data set. A MINimum library of Linear AlGebra (MIN-LINAG) is also provided for computing the main matrix process like: QR/QL decomposition, Cholesky solve of linear system, finding eigen value/eigen vectors, QR-solve/Eigen-solve of linear equations systems ... etc. STK is developed in C/C++, mainly under Linux OS, and it has been also partially implemented under MS-Windows. Usefull links: http://sourceforge.net/projects/seismic-toolkit/ http://sourceforge.net/p/seismic-toolkit/wiki/browse_pages/

Slow quench dynamics of a one-dimensional Bose gas confined to an optical lattice.

PubMed

Bernier, Jean-Sébastien; Roux, Guillaume; Kollath, Corinna

2011-05-20

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.

Asymptotic Bounds for Solutions to a System of Damped Integrodifferential Equations of Electromagnetic Theory.

DTIC Science & Technology

1979-05-28

of integrodiffereiTaT~- equations governs the evolution of the components of the electric displacement field in a simple class of rigid holohedral...vacuum so that j — C and J~ — c E , H = B. In0 [3] and [4] this author has treated the evolution equations associated with the Maxwell—Hopkinsofl...F .~~~~~~‘ r - — ~~~~~ ’~~~ “~ I I be viewed as a linearized version of a more general theory introduced by Volterra in 1912 [5] to treat the case

Genome sequence diversity and clues to the evolution of variola (smallpox) virus.

PubMed

Esposito, Joseph J; Sammons, Scott A; Frace, A Michael; Osborne, John D; Olsen-Rasmussen, Melissa; Zhang, Ming; Govil, Dhwani; Damon, Inger K; Kline, Richard; Laker, Miriam; Li, Yu; Smith, Geoffrey L; Meyer, Hermann; Leduc, James W; Wohlhueter, Robert M

2006-08-11

Comparative genomics of 45 epidemiologically varied variola virus isolates from the past 30 years of the smallpox era indicate low sequence diversity, suggesting that there is probably little difference in the isolates' functional gene content. Phylogenetic clustering inferred three clades coincident with their geographical origin and case-fatality rate; the latter implicated putative proteins that mediate viral virulence differences. Analysis of the viral linear DNA genome suggests that its evolution involved direct descent and DNA end-region recombination events. Knowing the sequences will help understand the viral proteome and improve diagnostic test precision, therapeutics, and systems for their assessment.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Parallel dynamics between non-Hermitian and Hermitian systems

NASA Astrophysics Data System (ADS)

Wang, P.; Lin, S.; Jin, L.; Song, Z.

2018-06-01

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system H , there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H , and we present the relations between {H ,H ,H†} .

A mathematical model of marine bacteriophage evolution.

PubMed

Pagliarini, Silvia; Korobeinikov, Andrei

2018-03-01

To explore how particularities of a host cell-virus system, and in particular host cell replication, affect viral evolution, in this paper we formulate a mathematical model of marine bacteriophage evolution. The intrinsic simplicity of real-life phage-bacteria systems, and in particular aquatic systems, for which the assumption of homogeneous mixing is well justified, allows for a reasonably simple model. The model constructed in this paper is based upon the Beretta-Kuang model of bacteria-phage interaction in an aquatic environment (Beretta & Kuang 1998 Math. Biosci. 149 , 57-76. (doi:10.1016/S0025-5564(97)10015-3)). Compared to the original Beretta-Kuang model, the model assumes the existence of a multitude of viral variants which correspond to continuously distributed phenotypes. It is noteworthy that the model is mechanistic (at least as far as the Beretta-Kuang model is mechanistic). Moreover, this model does not include any explicit law or mechanism of evolution; instead it is assumed, in agreement with the principles of Darwinian evolution, that evolution in this system can occur as a result of random mutations and natural selection. Simulations with a simplistic linear fitness landscape (which is chosen for the convenience of demonstration only and is not related to any real-life system) show that a pulse-type travelling wave moving towards increasing Darwinian fitness appears in the phenotype space. This implies that the overall fitness of a viral quasi-species steadily increases with time. That is, the simulations demonstrate that for an uneven fitness landscape random mutations combined with a mechanism of natural selection (for this particular system this is given by the conspecific competition for the resource) lead to the Darwinian evolution. It is noteworthy that in this system the speed of propagation of this wave (and hence the rate of evolution) is not constant but varies, depending on the current viral fitness and the abundance of susceptible bacteria. A specific feature of the original Beretta-Kuang model is that this model exhibits a supercritical Hopf bifurcation, leading to the loss of stability and the rise of self-sustained oscillations in the system. This phenomenon corresponds to the paradox of enrichment in the system. It is remarkable that under the conditions that ensure the bifurcation in the Beretta-Kuang model, the viral evolution model formulated in this paper also exhibits a rise in self-sustained oscillations of the abundance of all interacting populations. The propagation of the travelling wave, however, remains stable under these conditions. The only visible impact of the oscillations on viral evolution is a lower speed of the evolution.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model

NASA Astrophysics Data System (ADS)

Aubert, J.; Fournier, A.

2011-10-01

Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system e-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo.

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Instabilities and finger formation in replacement fronts driven by an oversaturated solution

NASA Astrophysics Data System (ADS)

Kondratiuk, Paweł; Tredak, Hanna; Upadhyay, Virat; Ladd, Anthony J. C.; Szymczak, Piotr

2017-08-01

We consider a simple model of infiltration-driven mineral replacement, in which the chemical coupling between precipitation and dissolution leads to the appearance of a reaction front advancing into the system. Such fronts are usually accompanied by a local increase of porosity. We analyze the linear stability of the replacement front to establish whether such a localized porosity increase can lead to global instability and pattern formation in these systems. We find that for a wide range of control parameters such fronts are unstable. However, both short- and long-wavelength perturbations are stabilized, whereas in a purely dissolutional instability only short wavelengths are stable. We analyze the morphologies of the dissolution patterns emerging in the later stages of the evolution of the system, when the dynamics are beyond the linear regime. Implications of these results for the natural systems are discussed, particularly in the context of karst formation in terra rossa-covered carbonate bedrock.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Dynamical systems for modeling the evolution of the magnetic field of stars and Earth

NASA Astrophysics Data System (ADS)

Popova, H.

2016-02-01

The cycles of solar magnetic activity are connected with a solar dynamo that operates in the convective zone. Solar dynamo mechanism is based on the combined action of the differential rotation and the alpha-effect. Application of these concepts allows us to get an oscillating solution as a wave of the toroidal field propagating from middle latitudes to the equator. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the solar magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the convection zone of the star. It was shown the possibility of coexistence of quiasi-biennial and 22-year cycle. We obtained the different regimes (oscillations, vacillations, dynamo-bursts) depending on the value of the dynamo-number, the meridional circulation, and thickness of the convection zone. We discuss the features of these regimes and compare them with the observed features of evolution of the solar and geo magnetic fields. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

The structural and electrical evolution of graphene by oxygen plasma-induced disorder.

PubMed

Kim, Dong Chul; Jeon, Dae-Young; Chung, Hyun-Jong; Woo, YunSung; Shin, Jai Kwang; Seo, Sunae

2009-09-16

Evolution of a single graphene layer with disorder generated by remote oxygen plasma irradiation is investigated using atomic force microscopy, Raman spectroscopy and electrical measurement. Gradual changes of surface morphology from planar graphene to isolated granular structure associated with a decrease of transconductance are accounted for by two-dimensional percolative conduction by disorder and the oxygen plasma-induced doping effect. The corresponding evolution of Raman spectra of graphene shows several peculiarities such as a sudden appearance of a saturated D peak followed by a linear decrease in its intensity, a relatively inert characteristic of a D' peak and a monotonic increase of a G peak position as the exposure time to oxygen plasma increases. These are discussed in terms of a disorder-induced change of Raman spectra in the graphite system.

Evolution of complexity following a quantum quench in free field theory

NASA Astrophysics Data System (ADS)

Alves, Daniel W. F.; Camilo, Giancarlo

2018-06-01

Using a recent proposal of circuit complexity in quantum field theories introduced by Jefferson and Myers, we compute the time evolution of the complexity following a smooth mass quench characterized by a time scale δ t in a free scalar field theory. We show that the dynamics has two distinct phases, namely an early regime of approximately linear evolution followed by a saturation phase characterized by oscillations around a mean value. The behavior is similar to previous conjectures for the complexity growth in chaotic and holographic systems, although here we have found that the complexity may grow or decrease depending on whether the quench increases or decreases the mass, and also that the time scale for saturation of the complexity is of order δ t (not parametrically larger).

SCM: A method to improve network service layout efficiency with network evolution.

PubMed

Zhao, Qi; Zhang, Chuanhao; Zhao, Zheng

2017-01-01

Network services are an important component of the Internet, which are used to expand network functions for third-party developers. Network function virtualization (NFV) can improve the speed and flexibility of network service deployment. However, with the evolution of the network, network service layout may become inefficient. Regarding this problem, this paper proposes a service chain migration (SCM) method with the framework of "software defined network + network function virtualization" (SDN+NFV), which migrates service chains to adapt to network evolution and improves the efficiency of the network service layout. SCM is modeled as an integer linear programming problem and resolved via particle swarm optimization. An SCM prototype system is designed based on an SDN controller. Experiments demonstrate that SCM could reduce the network traffic cost and energy consumption efficiently.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Irregular Collective Behavior of Heterogeneous Neural Networks

NASA Astrophysics Data System (ADS)

Luccioli, Stefano; Politi, Antonio

2010-10-01

We investigate a network of integrate-and-fire neurons characterized by a distribution of spiking frequencies. Upon increasing the coupling strength, the model exhibits a transition from an asynchronous regime to a nontrivial collective behavior. Numerical simulations of large systems indicate that, at variance with the Kuramoto model, (i) the macroscopic dynamics stays irregular and (ii) the microscopic (single-neuron) evolution is linearly stable.

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Bond, J. Richard; Mersini-Houghton, Laura, E-mail: j.braden@ucl.ac.uk, E-mail: bond@cita.utoronto.ca, E-mail: mersini@physics.unc.edu

2015-08-01

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Department of Physics, University of Toronto,60 St. George Street, Toronto, ON, M5S 3H8; Department of Physics and Astronomy, University College London,Gower Street, London, WC1E 6BT

2015-08-26

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

The effect of sanctions on the evolution of cooperation in linear division of labor.

PubMed

Nakamaru, Mayuko; Shimura, Hayato; Kitakaji, Yoko; Ohnuma, Susumu

2018-01-21

The evolution of cooperation is an unsolved research topic and has been investigated from the viewpoint of not only biology and other natural sciences but also social sciences. Much extant research has focused on the evolution of cooperation among peers. While, different players belonging to different organizations play different social roles, and players playing different social roles cooperate together to achieve their goals. We focus on the evolution of cooperation in linear division of labor that is defined as follows: a player in the i-th role interacts with a player in the i + 1-th role, and a player in the n-th role achieves their goal (1 ≤ i < n) if there are n roles in the division of labor. We take the industrial waste treatment process as an example for illustration. We consider three organizational roles and B i is the i-th role. The player of B i can choose two strategies: legal treatment or illegal dumping, which can be interpreted as cooperation or defection (i = 1-3). With legally required treatment, the player of B j pays a cost to ask the player of B j +1 to treat the waste (j = 1, 2). Then, the cooperator of B j +1 pays a cost to treat the waste properly. With illegal dumping, the player of B i dumps the waste and does not pay any cost (i = 1-3). However, the waste dumped by the defector has negative environmental consequences, which all players in all roles suffer from. This situation is equivalent to a social dilemma encountered in common-pool resource management contexts. The administrative organ in Japan introduces two sanction systems to address the illegal dumping problem: the actor responsibility system and the producer responsibility system. In the actor responsibility system, if players in any role who choose defection are monitored and discovered, they are penalized via a fine. However, it is difficult to monitor and detect the violators, and this system does not work well. While, in the producer responsibility system, the player in B 1 is fined if the player cannot hand the manifest to the local administrative organ because the players of B i (i = 1-3) who choose defection do not hand the manifest to the player of B 1 . We analyze this situation using the replicator equation. We reveal that (1) the three-role model has more empirical credibility than the two-role model including B 1 and B 3 , and (2) the producer responsibility system promotes the evolution of cooperation more than the system without sanctioning. (3) the actor responsibility system does not promote the evolution of cooperation if monitoring and detecting defectors is unsuccessful. Copyright © 2017 Elsevier Ltd. All rights reserved.

Particle number dependence in the non-linear evolution of N-body self-gravitating systems

NASA Astrophysics Data System (ADS)

Benhaiem, D.; Joyce, M.; Sylos Labini, F.; Worrakitpoonpon, T.

2018-01-01

Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large N. Using a study of the evolution from a simple space of spherical initial conditions - including a region characterized by so-called 'radial orbit instability' - we illustrate that the values of N at which such convergence is obtained can vary enormously. In the family of initial conditions we study, good convergence can be obtained up to a few dynamical times with N ∼ 103 - just large enough to suppress two body relaxation - for certain initial conditions, while in other cases such convergence is not attained at this time even in our largest simulations with N ∼ 105. The qualitative difference is due to the stability properties of fluctuations introduced by the N-body discretisation, of which the initial amplitude depends on N. We discuss briefly why the crucial role which such fluctuations can potentially play in the evolution of the N body system could, in particular, constitute a serious problem in cosmological simulations of dark matter.

About Tidal Evolution of Quasi-Periodic Orbits of Satellites

NASA Astrophysics Data System (ADS)

Ershkov, Sergey V.

2017-06-01

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi- periodic cycles via re-inversing of the proper ultra- elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)biology?

PubMed

Jedlicka, Peter

2017-01-01

The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system's behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics.

Physical Properties and Evolution of the Eclipsing Binary System XZ Canis Minoris

NASA Astrophysics Data System (ADS)

Poochaum, R.; Komonjinda, S.; Soonthornthum, B.; Rattanasoon, S.

2010-07-01

This research aims to study the eclipse binary system so that its physical properties and evolution can be determined and used as an example to teach high school astronomy. The study of an eclipsing binary system XZ Canis Minoris (XZ CMi) was done at Sirindhorn Observatory, Chiang Mai University using a 0.5-meter reflecting telescope with CCD photometric system (2184×1417 pixel) in B V and R bands of UVB System. The data obtained were used to construct the light curve for each wavelength band and to compute the times of its light minima. New elements were derived using observations with linear to all available minima. As a result, linear ephemeris is HDJmin I = .578 808 948+/-0.000 000 121+2450 515.321 26+/-0.001 07 E, and the new orbital period of XZ CMi is 0.578 808 948+/-0.000 000 121 day. The values obtained were used with the previously published times of minima to get O-C curve of XZ CMi. The result revealed that the orbital period of XZ CMi is continuously decreased at a rate of 0.007 31+/-0.000 57 sec/year. This result indicates that the binary stars are moving closer continuously. From the O-C residuals, there is significant change to indicate the existence of the third body or magnetic activity cycle on the star. However, further analysis of the physical properties of XZ CMi is required.

Thermalization and its mechanism for generic quantum isolated systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim; Dunjko, Vanja; Rigol, Marcos

2008-05-01

Time dynamics of isolated many-body quantum systems has long been an elusive subject, perhaps most urgently needed in the foundations of quantum statistical mechanics. In generic systems, one expects the nonequilibrium dynamics to lead to thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. The relaxation mechanism is not obvious, however; dynamical chaos cannot play the key role as it does in classical systems since quantum evolution is linear. Here we demonstrateootnotetextM. Rigol, V. Dunjko, and M. Olshanii, to appear in Nature (2008), using the results of an ab initio numerical experiment with 5 hard-core bosons moving in a 5x5 lattice, that in quantum systems thermalization happens not in course of time evolution but instead at the level of individual eigenstates, as first proposed by DeutschootnotetextJ. M. Deutsch, Phys.Rev. A 43, 2046 (1991) and SrednickiootnotetextM. Srednicki, Phys. Rev. E 50, 888 (1994).

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Analyzing systemic risk using non-linear marginal expected shortfall and its minimum spanning tree

NASA Astrophysics Data System (ADS)

Song, Jae Wook; Ko, Bonggyun; Chang, Woojin

2018-02-01

The aim of this paper is to propose a new theoretical framework for analyzing the systemic risk using the marginal expected shortfall (MES) and its correlation-based minimum spanning tree (MST). At first, we develop two parametric models of MES with their closed-form solutions based on the Capital Asset Pricing Model. Our models are derived from the non-symmetric quadratic form, which allows them to consolidate the non-linear relationship between the stock and market returns. Secondly, we discover the evidences related to the utility of our models and the possible association in between the non-linear relationship and the emergence of severe systemic risk by considering the US financial system as a benchmark. In this context, the evolution of MES also can be regarded as a reasonable proxy of systemic risk. Lastly, we analyze the structural properties of the systemic risk using the MST based on the computed series of MES. The topology of MST conveys the presence of sectoral clustering and strong co-movements of systemic risk leaded by few hubs during the crisis. Specifically, we discover that the Depositories are the majority sector leading the connections during the Non-Crisis period, whereas the Broker-Dealers are majority during the Crisis period.

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

First study of the evolution of the SeDeM expert system parameters based on percolation theory: Monitoring of their critical behavior.

PubMed

Galdón, Eduardo; Casas, Marta; Gayango, Manuel; Caraballo, Isidoro

2016-12-01

The deep understanding of products and processes has become a requirement for pharmaceutical industries to follow the Quality by Design principles promoted by the regulatory authorities. With this aim, SeDeM expert system was developed as a useful preformulation tool to predict the likelihood to process drugs and excipients through direct compression. SeDeM system is a step forward in the rational development of a formulation, allowing the normalisation of the rheological parameters and the identification of the weaknesses and strengths of a powder or a powder blend. However, this method is based on the assumption of a linear behavior of disordered systems. As percolation theory has demonstrated, powder blends behave as non-linear systems that can suffer abrupt changes in their properties near to geometrical phase transitions of the components. The aim of this paper was to analyze for the first time the evolution of the SeDeM parameters in drug/excipient powder blends from the point of view of the percolation theory and to compare the changes predicted by SeDeM with the predictions of Percolation theory. For this purpose, powder blends of lactose and theophylline with varying concentrations of the model drug have been prepared and the SeDeM analysis has been applied to each blend in order to monitor the evolution of their properties. On the other hand, percolation thresholds have been estimated for these powder blends where critical points have been found for important rheological parameters as the powder flow. Finally, the predictions of percolation theory and SeDeM have been compared concluding that percolation theory can complement the SeDeM method for a more accurate estimation of the Design Space. Copyright © 2016 Elsevier B.V. All rights reserved.

Long-wave instabilities of two interlaced helical vortices

NASA Astrophysics Data System (ADS)

Quaranta, H. U.; Brynjell-Rahkola, M.; Leweke, T.; Henningson, D. S.

2016-09-01

We present a comparison between experimental observations and theoretical predictions concerning long-wave displacement instabilities of the helical vortices in the wake of a two-bladed rotor. Experiments are performed with a small-scale rotor in a water channel, using a set-up that allows the individual triggering of various instability modes at different azimuthal wave numbers, leading to local or global pairing of successive vortex loops. The initial development of the instability and the measured growth rates are in good agreement with the predictions from linear stability theory, based on an approach where the helical vortex system is represented by filaments. At later times, local pairing develops into large-scale distortions of the vortices, whereas for global pairing the non-linear evolution returns the system almost to its initial geometry.

The stability cycle—A universal pathway for the stability of films over topography

NASA Astrophysics Data System (ADS)

Schörner, Mario; Aksel, Nuri

2018-01-01

In the present study on the linear stability of gravity-driven Newtonian films flowing over inclined topographies, we consider a fundamental question: Is there a universal principle, being valid to describe the parametric evolution of the flow's stability chart for variations of different system parameters? For this sake, we first screened all experimental and numerical stability charts available in the literature. In a second step, we performed experiments to fill the gaps which remained. Variations of the fluid's viscosity and the topography's specific shape, amplitude, wavelength, tip width, and inclination were considered. That way, we identified a set of six characteristic patterns of stability charts to be sufficient to describe and unify all results on the linear stability of Newtonian films flowing over undulated inclines. We unveiled a universal pathway—the stability cycle—along which the linear stability charts of all considered Newtonian films flowing down periodically corrugated inclines evolved when the system parameters were changed.

Phase space analysis in anisotropic optical systems

NASA Technical Reports Server (NTRS)

Rivera, Ana Leonor; Chumakov, Sergey M.; Wolf, Kurt Bernardo

1995-01-01

From the minimal action principle follows the Hamilton equations of evolution for geometric optical rays in anisotropic media. As in classical mechanics of velocity-dependent potentials, the velocity and the canonical momentum are not parallel, but differ by an anisotropy vector potential, similar to that of linear electromagnetism. Descartes' well known diagram for refraction is generalized and a factorization theorem holds for interfaces between two anisotropic media.

Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)biology?

PubMed Central

Jedlicka, Peter

2017-01-01

The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system’s behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics. PMID:29163041

Evolution of circular and linear polarization in scattering environments

DOE PAGES

van der Laan, John D.; Wright, Jeremy Benjamin; Scrymgeour, David A.; ...

2015-12-02

This study quantifies the polarization persistence and memory of circularly polarized light in forward-scattering and isotropic (Rayleigh regime) environments; and for the first time, details the evolution of both circularly and linearly polarized states through scattering environments. Circularly polarized light persists through a larger number of scattering events longer than linearly polarized light for all forward-scattering environments; but not for scattering in the Rayleigh regime. Circular polarization’s increased persistence occurs for both forward and backscattered light. The simulated environments model polystyrene microspheres in water with particle diameters of 0.1 μm, 2.0 μm, and 3.0 μm. The evolution of the polarizationmore » states as they scatter throughout the various environments are illustrated on the Poincaré sphere after one, two, and ten scattering events.« less

Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

DOE PAGES

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...

2016-01-06

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less

SCM: A method to improve network service layout efficiency with network evolution

PubMed Central

Zhao, Qi; Zhang, Chuanhao

2017-01-01

Network services are an important component of the Internet, which are used to expand network functions for third-party developers. Network function virtualization (NFV) can improve the speed and flexibility of network service deployment. However, with the evolution of the network, network service layout may become inefficient. Regarding this problem, this paper proposes a service chain migration (SCM) method with the framework of “software defined network + network function virtualization” (SDN+NFV), which migrates service chains to adapt to network evolution and improves the efficiency of the network service layout. SCM is modeled as an integer linear programming problem and resolved via particle swarm optimization. An SCM prototype system is designed based on an SDN controller. Experiments demonstrate that SCM could reduce the network traffic cost and energy consumption efficiently. PMID:29267299

DNA is structured as a linear "jigsaw puzzle" in the genomes of Arabidopsis, rice, and budding yeast.

PubMed

Liu, Yun-Hua; Zhang, Meiping; Wu, Chengcang; Huang, James J; Zhang, Hong-Bin

2014-01-01

Knowledge of how a genome is structured and organized from its constituent elements is crucial to understanding its biology and evolution. Here, we report the genome structuring and organization pattern as revealed by systems analysis of the sequences of three model species, Arabidopsis, rice and yeast, at the whole-genome and chromosome levels. We found that all fundamental function elements (FFE) constituting the genomes, including genes (GEN), DNA transposable elements (DTE), retrotransposable elements (RTE), simple sequence repeats (SSR), and (or) low complexity repeats (LCR), are structured in a nonrandom and correlative manner, thus leading to a hypothesis that the DNA of the species is structured as a linear "jigsaw puzzle". Furthermore, we showed that different FFE differ in their importance in the formation and evolution of the DNA jigsaw puzzle structure between species. DTE and RTE play more important roles than GEN, LCR, and SSR in Arabidopsis, whereas GEN and RTE play more important roles than LCR, SSR, and DTE in rice. The genes having multiple recognized functions play more important roles than those having single functions. These results provide useful knowledge necessary for better understanding genome biology and evolution of the species and for effective molecular breeding of rice.

Non-minimally coupled quintessence dark energy model with a cubic galileon term: a dynamical system analysis

NASA Astrophysics Data System (ADS)

Bhattacharya, Somnath; Mukherjee, Pradip; Roy, Amit Singha; Saha, Anirban

2018-03-01

We consider a scalar field which is generally non-minimally coupled to gravity and has a characteristic cubic Galilean-like term and a generic self-interaction, as a candidate of a Dark Energy model. The system is dynamically analyzed and novel fixed points with perturbative stability are demonstrated. Evolution of the system is numerically studied near a novel fixed point which owes its existence to the Galileon character of the model. It turns out that demanding the stability of this novel fixed point puts a strong restriction on the allowed non-minimal coupling and the choice of the self-interaction. The evolution of the equation of state parameter is studied, which shows that our model predicts an accelerated universe throughout and the phantom limit is only approached closely but never crossed. Our result thus extends the findings of Coley, Dynamical systems and cosmology. Kluwer Academic Publishers, Boston (2013) for more general NMC than linear and quadratic couplings.

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Reconstruction of DNA sequences using genetic algorithms and cellular automata: towards mutation prediction?

PubMed

Mizas, Ch; Sirakoulis, G Ch; Mardiris, V; Karafyllidis, I; Glykos, N; Sandaltzopoulos, R

2008-04-01

Change of DNA sequence that fuels evolution is, to a certain extent, a deterministic process because mutagenesis does not occur in an absolutely random manner. So far, it has not been possible to decipher the rules that govern DNA sequence evolution due to the extreme complexity of the entire process. In our attempt to approach this issue we focus solely on the mechanisms of mutagenesis and deliberately disregard the role of natural selection. Hence, in this analysis, evolution refers to the accumulation of genetic alterations that originate from mutations and are transmitted through generations without being subjected to natural selection. We have developed a software tool that allows modelling of a DNA sequence as a one-dimensional cellular automaton (CA) with four states per cell which correspond to the four DNA bases, i.e. A, C, T and G. The four states are represented by numbers of the quaternary number system. Moreover, we have developed genetic algorithms (GAs) in order to determine the rules of CA evolution that simulate the DNA evolution process. Linear evolution rules were considered and square matrices were used to represent them. If DNA sequences of different evolution steps are available, our approach allows the determination of the underlying evolution rule(s). Conversely, once the evolution rules are deciphered, our tool may reconstruct the DNA sequence in any previous evolution step for which the exact sequence information was unknown. The developed tool may be used to test various parameters that could influence evolution. We describe a paradigm relying on the assumption that mutagenesis is governed by a near-neighbour-dependent mechanism. Based on the satisfactory performance of our system in the deliberately simplified example, we propose that our approach could offer a starting point for future attempts to understand the mechanisms that govern evolution. The developed software is open-source and has a user-friendly graphical input interface.

Decomposition of fluctuating initial conditions and flow harmonics

NASA Astrophysics Data System (ADS)

Qian, Wei-Liang; Mota, Philipe; Andrade, Rone; Gardim, Fernando; Grassi, Frédérique; Hama, Yogiro; Kodama, Takeshi

2014-01-01

Collective flow observed in heavy-ion collisions is largely attributed to initial geometrical fluctuations, and it is the hydrodynamic evolution of the system that transforms those initial spatial irregularities into final state momentum anisotropies. Cumulant analysis provides a mathematical tool to decompose those initial fluctuations in terms of radial and azimuthal components. It is usually thought that a specified order of azimuthal cumulant, for the most part, linearly produces flow harmonics of the same order. In this work, by considering the most central collisions (0%-5%), we carry out a systematic study on the connection between cumulants and flow harmonics using a hydrodynamic code called NeXSPheRIO. We conduct three types of calculation, by explicitly decomposing the initial conditions into components corresponding to a given eccentricity and studying the out-coming flow through hydrodynamic evolution. It is found that for initial conditions deviating significantly from Gaussian, such as those from NeXuS, the linearity between eccentricities and flow harmonics partially breaks down. Combined with the effect of coupling between cumulants of different orders, it causes the production of extra flow harmonics of higher orders. We argue that these results can be seen as a natural consequence of the non-linear nature of hydrodynamics, and they can be understood intuitively in terms of the peripheral-tube model.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Sculpting Pickering Emulsion Droplets by Arrest and Jamming

NASA Astrophysics Data System (ADS)

Burke, Christopher; Wei, Zengyi; Caggioni, Marco; Spicer, Patrick; Atherton, Tim

Pickering emulsion droplets can be arrested into non-spherical shapes--useful for applications such as active delivery--through a general mechanism of deformation followed by absorption of additional colloidal particles onto the interface, relaxation of the droplet caused by surface tension and arrest at some point due to crowding of the particles. We perform simulations of the arrest process to clarify the relative importance of diffusive rearrangement of particles and collective forcing due to surface evolution. Experiment and theory are compared, giving insight into the stability of the resulting capsules and the robustness of the production process for higher-throughput production in, for example, microfluidic systems. We adapt theoretical tools from the jamming literature to better understand the arrested configurations and long timescale evolution of the system: using linear programming and a penalty function approach, we identify unjamming motions in kinetically arrested states. We propose a paradigm of ``metric jamming'' to describe the limiting behavior of this class of system: a structure is metric-jammed if it is stable with respect to collective motion of the particles as well as evolution of the hypersurface on which the packing is embedded. Supported by a Cottrell Award from the Research Corporation for Science Advancement.

Imperfect information facilitates the evolution of reciprocity.

PubMed

Kurokawa, Shun

2016-06-01

The existence of cooperation demands explanation since cooperation is costly to the actor. Reciprocity has long been regarded as a potential explanatory mechanism for the existence of cooperation. Reciprocity is a mechanism wherein a cooperator responds to an opponent's behavior by switching his/her own behavior. Hence, a possible problematic case relevant to the theory of reciprocity evolution arises when the mechanism is such that the information regarding an opponent's behavior is imperfect. Although it has been confirmed also by previous theoretical studies that imperfect information interferes with the evolution of reciprocity, this argument is based on the assumption that there are no mistakes in behavior. And, a previous study presumed that it might be expected that when such mistakes occur, reciprocity can more readily evolve in the case of imperfect information than in the case of perfect information. The reason why the previous study considers so is that in the former case, reciprocators can miss defections incurred by other reciprocators' mistakes due to imperfect information, allowing cooperation to persist when such reciprocators meet. However, contrary to this expectation, the previous study has shown that even when mistakes occur, imperfect information interferes with the evolution of reciprocity. Nevertheless, the previous study assumed that payoffs are linear (i.e., that the effect of behavior is additive and there are no synergetic effects). In this study, we revisited the same problem but removed the assumption that payoffs are linear. We used evolutionarily stable strategy analysis to compare the condition for reciprocity to evolve when mistakes occur and information is imperfect with the condition for reciprocity to evolve when mistakes occur and information is perfect. Our study revealed that when payoffs are not linear, imperfect information can facilitate the evolution of reciprocity when mistakes occur; while when payoffs are linear, imperfect information disturbs the evolution of reciprocity even when mistakes occur. Imperfect information can encourage the evolution of cooperation. Copyright © 2016 Elsevier Inc. All rights reserved.

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

The Evolution of Data-Information-Knowledge-Wisdom in Nursing Informatics.

PubMed

Ronquillo, Charlene; Currie, Leanne M; Rodney, Paddy

2016-01-01

The data-information-knowledge-wisdom (DIKW) model has been widely adopted in nursing informatics. In this article, we examine the evolution of DIKW in nursing informatics while incorporating critiques from other disciplines. This includes examination of assumptions of linearity and hierarchy and an exploration of the implicit philosophical grounding of the model. Two guiding questions are considered: (1) Does DIKW serve clinical information systems, nurses, or both? and (2) What level of theory does DIKW occupy? The DIKW model has been valuable in advancing the independent field of nursing informatics. We offer that if the model is to continue to move forward, its role and functions must be explicitly addressed.

A perturbation analysis of a mechanical model for stable spatial patterning in embryology

NASA Astrophysics Data System (ADS)

Bentil, D. E.; Murray, J. D.

1992-12-01

We investigate a mechanical cell-traction mechanism that generates stationary spatial patterns. A linear analysis highlights the model's potential for these heterogeneous solutions. We use multiple-scale perturbation techniques to study the evolution of these solutions and compare our solutions with numerical simulations of the model system. We discuss some potential biological applications among which are the formation of ridge patterns, dermatoglyphs, and wound healing.

The femur-tibia control system in a proscopiid (Caelifera, Orthoptera): a test for assumptions on the functional basis and evolution of twig mimesis in stick insects.

PubMed

Wolf, H; Bässler, U; Spiess, R; Kittmann, R

2001-11-01

The extremely slow return movements observed in stick insects (phasmids) after imposed changes in posture are termed catalepsy. In the literature, catalepsy is treated as a behavioural component of the twig mimesis observed in walking stick insects. It is produced by the high gain of the velocity-sensitive component of the relevant joint control systems and by the non-linear dependency of its time constant on movement velocity. The high gain, in turn, causes the system to work close to instability, and this may have driven the evolution of gain control mechanisms. Although these statements represent plausible assumptions, based on correlated occurrence, they remain largely hypothetical like many ideas concerning evolutionary tendencies. To test these hypotheses, we studied catalepsy and the relevant properties of the femur-tibia control system in the middle and hind legs of Prosarthria teretrirostris.cf. Prosarthria teretrirostris is a proscopiid closely related to grasshoppers and locusts. With its slender, green-to-brown body and legs, it shows clear morphological twig mimesis, which has evolved independently of the well-known twig mimesis in stick insects. The animals show clear catalepsy. The main properties of femur-tibia joint control are remarkably similar between proscopiids and stick insects (e.g. the marked sensitivity to movement velocity rather than to joint position and the non-linear dependency of the time constants of response decay on movement velocity), but there are also important differences (habituation and activity-related mechanisms of gain control are absent). Together, these results validate the main concepts that have been developed concerning the neural basis and evolution of catalepsy in stick insects and its relationship to twig mimesis, while demonstrating that ideas on the role of habituation and gain control should be refined.

Non-modal analysis of the diocotron instability for cylindrical geometry with conducting boundary

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

Mikhailenko, V. V.; Seok Kim, Jin; Jo, Younghyun

2014-05-15

The temporal evolution of the linear diocotron instability of a cylindrical annular plasma column surrounded by a conducting boundary has been investigated by using the methodology of the cylindrical shearing modes. The linear solution of the initial and boundary-value problems is obtained which is valid for any time at which linear effects dominate. The solution reveals that the initial perturbations of the electron density pass through the stage of the non-modal evolution when the perturbation experiences spatio-temporal distortion pertinent to the considered geometry of the electron column. The result is confirmed by a two-dimensional cylindrical particle-in-cell simulation.

Phase space evolution in linear instabilities

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

Pantellini, F.G.E.; Burgess, D.; Schwartz, S.J.

1994-12-01

A simple and powerful way to investigate the linear evolution of particle distribution functions in kinetic instabilities in a homogeneous collisionless plasma is presented. The method can be applied to any kind of instability, provided the characteristics (growth rate, frequency, wave vector, and polarization) of the mode are known and can also be used to estimate the amplitude of the waves at the end of the linear phase of growth. Two didactic examples are used to illustrate the versatility of the technique: the Alfven Ion Cyclotron (AIC) instability, which is electromagnetic, and the Electron Ion Cyclotron (EIC) instability, which ismore » electrostatic.« less

Using Dynamic Multi-Task Non-Negative Matrix Factorization to Detect the Evolution of User Preferences in Collaborative Filtering

PubMed Central

Ju, Bin; Qian, Yuntao; Ye, Minchao; Ni, Rong; Zhu, Chenxi

2015-01-01

Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time. PMID:26270539

Using Dynamic Multi-Task Non-Negative Matrix Factorization to Detect the Evolution of User Preferences in Collaborative Filtering.

PubMed

Ju, Bin; Qian, Yuntao; Ye, Minchao; Ni, Rong; Zhu, Chenxi

2015-01-01

Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time.

EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS

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

Yuan, D.; Li, B.; Pascoe, D. J.

2015-02-01

We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wavemore » pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.« less

Graph Structured Program Evolution: Evolution of Loop Structures

NASA Astrophysics Data System (ADS)

Shirakawa, Shinichi; Nagao, Tomoharu

Recently, numerous automatic programming techniques have been developed and applied in various fields. A typical example is genetic programming (GP), and various extensions and representations of GP have been proposed thus far. Complex programs and hand-written programs, however, may contain several loops and handle multiple data types. In this chapter, we propose a new method called Graph Structured Program Evolution (GRAPE). The representation of GRAPE is a graph structure; therefore, it can represent branches and loops using this structure. Each programis constructed as an arbitrary directed graph of nodes and a data set. The GRAPE program handles multiple data types using the data set for each type, and the genotype of GRAPE takes the form of a linear string of integers. We apply GRAPE to three test problems, factorial, exponentiation, and list sorting, and demonstrate that the optimum solution in each problem is obtained by the GRAPE system.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing

NASA Astrophysics Data System (ADS)

Lu, Yanfei; Lekszycki, Tomasz

2016-10-01

During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.

Image science team

NASA Technical Reports Server (NTRS)

Ando, K.

1982-01-01

A substantial technology base of solid state pushbroom sensors exists and is in the process of further evolution at both GSFC and JPL. Technologies being developed relate to short wave infrared (SWIR) detector arrays; HgCdTe hybrid detector arrays; InSb linear and area arrays; passive coolers; spectral beam splitters; the deposition of spectral filters on detector arrays; and the functional design of the shuttle/space platform imaging spectrometer (SIS) system. Spatial and spectral characteristics of field, aircraft and space multispectral sensors are summaried. The status, field of view, and resolution of foreign land observing systems are included.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

Computation of Turbulent Wake Flows in Variable Pressure Gradient

NASA Technical Reports Server (NTRS)

Duquesne, N.; Carlson, J. R.; Rumsey, C. L.; Gatski, T. B.

1999-01-01

Transport aircraft performance is strongly influenced by the effectiveness of high-lift systems. Developing wakes generated by the airfoil elements are subjected to strong pressure gradients and can thicken very rapidly, limiting maximum lift. This paper focuses on the effects of various pressure gradients on developing symmetric wakes and on the ability of a linear eddy viscosity model and a non-linear explicit algebraic stress model to accurately predict their downstream evolution. In order to reduce the uncertainties arising from numerical issues when assessing the performance of turbulence models, three different numerical codes with the same turbulence models are used. Results are compared to available experimental data to assess the accuracy of the computational results.

Stability of Local Quantum Dissipative Systems

NASA Astrophysics Data System (ADS)

Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David

2015-08-01

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.

Geologic Studies of Planetary Surfaces Using Radar Polarimetric Imaging

NASA Technical Reports Server (NTRS)

Carter, Lynn M.; Campbell, Donald B.; Campbell, Bruce A.

2010-01-01

Radar is a useful remote sensing tool for studying planetary geology because it is sensitive to the composition, structure, and roughness of the surface and can penetrate some materials to reveal buried terrain. The Arecibo Observatory radar system transmits a single sense of circular polarization, and both senses of circular polarization are received, which allows for the construction of the Stokes polarization vector. From the Stokes vector, daughter products such as the circular polarization ratio, the degree of linear polarization, and linear polarization angle are obtained. Recent polarimetric imaging using Arecibo has included Venus and the Moon. These observations can be compared to radar data for terrestrial surfaces to better understand surface physical properties and regional geologic evolution. For example, polarimetric radar studies of volcanic settings on Venus, the Moon and Earth display some similarities, but also illustrate a variety of different emplacement and erosion mechanisms. Polarimetric radar data provides important information about surface properties beyond what can be obtained from single-polarization radar. Future observations using polarimetric synthetic aperture radar will provide information on roughness, composition and stratigraphy that will support a broader interpretation of surface evolution.

Density and magnetic fluctuations in type III-ELM pedestal evolution in JET: experimental and numerical characterization

NASA Astrophysics Data System (ADS)

De Masi, G.; Predebon, I.; Spagnolo, S.; Meneses, L.; Delabie, E.; Lupelli, I.; Hillesheim, J. C.; Maggi, C.; Contributors, JET

2018-04-01

Density and magnetic fluctuation measurements in low-β type-III ELM discharges are obtained in the Joint European Torus (JET). They are observed during the inter-ELM pedestal evolution, after the LH transition phase, at about 60-70 kHz. Density fluctuations are measured with a correlation reflectometer system installed on the low-field side and they are localized at the pedestal top. Magnetic fluctuations with a spatial scale k_yρ_i˜ 0.1 are measured through a high resolution coil array. The main features and the relations with local plasma parameters are presented. The nature of these fluctuations is discussed along with linear gyrokinetic simulations. Ion temperature gradient (ITG) modes are the dominant instabilities in the frequency range of interest. In terms of radial localization, typical oscillation frequency and qualitative relation with the possible linear drive, ITG modes are consistent with the experimental density fluctuations measurements. Micro-tearing modes (MTMs), found unstable with a lower growth rate, appear a possible explanation for magnetic fluctuations in terms of typical wavenumbers and direction of propagation.

Probability distributions of continuous measurement results for conditioned quantum evolution

NASA Astrophysics Data System (ADS)

Franquet, A.; Nazarov, Yuli V.

2017-02-01

We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the postselection in the end of the evolution. The statistics may drastically differ from the nonconditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of nonconditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, and evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of nontrivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extending the analytical results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence.

Time reversal and charge conjugation in an embedding quantum simulator.

PubMed

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-08-04

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a (171)Yb(+) ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones.

Time reversal and charge conjugation in an embedding quantum simulator

PubMed Central

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-01-01

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a 171Yb+ ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones. PMID:26239028

The evolution of contralateral control of the body by the brain: is it a protective mechanism?

PubMed

Whitehead, Lorne; Banihani, Saleh

2014-01-01

Contralateral control, the arrangement whereby most of the human motor and sensory fibres cross the midline in order to provide control for contralateral portions of the body, presents a puzzle from an evolutionary perspective. What caused such a counterintuitive and complex arrangement to become dominant? In this paper we offer a new perspective on this question by showing that in a complex interactive control system there could be a significant net survival advantage with contralateral control, associated with the effect of injuries of intermediate severity. In such cases an advantage could arise from a combination of non-linear system response combined with correlations between injuries on the same side of the head and body. We show that a simple mathematical model of these ideas emulates such an advantage. Based on this model, we conclude that effects of this kind are a plausible driving force for the evolution of contralateral control.

Observation of Rayleigh-Taylor-instability evolution in a plasma with magnetic and viscous effects

DOE PAGES

Adams, Colin S.; Moser, Auna L.; Hsu, Scott C.

2015-11-06

We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time (~10μs) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density (~10 14cm–3) and deceleration (~10 9 m/s 2). The observed mode wavelength (≳1 cm) nearly doubles within a linear growth time. Furthermore, theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Simple stochastic birth and death models of genome evolution: was there enough time for us to evolve?

PubMed

Karev, Georgy P; Wolf, Yuri I; Koonin, Eugene V

2003-10-12

The distributions of many genome-associated quantities, including the membership of paralogous gene families can be approximated with power laws. We are interested in developing mathematical models of genome evolution that adequately account for the shape of these distributions and describe the evolutionary dynamics of their formation. We show that simple stochastic models of genome evolution lead to power-law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation Models (BDIM), represent a special class of balanced birth-and-death processes, in which domain duplication and deletion rates are asymptotically equal up to the second order. The simplest, linear BDIM shows an excellent fit to the observed distributions of domain family size in diverse prokaryotic and eukaryotic genomes. However, the stochastic version of the linear BDIM explored here predicts that the actual size of large paralogous families is reached on an unrealistically long timescale. We show that introduction of non-linearity, which might be interpreted as interaction of a particular order between individual family members, allows the model to achieve genome evolution rates that are much better compatible with the current estimates of the rates of individual duplication/loss events.

Evolution of pairwise entanglement in a coupled n-body system

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

Pineda, Carlos; Centro de Ciencias Fisicas, University of Mexico; Seligman, Thomas H.

2006-01-15

We study the exact evolution of two noninteracting qubits, initially in a Bell state, in the presence of an environment, modeled by a kicked Ising spin chain. Dynamics of this model range from integrable to chaotic and we can handle numerics for a large number of qubits. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity,more » while a chaotic environment causes linear decay. Both quantities display recurrences in an integrable environment.« less

The Evolution of El Nino-Precipitation Relationships from Satellites and Gauges

NASA Technical Reports Server (NTRS)

Curtis, Scott; Adler, Robert F.; Starr, David OC (Technical Monitor)

2002-01-01

This study uses a twenty-three year (1979-2001) satellite-gauge merged community data set to further describe the relationship between El Nino Southern Oscillation (ENSO) and precipitation. The globally complete precipitation fields reveal coherent bands of anomalies that extend from the tropics to the polar regions. Also, ENSO-precipitation relationships were analyzed during the six strongest El Ninos from 1979 to 2001. Seasons of evolution, Pre-onset, Onset, Peak, Decay, and Post-decay, were identified based on the strength of the El Nino. Then two simple and independent models, first order harmonic and linear, were fit to the monthly time series of normalized precipitation anomalies for each grid block. The sinusoidal model represents a three-phase evolution of precipitation, either dry-wet-dry or wet-dry-wet. This model is also highly correlated with the evolution of sea surface temperatures in the equatorial Pacific. The linear model represents a two-phase evolution of precipitation, either dry-wet or wet-dry. These models combine to account for over 50% of the precipitation variability for over half the globe during El Nino. Most regions, especially away from the Equator, favor the linear model. Areas that show the largest trend from dry to wet are southeastern Australia, eastern Indian Ocean, southern Japan, and off the coast of Peru. The northern tropical Pacific and Southeast Asia show the opposite trend.

Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

NASA Astrophysics Data System (ADS)

Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.

1989-01-01

Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Linear dynamical modes as new variables for data-driven ENSO forecast

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Seleznev, Aleksei; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen

2018-05-01

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Exponential Sensitivity and its Cost in Quantum Physics

PubMed Central

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-01-01

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076

Hybrid microscopy of human carotid atheroma by means of optical-resolution optoacoustic and non-linear optical microscopy

NASA Astrophysics Data System (ADS)

Seeger, Markus; Karlas, Angelos; Soliman, Dominik; Pelisek, Jaroslav; Ntziachristos, Vasilis

2017-03-01

Carotid atheromatosis is causally related to stroke, a leading cause of disability and death. We present the analysis of a human carotid atheroma using a novel hybrid microscopy system that combines optical-resolution optoacoustic (photoacoustic) microscopy and several non-linear optical microscopy modalities (second and third harmonic generation, as well as, two-photon excitation fluorescence) to achieve a multimodal examination of the extracted tissue within the same imaging framework. Our system enables the label-free investigation of atheromatous human carotid tissue with a resolution of about 1 μm and allows for the congruent interrogation of plaque morphology and clinically relevant constituents such as red blood cells, collagen, and elastin. Our data reveal mutual interactions between blood embeddings and connective tissue within the atheroma, offering comprehensive insights into its stage of evolution and severity, and potentially facilitating the further development of diagnostic tools, as well as treatment strategies.

Exponential Sensitivity and its Cost in Quantum Physics.

PubMed

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-02-10

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.

Navigation Strategies for Primitive Solar System Body Rendezvous and Proximity Operations

NASA Technical Reports Server (NTRS)

Getzandanner, Kenneth M.

2011-01-01

A wealth of scientific knowledge regarding the composition and evolution of the solar system can be gained through reconnaissance missions to primitive solar system bodies. This paper presents analysis of a baseline navigation strategy designed to address the unique challenges of primitive body navigation. Linear covariance and Monte Carlo error analysis was performed on a baseline navigation strategy using simulated data from a· design reference mission (DRM). The objective of the DRM is to approach, rendezvous, and maintain a stable orbit about the near-Earth asteroid 4660 Nereus. The outlined navigation strategy and resulting analyses, however, are not necessarily limited to this specific target asteroid as they may he applicable to a diverse range of mission scenarios. The baseline navigation strategy included simulated data from Deep Space Network (DSN) radiometric tracking and optical image processing (OpNav). Results from the linear covariance and Monte Carlo analyses suggest the DRM navigation strategy is sufficient to approach and perform proximity operations in the vicinity of the target asteroid with meter-level accuracy.

Effects of Saharan Mineral Dust Aerosols on the Dynamics of an Idealized African Easterly Jet-African Easterly Wave System over North Africa

NASA Astrophysics Data System (ADS)

Grogan, Dustin Francis Phillip

The central objective of this work is to examine the direct radiative effects of Saharan mineral dust aerosols on the dynamics of African easterly waves (AEWs) and the African easterly jet (AEJ). Achieving this objective is built around two tasks that use the Weather Research and Forecasting (WRF) model coupled to an online dust model (WRF-dust model). The first task (Chapter 2) examines the linear dynamics of AEWs; the second task (Chapter 3) examines the nonlinear evolution of AEWs and their interactions with the AEJ. In Chapter 2, the direct radiative effects of dust on the linear dynamics of AEWs are examined analytically and numerically. The analytical analysis combines the thermodynamic equation with a dust continuity equation to form an expression for the generation of eddy available potential energy (APE) by the dust field. The generation of eddy APE is a function of the transmissivity and spatial gradients of the dust, which are modulated by the Doppler-shifted frequency. The expression predicts that for a fixed dust distribution, the wave response will be largest in regions where the dust gradients are maximized and the Doppler-shifted frequency vanishes. The numerical analysis calculates the linear dynamics of AEWs using zonally averaged basic states for wind, temperature and dust consistent with summertime conditions over North Africa. For the fastest growing AEW, the dust increases the growth rate from ~15% to 90% for aerosol optical depths ranging from tau=1.0 to tau=2.5. A local energetics analysis shows that for tau=1.0, the dust increases the maximum barotropic and baroclinic energy conversions by ~50% and ~100%, respectively. The maxima in the generation of APE and conversions of energy are co-located and occur where the meridional dust gradient is maximized near the critical layer, i.e., where the Doppler-shifted frequency is small, in agreement with the prediction from the analytical analysis. In Chapter 3, the direct radiative effects of dust on the evolution of AEJ-AEW system are examined using the WRF-dust model. The model is initialized with zonal-mean distributions of wind, temperature and dust used in linear study (Chapter 2). The dust modifies the lifecycle of the AEWs in the following way: the domain-averaged eddy kinetic energy (EKE) is enhanced during the linear and nonlinear growth phases, reaching a larger peak amplitude that subsequently decays more rapidly, eventually equilibrating at lower amplitude. The increase in EKE during the growth phases is due to local increases in barotropic energy conversions in the dust plume north of the AEJ. The dust-modified, rapidly decaying phase is primarily associated with enhanced barotropic decay that occurs near the top of the plume north of the AEJ. The timing of peak EKE depends on the initial dust concentration. Throughout the evolution of the AEJ-AEW system, the dust increases the maximum zonal-mean wind speeds. The increase is due to the dust-modified mean meridional circulation during the AEW growth phase and the dust-modified wave fluxes during the AEW decay phase. During AEW growth, the dust-modified maximum wind speeds are also displaced farther southward and upward, which is due to the enhanced wave fluxes decelerating the flow more efficiently north of the AEJ. These changes to the AEJ structure affect the critical surface, which expands vertically and meridionally as the AEW grows to finite amplitude. The dust-modified effects on the evolution of the AEJ-AEW system are discussed in light of tropical cyclogenesis. By better understanding the direct radiative effects of dust on the AEJ-AEW system, we can expect improvements in the modeling, forecasting and understanding of the connection between AEWs and the meteorology over North Africa and the Eastern Atlantic Ocean.

Prediction of dynamical systems by symbolic regression

NASA Astrophysics Data System (ADS)

Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K.; Noack, Bernd R.

2016-07-01

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

In-process, non-destructive multimodal dynamic testing of high-speed composite rotors

NASA Astrophysics Data System (ADS)

Kuschmierz, Robert; Filippatos, Angelos; Langkamp, Albert; Hufenbach, Werner; Czarske, Jürgern W.; Fischer, Andreas

2014-03-01

Fibre reinforced plastic (FRP) rotors are lightweight and offer great perspectives in high-speed applications such as turbo machinery. Currently, novel rotor structures and materials are investigated for the purpose of increasing machine efficiency, lifetime and loading limits. Due to complex rotor structures, high anisotropy and non-linear behavior of FRP under dynamic loads, an in-process measurement system is necessary to monitor and to investigate the evolution of damages under real operation conditions. A non-invasive, optical laser Doppler distance sensor measurement system is applied to determine the biaxial deformation of a bladed FRP rotor with micron uncertainty as well as the tangential blade vibrations at surface speeds above 300 m/s. The laser Doppler distance sensor is applicable under vacuum conditions. Measurements at varying loading conditions are used to determine elastic and plastic deformations. Furthermore they allow to determine hysteresis, fatigue, Eigenfrequency shifts and loading limits. The deformation measurements show a highly anisotropic and nonlinear behavior and offer a deeper understanding of the damage evolution in FRP rotors. The experimental results are used to validate and to calibrate a simulation model of the deformation. The simulation combines finite element analysis and a damage mechanics model. The combination of simulation and measurement system enables the monitoring and prediction of damage evolutions of FRP rotors in process.

The emphasis given to evolution in state science standards: A lever for change in evolution education?

NASA Astrophysics Data System (ADS)

Skoog, Gerald; Bilica, Kimberly

2002-07-01

This study analyzed the science frameworks of 49 states and the District of Colombia to determine the emphasis given to evolution in these documents at the middle and secondary levels. These concepts were species evolve over time, speciation, diversity of life, descent with modification from common ancestry, evidence of evolution, natural selection, pace and direction of evolution, and human evolution. Collectively, the 50 science frameworks emphasized evolution in a manner that suggests that if the public's support for standards-based curricula is a reality, the study of evolution will be emphasized in an unprecedented manner in the nation's schools in the near future. However, all concepts were not emphasized equally in these documents. For example, human evolution was included in only seven documents. The word evolution is absent from some standards. Despite these negatives, recent actions to improve existing standards or to adopt new standards that emphasize evolution have occurred. The metaphor lever of change is often used in the context of school reform. This metaphor suggests a simple system where one change can result in a desired outcome. However, in classrooms where curriculum decisions evolve constantly, multiple factors interact and reinforce one another in response to both internal and external contingencies that emerge. Educational change can not be reduced to a simple linear cause/effect situation. The change process involved is nonlinear where what goes in is not proportional to what comes out because of feedback loops and other factors that complicate results. This nonlinearity is reflected in the varied responses of teachers to specific contingencies. Yet, systems can be changed and nudged towards a structure where desired outcomes will emerge. Judicial rulings indicating that the teaching of evolution cannot be prohibited or equal time for creationism mandated, improved coverage of evolution in secondary school biology textbooks, the negative response of many leaders, scientists, organizations, and editorial writers to the 1999 decision of the Kansas State Board of Education to deemphasize and misrepresent evolution in the state's science standards, and the emphasis given to evolution in the standards reviewed for this study, all coalesce to provide needed support for administrators and teachers who are striving to create science curricula that emphasize evolution in a manner commensurate with its importance in understanding the natural world and our place within it.

Linear vs non-linear QCD evolution in the neutrino-nucleon cross section

NASA Astrophysics Data System (ADS)

Albacete, Javier L.; Illana, José I.; Soto-Ontoso, Alba

2016-03-01

Evidence for an extraterrestrial flux of ultra-high-energy neutrinos, in the order of PeV, has opened a new era in Neutrino Astronomy. An essential ingredient for the determination of neutrino fluxes from the number of observed events is the precise knowledge of the neutrino-nucleon cross section. In this work, based on [1], we present a quantitative study of σνN in the neutrino energy range 104 < Eν < 1014 GeV within two transversal QCD approaches: NLO DGLAP evolution using different sets of PDFs and BK small-x evolution with running coupling and kinematical corrections. Further, we translate this theoretical uncertainty into upper bounds for the ultra-high-energy neutrino flux for different experiments.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

NASA Astrophysics Data System (ADS)

Inoue, Rei; Lam, Thomas; Pylyavskyy, Pavlo

2016-11-01

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

Dynamics and thermodynamics of linear quantum open systems.

PubMed

Martinez, Esteban A; Paz, Juan Pablo

2013-03-29

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Fully kinetic Biermann battery and associated generation of pressure anisotropy

NASA Astrophysics Data System (ADS)

Schoeffler, K. M.; Loureiro, N. F.; Silva, L. O.

2018-03-01

The dynamical evolution of a fully kinetic, collisionless system with imposed background density and temperature gradients is investigated analytically. The temperature gradient leads to the generation of temperature anisotropy, with the temperature along the gradient becoming larger than that in the direction perpendicular to it. This causes the system to become unstable to pressure anisotropy driven instabilities, dominantly to the electron Weibel instability. When both density and temperature gradients are present and nonparallel to each other, we obtain a Biermann-like linear-in-time magnetic field growth. Accompanying particle-in-cell numerical simulations are shown to confirm our analytical results.

A Solution Space for a System of Null-State Partial Differential Equations: Part 3

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the third of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE κ ). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban, in Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Extending these results, we prove in this article that dim and entirely consists of (real-valued) solutions constructed with the CFT Coulomb gas (contour integral) formalism. In order to prove this claim, we show that a certain set of C N such solutions is linearly independent. Because the formulas for these solutions are complicated, we prove linear independence indirectly. We use the linear injective map of Lemma 15 in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012) to send each solution of the mentioned set to a vector in , whose components we find as inner products of elements in a Temperley-Lieb algebra. We gather these vectors together as columns of a symmetric matrix, with the form of a meander matrix. If the determinant of this matrix does not vanish, then the set of C N Coulomb gas solutions is linearly independent. And if this determinant does vanish, then we construct an alternative set of C N Coulomb gas solutions and follow a similar procedure to show that this set is linearly independent. The latter situation is closely related to CFT minimal models. We emphasize that, although the system of PDEs arises in CFT in away that is typically non-rigorous, our treatment of this system here and in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014; Commun Math Phys, arXiv:1405.2747, 2014) is completely rigorous.

Double-time correlation functions of two quantum operations in open systems

NASA Astrophysics Data System (ADS)

Ban, Masashi

2017-10-01

A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.

Effects of high pressure on microstructure evolution and crystallization mechanisms during solidification of nickel

NASA Astrophysics Data System (ADS)

Zhang, Hai-Tao; Mo, Yun-Fei; Liu, Rang-Su; Tian, Ze-An; Liu, Hai-Rong; Hou, Zhao-Yang; Zhou, Li-Li; Liang, Yong-Chao; Peng, Ping

2018-03-01

To deeply understand the effects of high pressure on microstructural evolutions and crystallization mechanisms of liquid metal Ni during solidification process, MD simulation studies have been performed under 7 pressures of 0 ˜ 30 GPa, at cooling rate of 1.0 × 1011 K s-1. Adopting several microstructural analyzing methods, especially the cluster-type index method (CTIM-2) to analyze the local microstructures in the system. It is found that the pressure has important influence on the formation and evolution of microstructures, especially of the main basic clusters in the system. All the simulation systems are directly solidified into crystal structures, and the 1421, 1422, 1441 and 1661 bond-types, as well the FCC (12 0 0 0 12 0), HCP (12 0 0 0 6 6) and BCC (14 6 0 8 0 0) clusters play a key role in the microstructure transitions from liquid to crystal structures. The crystallization temperature T c is enhanced almost linearly with the increase of pressure. Highly interesting, it is found for the first time that there is an important phase transformation point from FCC to BCC structures between 20 ˜ 22.5 GPa during the solidification processes from the same initial liquid system at the same cooling rate. And the effect of increasing pressure is similar to that of decreasing cooling rate for the phase transformation of microstructures during solidification process of liquid metal Ni system, though they have different concrete effecting mechanisms.

Evolution of a primary pulse in the granular dimers mounted on a linear elastic foundation: An analytical and numerical study.

PubMed

Ahsan, Zaid; Jayaprakash, K R

2016-10-01

In this exposition we consider the wave dynamics of a one-dimensional periodic granular dimer (diatomic) chain mounted on a damped and an undamped linear elastic foundation (otherwise called the on-site potential). It is very well known that periodic granular dimers support solitary wave propagation (similar to that in the homogeneous granular chains) for a specific discrete set of mass ratios. In this work we present the analytical investigation of the evolution of solitary waves and primary pulses in granular dimers when they are mounted on on-site potential with and without velocity proportional foundation damping. We invoke a methodology based on the multiple time-scale asymptotic analysis and partition the dynamics of the perturbed dimer chain into slow and fast components. The dynamics of the dimer chain in the limit of large mass mismatch (auxiliary chain) mounted on on-site potential and foundation damping is used as the basis for the analysis. A systematic analytical procedure is then developed for the slowly varying response of the beads and in estimating primary pulse amplitude evolution resulting in a nonlinear map relating the relative displacement amplitudes of two adjacent beads. The methodology is applicable for arbitrary mass ratios between the beads. We present several examples to demonstrate the efficacy of the proposed method. It is observed that the amplitude evolution predicted by the described methodology is in good agreement with the numerical simulation of the original system. This work forms a basis for further application of the considered methodology to weakly coupled granular dimers which finds practical relevance in designing shock mitigating granular layers.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology.

PubMed

Mittal, Khushboo; Gupta, Shalabh

2017-05-01

Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes. This paper addresses this research gap by using topological data analysis as a tool to study system evolution and develop a mathematical framework for detecting the topological changes in the underlying system using persistent homology. Using the proposed technique, topological features (e.g., number of relevant k-dimensional holes, etc.) are extracted from nonlinear time series data which are useful for deeper analysis of the system behavior and early detection of bifurcations and chaos. When applied to a Logistic map, a Duffing oscillator, and a real life Op-amp based Jerk circuit, these features are shown to accurately characterize the system dynamics and detect the onset of chaos.

Adaptive convex combination approach for the identification of improper quaternion processes.

PubMed

Ujang, Bukhari Che; Jahanchahi, Cyrus; Took, Clive Cheong; Mandic, Danilo P

2014-01-01

Data-adaptive optimal modeling and identification of real-world vector sensor data is provided by combining the fractional tap-length (FT) approach with model order selection in the quaternion domain. To account rigorously for the generality of such processes, both second-order circular (proper) and noncircular (improper), the proposed approach in this paper combines the FT length optimization with both the strictly linear quaternion least mean square (QLMS) and widely linear QLMS (WL-QLMS). A collaborative approach based on QLMS and WL-QLMS is shown to both identify the type of processes (proper or improper) and to track their optimal parameters in real time. Analysis shows that monitoring the evolution of the convex mixing parameter within the collaborative approach allows us to track the improperness in real time. Further insight into the properties of those algorithms is provided by establishing a relationship between the steady-state error and optimal model order. The approach is supported by simulations on model order selection and identification of both strictly linear and widely linear quaternion-valued systems, such as those routinely used in renewable energy (wind) and human-centered computing (biomechanics).

Healthcare service quality perception in Japan.

PubMed

Eleuch, Amira ep Koubaa

2011-01-01

This study aims to assess Japanese patients' healthcare service quality perceptions and to shed light on the most meaningful service features. It follows-up a study published in IJHCQA Vol. 21 No. 7. Through a non-linear approach, the study relied on the scatter model to detect healthcare service features' importance in forming overall quality judgment. Japanese patients perceive healthcare services through a linear compensatory process. Features related to technical quality and staff behavior compensate for each other to decide service quality. A limitation of the study is the limited sample size. Non-linear approaches could help researchers to better understand patients' healthcare service quality perceptions. The study highlights a need to adopt an evolution that enhances technical quality and medical practices in Japanese healthcare settings. The study relies on a non-linear approach to assess patient overall quality perceptions in order to enrich knowledge. Furthermore, the research is conducted in Japan where healthcare marketing studies are scarce owing to cultural and language barriers. Japanese culture and healthcare system characteristics are used to explain and interpret the results.

Improvements to the construction of binary black hole initial data

NASA Astrophysics Data System (ADS)

Ossokine, Serguei; Foucart, Francois; Pfeiffer, Harald P.; Boyle, Michael; Szilágyi, Béla

2015-12-01

Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the spectral Einstein code, to allow robust construction of initial data for mass-ratio above 10:1, and for dimensionless black hole spins above 0.9, while improving efficiency for lower mass-ratios and spins. We implement a more flexible domain decomposition, adaptive mesh refinement and an updated method for choosing free parameters. We also introduce a new method to control and eliminate residual linear momentum in initial data for precessing systems, and demonstrate that it eliminates gravitational mode mixing during the evolution. Finally, the new code is applied to construct initial data for hyperbolic scattering and for binaries with very small separation.

Conjugated Polymers: Catalysts for Photocatalytic Hydrogen Evolution.

PubMed

Zhang, Guigang; Lan, Zhi-An; Wang, Xinchen

2016-12-19

Conjugated polymers, comprising fully π-conjugated systems, present a new generation of heterogeneous photocatalysts for solar-energy utilization. They have three key features, namely robustness, nontoxicity, and visible-light activity, for photocatalytic processes, thus making them appealing candidates for scale-up. Presented in this Minireview, is a brief summary on the recent development of various promising polymer photocatalysts for hydrogen evolution from aqueous solutions, including linear polymers, planarized polymers, triazine/heptazine polymers, and other related organic conjugated semiconductors, with a particular focus on the rational manipulation in the composition, architectures, and optical and electronic properties that are relevant to photophysical and photochemical properties. Some future trends and prospects for organic conjugated photocatalysts in artificial photosynthesis, by water splitting, are also envisaged. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Emergence, reductionism and landscape response to climate change

NASA Astrophysics Data System (ADS)

Harrison, Stephan; Mighall, Tim

2010-05-01

Predicting landscape response to external forcing is hampered by the non-linear, stochastic and contingent (ie dominated by historical accidents) forcings inherent in landscape evolution. Using examples from research carried out in southwest Ireland we suggest that non-linearity in landform evolution is likely to be a strong control making regional predictions of landscape response to climate change very difficult. While uncertainties in GCM projections have been widely explored in climate science much less attention has been directed by geomorphologists to the uncertainties in landform evolution under conditions of climate change and this problem may be viewed within the context of philosophical approaches to reductionsim and emergence. Understanding the present and future trajectory of landform change may also guide us to provide an enhanced appreciation of how landforms evolved in the past.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Pre-inflationary universe in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin

2017-10-01

The evolutions of the flat Friedmann-Lemaître-Robertson-Walker universe and its linear perturbations are studied systematically in the dressed metric approach of loop quantum cosmology. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating: bouncing, transition and slow-roll inflation. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential-dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the preinflationary dynamics, the scalar and tensor power spectra become scale dependent. By comparing our results with the Planck 2015 data, we find constraints on the total number of e -folds since the bounce, in order to be consistent with current observations.

Network evolution induced by the dynamical rules of two populations

NASA Astrophysics Data System (ADS)

Platini, Thierry; Zia, R. K. P.

2010-10-01

We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely extrovert (a) and introvert (b). In our model, each group is characterized by its size (Na and Nb) and preferred degree (κa and \\kappa_b\\ll \\kappa_a ). The network dynamics is governed by the competing microscopic rules of each population that consist of the creation and destruction of links. Starting from an unconnected network, we give a detailed analysis of the mean field approach which is compared to Monte Carlo simulation data. The time evolution of the restricted degrees langkbbrang and langkabrang presents three time regimes and a non-monotonic behavior well captured by our theory. Surprisingly, when the population sizes are equal Na = Nb, the ratio of the restricted degree θ0 = langkabrang/langkbbrang appears to be an integer in the asymptotic limits of the three time regimes. For early times (defined by t < t1 = κb) the total number of links presents a linear evolution, where the two populations are indistinguishable and where θ0 = 1. Interestingly, in the intermediate time regime (defined for t_1\\lt t\\lt t_2\\propto \\kappa_a and for which θ0 = 5), the system reaches a transient stationary state, where the number of contacts among introverts remains constant while the number of connections increases linearly in the extrovert population. Finally, due to the competing dynamics, the network presents a frustrated stationary state characterized by a ratio θ0 = 3.

From Data to Images:. a Shape Based Approach for Fluorescence Tomography

NASA Astrophysics Data System (ADS)

Dorn, O.; Prieto, K. E.

2012-12-01

Fluorescence tomography is treated as a shape reconstruction problem for a coupled system of two linear transport equations in 2D. The shape evolution is designed in order to minimize the least squares data misfit cost functional either in the excitation frequency or in the emission frequency. Furthermore, a level set technique is employed for numerically modelling the evolving shapes. Numerical results are presented which demonstrate the performance of this novel technique in the situation of noisy simulated data in 2D.

Kinetic Rate Kernels via Hierarchical Liouville-Space Projection Operator Approach.

PubMed

Zhang, Hou-Dao; Yan, YiJing

2016-05-19

Kinetic rate kernels in general multisite systems are formulated on the basis of a nonperturbative quantum dissipation theory, the hierarchical equations of motion (HEOM) formalism, together with the Nakajima-Zwanzig projection operator technique. The present approach exploits the HEOM-space linear algebra. The quantum non-Markovian site-to-site transfer rate can be faithfully evaluated via projected HEOM dynamics. The developed method is exact, as evident by the comparison to the direct HEOM evaluation results on the population evolution.

NLO evolution of color dipole

DOE PAGES

Balitsky, Ian; Chirilli, Giovanni A.

2008-09-01

The small-x deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities.

Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons

NASA Astrophysics Data System (ADS)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Font, José A.; Herdeiro, Carlos; Radu, Eugen

2017-08-01

Recent numerical relativity simulations within the Einstein-Maxwell-(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordström BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

First complete mitochondrial genome sequence from a box jellyfish reveals a highly fragmented linear architecture and insights into telomere evolution.

PubMed

Smith, David Roy; Kayal, Ehsan; Yanagihara, Angel A; Collins, Allen G; Pirro, Stacy; Keeling, Patrick J

2012-01-01

Animal mitochondrial DNAs (mtDNAs) are typically single circular chromosomes, with the exception of those from medusozoan cnidarians (jellyfish and hydroids), which are linear and sometimes fragmented. Most medusozoans have linear monomeric or linear bipartite mitochondrial genomes, but preliminary data have suggested that box jellyfish (cubozoans) have mtDNAs that consist of many linear chromosomes. Here, we present the complete mtDNA sequence from the winged box jellyfish Alatina moseri (the first from a cubozoan). This genome contains unprecedented levels of fragmentation: 18 unique genes distributed over eight 2.9- to 4.6-kb linear chromosomes. The telomeres are identical within and between chromosomes, and recombination between subtelomeric sequences has led to many genes initiating or terminating with sequences from other genes (the most extreme case being 150 nt of a ribosomal RNA containing the 5' end of nad2), providing evidence for a gene conversion-based model of telomere evolution. The silent-site nucleotide variation within the A. moseri mtDNA is among the highest observed from a eukaryotic genome and may be associated with elevated rates of recombination.

Coarse-grained description of cosmic structure from Szekeres models

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

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos, E-mail: sussman@nucleares.unam.mx, E-mail: ismael.delgadog@uaem.edu.mx, E-mail: hidalgo@fis.unam.mx

2016-03-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities ofmore » structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.« less

Information slows down hierarchy growth

NASA Astrophysics Data System (ADS)

Czaplicka, Agnieszka; Suchecki, Krzysztof; Miñano, Borja; Trias, Miquel; Hołyst, Janusz A.

2014-06-01

We consider models of growing multilevel systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy level (a level nearest to the tree root). The proposed evolution reflects limited information on system properties available to new nodes. It can also be expressed in terms of population dynamics. Two models are considered: a constant tournament (CT) model wherein the number of tournament participants is constant throughout system evolution, and a proportional tournament (PT) model where this number increases proportionally to the growing size of the system itself. The results of analytical calculations based on a rate equation fit well to numerical simulations for both models. In the CT model all hierarchy levels emerge, but the birth time of a consecutive hierarchy level increases exponentially or faster for each new level. The number of nodes at the first hierarchy level grows logarithmically in time, while the size of the last, "worst" hierarchy level oscillates quasi-log-periodically. In the PT model, the occupations of the first two hierarchy levels increase linearly, but worse hierarchy levels either do not emerge at all or appear only by chance in the early stage of system evolution to further stop growing at all. The results allow us to conclude that information available to each new node in tournament dynamics restrains the emergence of new hierarchy levels and that it is the absolute amount of information, not relative, which governs such behavior.

Information slows down hierarchy growth.

PubMed

Czaplicka, Agnieszka; Suchecki, Krzysztof; Miñano, Borja; Trias, Miquel; Hołyst, Janusz A

2014-06-01

We consider models of growing multilevel systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy level (a level nearest to the tree root). The proposed evolution reflects limited information on system properties available to new nodes. It can also be expressed in terms of population dynamics. Two models are considered: a constant tournament (CT) model wherein the number of tournament participants is constant throughout system evolution, and a proportional tournament (PT) model where this number increases proportionally to the growing size of the system itself. The results of analytical calculations based on a rate equation fit well to numerical simulations for both models. In the CT model all hierarchy levels emerge, but the birth time of a consecutive hierarchy level increases exponentially or faster for each new level. The number of nodes at the first hierarchy level grows logarithmically in time, while the size of the last, "worst" hierarchy level oscillates quasi-log-periodically. In the PT model, the occupations of the first two hierarchy levels increase linearly, but worse hierarchy levels either do not emerge at all or appear only by chance in the early stage of system evolution to further stop growing at all. The results allow us to conclude that information available to each new node in tournament dynamics restrains the emergence of new hierarchy levels and that it is the absolute amount of information, not relative, which governs such behavior.

Tumor evolution: Linear, branching, neutral or punctuated?☆

PubMed Central

Davis, Alexander; Gao, Ruli; Navin, Nicholas

2017-01-01

Intratumor heterogeneity has been widely reported in human cancers, but our knowledge of how this genetic diversity emerges over time remains limited. A central challenge in studying tumor evolution is the difficulty in collecting longitudinal samples from cancer patients. Consequently, most studies have inferred tumor evolution from single time-point samples, providing very indirect information. These data have led to several competing models of tumor evolution: linear, branching, neutral and punctuated. Each model makes different assumptions regarding the timing of mutations and selection of clones, and therefore has different implications for the diagnosis and therapeutic treatment of cancer patients. Furthermore, emerging evidence suggests that models may change during tumor progression or operate concurrently for different classes of mutations. Finally, we discuss data that supports the theory that most human tumors evolve from a single cell in the normal tissue. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby. PMID:28110020

Linear motif-mediated interactions have contributed to the evolution of modularity in complex protein interaction networks.

PubMed

Kim, Inhae; Lee, Heetak; Han, Seong Kyu; Kim, Sanguk

2014-10-01

The modular architecture of protein-protein interaction (PPI) networks is evident in diverse species with a wide range of complexity. However, the molecular components that lead to the evolution of modularity in PPI networks have not been clearly identified. Here, we show that weak domain-linear motif interactions (DLIs) are more likely to connect different biological modules than strong domain-domain interactions (DDIs). This molecular division of labor is essential for the evolution of modularity in the complex PPI networks of diverse eukaryotic species. In particular, DLIs may compensate for the reduction in module boundaries that originate from increased connections between different modules in complex PPI networks. In addition, we show that the identification of biological modules can be greatly improved by including molecular characteristics of protein interactions. Our findings suggest that transient interactions have played a unique role in shaping the architecture and modularity of biological networks over the course of evolution.

Evolution of Wigner function in laser process under the action of linear resonance force and its application

NASA Astrophysics Data System (ADS)

Dao-ming, Lu

2018-05-01

The negativity of Wigner function (WF) is one of the important symbols of non-classical properties of light field. Therefore, it is of great significance to study the evolution of WF in dissipative process. The evolution formula of WF in laser process under the action of linear resonance force is given by virtue of thermo entangled state representation and the technique of integration within an ordered product of operator. As its application, the evolution of WF of thermal field and that of single-photon-added coherent state are discussed. The results show that the WF of thermal field maintains its original character. On the other hand, the negative region size and the depth of negativity of WF of single- photon-added coherent state decrease until it vanishes with dissipation. This shows that the non-classical property of single-photon-added coherent state is weakened, until it disappears with dissipation time increasing.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution

NASA Technical Reports Server (NTRS)

Balbus, Steven A.; Hawley, John F.

1991-01-01

A broad class of astronomical accretion disks is presently shown to be dynamically unstable to axisymmetric disturbances in the presence of a weak magnetic field, an insight with consequently broad applicability to gaseous, differentially-rotating systems. In the first part of this work, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate, which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field. Fluid motions associated with the instability directly generate both poloidal and toroidal field components. In the second part of this investigation, the scaling relation between the instability's wavenumber and the Alfven velocity is demonstrated, and the independence of the maximum growth rate from magnetic field strength is confirmed.

Earth survey applications division: Research leading to the effective use of space technology in applications relating to the Earth's surface and interior

NASA Technical Reports Server (NTRS)

Carpenter, L. (Editor)

1980-01-01

Accomplishments and future plans are described for the following areas: (1) geology - geobotanical indicators and geopotential data; (2) modeling magnetic fields; (3) modeling the structure, composition, and evolution of the Earth's crust; (4) global and regional motions of the Earth's crust and earthquake occurrence; (5) modeling geopotential from satellite tracking data; (6) modeling the Earth's gravity field; (7) global Earth dynamics; (8) sea surface topography, ocean dynamics; and geophysical interpretation; (9) land cover and land use; (10) physical and remote sensing attributes important in detecting, measuring, and monitoring agricultural crops; (11) prelaunch studies using LANDSAT D; (12) the multispectral linear array; (13) the aircraft linear array pushbroom radiometer; and (14) the spaceborne laser ranging system.

Temporal evolution of age data under transient pumping conditions

NASA Astrophysics Data System (ADS)

Leray, S.; De Dreuzy, J.; Aquilina, L.; Vergnaud, V.; Labasque, T.; Bour, O.; Le Borgne, T.

2013-12-01

While most age data derived from tracers have been analyzed in steady-state flow conditions, we determine their temporal evolution under transient pumping conditions. Starting pumping in a well modifies the natural flow patterns induced by the topographical gradient to a mainly convergent flow to the well. Our study is based on a set of models made up of a shallowly dipping aquifer overlain by a less permeable aquitard. These settings are characteristic of the crystalline aquifer of Plœmeur (Brittany, France) located in a highly fractured zone at the contact between a granite and micaschists. Under a pseudo steady-state flow assumption (instantaneous shift between two steady-state flow fields), we solve the transport equation with a backward particle-tracking method and determine the temporal evolution of the concentrations at the pumping well of the four atmospheric tracers CFC 11, CFC 12, CFC 113 and SF6. We show that apparent ages deduced from these concentrations evolve both because of the flow patterns modifications and because of the non-linear evolution of the atmospheric tracer concentrations. Flow patterns modifications only intervene just after the start of pumping, when the initially piston-like residence time distribution is transformed to a broader distribution mixing residence times from a wide variety of flow lines. Later, while flow patterns and the supplying volume of the pumping well still evolve, the residence time distributions are hardly modified and apparent ages are solely altered by the non-linear atmospheric tracer concentrations that progressively modifies the weighting of the residence time distribution. These results are confirmed by the observations at the site of Plœmeur in the pumping area. First, long term chloride observations confirm the quick evolution of the flow patterns after the start of pumping. Second, posterior and more recent evolutions of apparent ages derived from CFCs are consistent with the modeling results revealing in turn the marginal effect of the 20-year pumping on the first 70 years of the residence time distribution. We conclude that the temporal evolution of apparent ages should be used with great care for identifying the temporal evolution of the flow patterns as the apparent age evolution can have two sources - the transient flow patterns and transient tracer atmospheric concentrations. We argue that both evolutions either controlled by transient flow patterns or by transient tracer atmospheric concentrations provide key information that can be further used for the characterization of the hydrogeological system. This study illustrates that the temporal evolution of apparent ages could be used for models segregation and slightly compensate for the small number of tracers.

A variational approach to the strongly nonlinear regime of the Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Yoshikawa, Toshio

The Rayleigh-Taylor instability is the instability of the interface between two fluids of different densities. When a heavy fluid is superposed over a light fluid. small disturbances on the interface develop into a complex form with heavy fluid ``fingers'' and light fluid ``bubbles.'' We propose a variational method for the description of the evolution of the fingers and bubbles in the late stage of the instability. In this method, the fluid region is represented as the image of a time-dependent conformal mapping; the dynamics of the mapping is determined by the least action principle for the Lagrangian. i.e., the kinetic energy minus the potential energy. The evolution of a single finger and bubble is investigated by this method. We first consider a symmetric finger and bubble in a zero gravitational field. We derive an integrable Hamiltonian system with two degrees of freedom that governs the dynamics of the symmetric finger and bubble. We present a general solution of the system. The solution predicts the linear growth of the finger and the saturation of the bubble growth. It is shown that this solution is asymptotically exact. We consider a symmetric finger and bubble with perturbations. We show that the dynamics of the finger and bubble and that of the perturbations are decoupled. We next consider an inclined finger and bubble in a zero gravitational field. We derive a Hamiltonian system with four degrees of freedom that governs the dynamics of the inclined finger and bubble. The system has four integrals of motion, one of them depends on time explicitly. When there is no lateral motion, the system reduces to an integrable Hamiltonian system with three degrees of freedom. A general solution of the system is presented. The solution predicts the linear growth of the finger toward a direction and the saturation of the bubble growth. Finally, we consider a symmetric finger and bubble in a uniform gravitational field. We derive a Hamiltonian system with two degrees of freedom that governs the dynamics of the symmetric finger and bubble. Since the system includes a potential energy term, it is not integrable in general. However, we present a general solution in the case of the total energy being zero. This case corresponds to an interesting case where the evolution starts from a flat surface. The solution predicts that the finger grows as the square of time, and the bubble as the square root of time.

Genetic reinforcement learning through symbiotic evolution for fuzzy controller design.

PubMed

Juang, C F; Lin, J Y; Lin, C T

2000-01-01

An efficient genetic reinforcement learning algorithm for designing fuzzy controllers is proposed in this paper. The genetic algorithm (GA) adopted in this paper is based upon symbiotic evolution which, when applied to fuzzy controller design, complements the local mapping property of a fuzzy rule. Using this Symbiotic-Evolution-based Fuzzy Controller (SEFC) design method, the number of control trials, as well as consumed CPU time, are considerably reduced when compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes. Moreover, unlike traditional fuzzy controllers, which partition the input space into a grid, SEFC partitions the input space in a flexible way, thus creating fewer fuzzy rules. In SEFC, different types of fuzzy rules whose consequent parts are singletons, fuzzy sets, or linear equations (TSK-type fuzzy rules) are allowed. Further, the free parameters (e.g., centers and widths of membership functions) and fuzzy rules are all tuned automatically. For the TSK-type fuzzy rule especially, which put the proposed learning algorithm in use, only the significant input variables are selected to participate in the consequent of a rule. The proposed SEFC design method has been applied to different simulated control problems, including the cart-pole balancing system, a magnetic levitation system, and a water bath temperature control system. The proposed SEFC has been verified to be efficient and superior from these control problems, and from comparisons with some traditional GA-based fuzzy systems.

Conceptual problems in detecting the evolution of dark energy when using distance measurements

NASA Astrophysics Data System (ADS)

Bolejko, K.

2011-01-01

Context. Dark energy is now one of the most important and topical problems in cosmology. The first step to reveal its nature is to detect the evolution of dark energy or to prove beyond doubt that the cosmological constant is indeed constant. However, in the standard approach to cosmology, the Universe is described by the homogeneous and isotropic Friedmann models. Aims: We aim to show that in the perturbed universe (even if perturbations vanish if averaged over sufficiently large scales) the distance-redshift relation is not the same as in the unperturbed universe. This has a serious consequence when studying the nature of dark energy and, as shown here, can impair the analysis and studies of dark energy. Methods: The analysis is based on two methods: the linear lensing approximation and the non-linear Szekeres Swiss-Cheese model. The inhomogeneity scale is ~50 Mpc, and both models have the same density fluctuations along the line of sight. Results: The comparison between linear and non-linear methods shows that non-linear corrections are not negligible. When inhomogeneities are present the distance changes by several percent. To show how this change influences the measurements of dark energy, ten future observations with 2% uncertainties are generated. It is shown the using the standard methods (i.e. under the assumption of homogeneity) the systematics due to inhomogeneities can distort our analysis, and may lead to a conclusion that dark energy evolves when in fact it is constant (or vice versa). Conclusions: Therefore, if future observations are analysed only within the homogeneous framework then the impact of inhomogeneities (such as voids and superclusters) can be mistaken for evolving dark energy. Since the robust distinction between the evolution and non-evolution of dark energy is the first step to understanding the nature of dark energy a proper handling of inhomogeneities is essential.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Thermal Evolution of the Earth from a Plate Tectonics Point of View

NASA Astrophysics Data System (ADS)

Grigne, C.; Combes, M.; Le Yaouanq, S.; Husson, L.; Conrad, C. P.; Tisseau, C.

2011-12-01

Earth's thermal history is classically studied using scaling laws that link the surface heat loss to the temperature and viscosity of the convecting mantle. When such a parameterization is used in the global heat budget of the Earth to integrate the mantle temperature backwards in time, a runaway increase of temperature is obtained, leading to the so-called "thermal catastrophe". We propose a new approach that does not rely on convective scaling laws but instead considers the dynamics of plate tectonics, including temperature-dependent surface processes. We use a multi-agent system to simulate time-dependent plate tectonics in a 2D cylindrical geometry with evolutive plate boundaries. Plate velocities are computed using local force balance and explicit parameterizations for plate boundary processes such as trench migration, subduction initiation, continental breakup and plate suturing. The number of plates is not imposed but emerges naturally. At a given time step, heat flux is integrated from the seafloor age distribution and a global heat budget is used to compute the evolution of mantle temperature. This approach has a very low computational cost and allows us to study the effect of a wide range of input parameters on the long-term thermal evolution of the system. For Earth-like parameters, an average cooling rate of 60-70K per billion years is obtained, which is consistent with petrological and rheological constraints. Two time scales arise in the evolution of the heat flux: a linear long-term decrease and high-amplitude short-term fluctuations due to tectonic rearrangements. We show that the viscosity of the mantle is not a key parameter in the thermal evolution of the system and that no thermal catastrophe occurs when considering tectonic processes. The cooling rate of the Earth depends mainly on its ability to replace old insulating seafloor by young thin oceanic lithosphere. Therefore, the main controlling factors are parameters such as the resistance of continental lithosphere to breakup or the critical age for subduction initiation. We infer that simple convective considerations alone cannot account for the complex nature of mantle heat loss and that tectonic processes dictate the thermal evolution of the Earth.

Nonlinear Dynamics of a Diffusing Interface

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Convergence Time towards Periodic Orbits in Discrete Dynamical Systems

PubMed Central

San Martín, Jesús; Porter, Mason A.

2014-01-01

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice. PMID:24736594

Role of oxygen functionality on the band structure evolution and conductance of reduced graphene oxide

NASA Astrophysics Data System (ADS)

Roy, Rajarshi; Thapa, Ranjit; Chakrabarty, Soubhik; Jha, Arunava; Midya, Priyanka R.; Kumar, E. Mathan; Chattopadhyay, Kalyan K.

2017-06-01

Here we report, structural and electrical transport properties of reduced graphene oxide as a function of oxygen bonding configuration. We find that mainly epoxy (Csbnd Osbnd C) and carbonyl (Cdbnd O) functional groups remain as major residual components after reduction using three different reducing agents. We calculate the band structure in the presence of epoxy and carbonyl groups and defects. Finally, we calculate the theoretical band mobility and find that it is less for the carbonyl with epoxy system. We correlate the distortion of linear dispersion and opening of bandgap at K-point with conductance for different graphene system in presence of oxygen moieties.

Collisional effects on the numerical recurrence in Vlasov-Poisson simulations

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

Pezzi, Oreste; Valentini, Francesco; Camporeale, Enrico

The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used,more » an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.« less

Oligopolies with contingent workforce and unemployment insurance systems

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2015-10-01

In the recent literature the introduction of modified cost functions has added reality into the classical oligopoly analysis. Furthermore, the market evolution requires much more flexibility to firms, and in several countries contingent workforce plays an important role in the production choices by the firms. Therefore, an analysis of dynamic adjustment costs is in order to understand oligopoly dynamics. In this paper, dynamic single-product oligopolies without product differentiation are first examined with the additional consideration of production adjustment costs. Linear inverse demand and cost functions are considered and it is assumed that the firms adjust their outputs partially toward best response. The set of the steady states is characterized by a system of linear inequalities and there are usually infinitely many steady states. The asymptotic behavior of the output trajectories is examined by using computer simulation. The numerical results indicate that the resulting dynamics is richer than in the case of the classical Cournot model. This model and results are then compared to oligopolies with unemployment insurance systems when the additional cost is considered if firms do not use their maximum capacities.

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.

Holographic dark energy in higher derivative gravity with time varying model parameter c2

NASA Astrophysics Data System (ADS)

Borah, B.; Ansari, M.

2015-01-01

Purpose of this paper is to study holographic dark energy in higher derivative gravity assuming the model parameter c2 as a slowly time varying function. Since dark energy emerges as combined effect of linear as well as non-linear terms of curvature, therefore it is important to see holographic dark energy at higher derivative gravity, where action contains both linear as well as non-linear terms of Ricci curvature R. We consider non-interacting scenario of the holographic dark energy with dark matter in spatially flat universe and obtain evolution of the equation of state parameter. Also, we determine deceleration parameter as well as the evolution of dark energy density to explain expansion of the universe. Further, we investigate validity of generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of holographic dark energy for low red-shifts containing c2 correction.

A new modified conjugate gradient coefficient for solving system of linear equations

NASA Astrophysics Data System (ADS)

Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

Linear dynamics of classical spin as Mobius transformation

DOE PAGES

Galda, Alexey; Vinokur, Valerii М.

2017-04-26

Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phasemore » transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.« less

Computing with dynamical systems based on insulator-metal-transition oscillators

NASA Astrophysics Data System (ADS)

Parihar, Abhinav; Shukla, Nikhil; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2017-04-01

In this paper, we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states with hysteresis. By harnessing the dynamics of complex, connected systems, we embrace the philosophy of "let physics do the computing" and demonstrate how complex phase and frequency dynamics of such systems can be controlled, programmed, and observed to solve computationally hard problems. Although our discussion in this paper is limited to insulator-to-metallic state transition devices, the general philosophy of such computing paradigms can be translated to other mediums including optical systems. We present the necessary mathematical treatments necessary to understand the time evolution of these systems and demonstrate through recent experimental results the potential of such computational primitives.

The Jukes-Cantor Model of Molecular Evolution

ERIC Educational Resources Information Center

Erickson, Keith

2010-01-01

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

Secular evolution of eccentricity in protoplanetary discs with gap-opening planets

NASA Astrophysics Data System (ADS)

Teyssandier, Jean; Ogilvie, Gordon I.

2017-06-01

We explore the evolution of the eccentricity of an accretion disc perturbed by an embedded planet whose mass is sufficient to open a large gap in the disc. Various methods for representing the orbit-averaged motion of an eccentric disc are discussed. We characterize the linear instability that leads to the growth of eccentricity by means of hydrodynamical simulations. We numerically recover the known result that eccentricity growth in the disc is possible when the planet-to-star mass ratio exceeds 3 × 10-3. For mass ratios larger than this threshold, the precession rates and growth rates derived from simulations, as well as the shape of the eccentric mode, compare well with the predictions of a linear theory of eccentric discs. We study mechanisms by which the eccentricity growth eventually saturates into a non-linear regime.

Electron acceleration via magnetic island coalescence

NASA Astrophysics Data System (ADS)

Shinohara, I.; Yumura, T.; Tanaka, K. G.; Fujimoto, M.

2009-06-01

Electron acceleration via fast magnetic island coalescence that happens as quick magnetic reconnection triggering (QMRT) proceeds has been studied. We have carried out a three-dimensional full kinetic simulation of the Harris current sheet with a large enough simulation run for two magnetic islands coalescence. Due to the strong inductive electric field associated with the non-linear evolution of the lower-hybrid-drift instability and the magnetic island coalescence process observed in the non-linear stage of the collisionless tearing mode, electrons are significantly accelerated at around the neutral sheet and the subsequent X-line. The accelerated meandering electrons generated by the non-linear evolution of the lower-hybrid-drift instability are resulted in QMRT, and QMRT leads to fast magnetic island coalescence. As a whole, the reconnection triggering and its transition to large-scale structure work as an effective electron accelerator.

Kalman filter with a linear state model for PDR+WLAN positioning and its application to assisting a particle filter

NASA Astrophysics Data System (ADS)

Raitoharju, Matti; Nurminen, Henri; Piché, Robert

2015-12-01

Indoor positioning based on wireless local area network (WLAN) signals is often enhanced using pedestrian dead reckoning (PDR) based on an inertial measurement unit. The state evolution model in PDR is usually nonlinear. We present a new linear state evolution model for PDR. In simulated-data and real-data tests of tightly coupled WLAN-PDR positioning, the positioning accuracy with this linear model is better than with the traditional models when the initial heading is not known, which is a common situation. The proposed method is computationally light and is also suitable for smoothing. Furthermore, we present modifications to WLAN positioning based on Gaussian coverage areas and show how a Kalman filter using the proposed model can be used for integrity monitoring and (re)initialization of a particle filter.

Frequency of Behavior Witnessed and Conformity in an Everyday Social Context

PubMed Central

Claidière, Nicolas; Bowler, Mark; Brookes, Sarah; Brown, Rebecca; Whiten, Andrew

2014-01-01

Conformity is thought to be an important force in human evolution because it has the potential to stabilize cultural homogeneity within groups and cultural diversity between groups. However, the effects of such conformity on cultural and biological evolution will depend much on the particular way in which individuals are influenced by the frequency of alternative behavioral options they witness. In a previous study we found that in a natural situation people displayed a tendency to be ‘linear-conformist’. When visitors to a Zoo exhibit were invited to write or draw answers to questions on cards to win a small prize and we manipulated the proportion of text versus drawings on display, we found a strong and significant effect of the proportion of text displayed on the proportion of text in the answers, a conformist effect that was largely linear with a small non-linear component. However, although this overall effect is important to understand cultural evolution, it might mask a greater diversity of behavioral responses shaped by variables such as age, sex, social environment and attention of the participants. Accordingly we performed a further study explicitly to analyze the effects of these variables, together with the quality of the information participants' responses made available to further visitors. Results again showed a largely linear conformity effect that varied little with the variables analyzed. PMID:24950212

Direct measurement of nonlinear dispersion relation for water surface waves

NASA Astrophysics Data System (ADS)

Magnus Arnesen Taklo, Tore; Trulsen, Karsten; Elias Krogstad, Harald; Gramstad, Odin; Nieto Borge, José Carlos; Jensen, Atle

2013-04-01

The linear dispersion relation for water surface waves is often taken for granted for the interpretation of wave measurements. High-resolution spatiotemporal measurements suitable for direct validation of the linear dispersion relation are on the other hand rarely available. While the imaging of the ocean surface with nautical radar does provide the desired spatiotemporal coverage, the interpretation of the radar images currently depends on the linear dispersion relation as a prerequisite, (Nieto Borge et al., 2004). Krogstad & Trulsen (2010) carried out numerical simulations with the nonlinear Schrödinger equation and its generalizations demonstrating that the nonlinear evolution of wave fields may render the linear dispersion relation inadequate for proper interpretation of observations, the reason being that the necessary domain of simultaneous coverage in space and time would allow significant nonlinear evolution. They found that components above the spectral peak can have larger phase and group velocities than anticipated by linear theory, and that the spectrum does not maintain a thin dispersion surface. We have run laboratory experiments and accurate numerical simulations designed to have sufficient resolution in space and time to deduce the dispersion relation directly. For a JONSWAP spectrum we find that the linear dispersion relation can be appropriate for the interpretation of spatiotemporal measurements. For a Gaussian spectrum with narrower bandwidth we find that the dynamic nonlinear evolution in space and time causes the directly measured dispersion relation to deviate from the linear dispersion surface in good agreement with our previous numerical predictions. This work has been supported by RCN grant 214556/F20. Krogstad, H. E. & Trulsen, K. (2010) Interpretations and observations of ocean wave spectra. Ocean Dynamics 60:973-991. Nieto Borge, J. C., Rodríguez, G., Hessner, K., Izquierdo, P. (2004) Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean. Tech. 21:1291-1300.

Radiation reaction for spinning bodies in effective field theory. I. Spin-orbit effects

NASA Astrophysics Data System (ADS)

Maia, Natália T.; Galley, Chad R.; Leibovich, Adam K.; Porto, Rafael A.

2017-10-01

We compute the leading post-Newtonian (PN) contributions at linear order in the spin to the radiation-reaction acceleration and spin evolution for binary systems, which enter at fourth PN order. The calculation is carried out, from first principles, using the effective field theory framework for spinning compact objects, in both the Newton-Wigner and covariant spin supplementary conditions. A nontrivial consistency check is performed on our results by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone, up to so-called "Schott terms." We also find that, at this order, the radiation reaction has no net effect on the evolution of the spins. The spin-spin contributions to radiation reaction are reported in a companion paper.

The evolution of phenotypic correlations and ‘developmental memory’

PubMed Central

Watson, Richard A.; Wagner, Günter P.; Pavlicev, Mihaela; Weinreich, Daniel M.; Mills, Rob

2014-01-01

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent non-linear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can ‘store’ and ‘recall’ multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and ‘generalise’ (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviours follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well-understood in the context of neural networks. This helps to explain how development facilitates the evolution of high-fitness phenotypes and how this ability changes over evolutionary time. PMID:24351058

Dynamical recovery of SU(2) symmetry in the mass-quenched Hubbard model

NASA Astrophysics Data System (ADS)

Du, Liang; Fiete, Gregory A.

2018-02-01

We use nonequilibrium dynamical mean-field theory with iterative perturbation theory as an impurity solver to study the recovery of SU(2) symmetry in real time following a hopping integral parameter quench from a mass-imbalanced to a mass-balanced single-band Hubbard model at half filling. A dynamical order parameter γ (t ) is defined to characterize the evolution of the system towards SU(2) symmetry. By comparing the momentum-dependent occupation from an equilibrium calculation [with the SU(2) symmetric Hamiltonian after the quench at an effective temperature] with the data from our nonequilibrium calculation, we conclude that the SU(2) symmetry recovered state is a thermalized state. Further evidence from the evolution of the density of states supports this conclusion. We find the order parameter in the weak Coulomb interaction regime undergoes an approximate exponential decay. We numerically investigate the interplay of the relevant parameters (initial temperature, Coulomb interaction strength, initial mass-imbalance ratio) and their combined effect on the thermalization behavior. Finally, we study evolution of the order parameter as the hopping parameter is changed with either a linear ramp or a pulse. Our results can be useful in strategies to engineer the relaxation behavior of interacting quantum many-particle systems.

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus.

PubMed

Fan, Denggui; Wang, Qingyun; Su, Jianzhong; Xi, Hongguang

2017-12-01

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

Mathematical model of unmanned aerial vehicle used for endurance autonomous monitoring

NASA Astrophysics Data System (ADS)

Chelaru, Teodor-Viorel; Chelaru, Adrian

2014-12-01

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system, based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.

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

Chelaru, Teodor-Viorel, E-mail: teodor.chelaru@upb.ro; Chelaru, Adrian, E-mail: achelaru@incas.ro

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system,more » based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.« less

Thermodynamic Modelling of Phase Transformation in a Multi-Component System

NASA Astrophysics Data System (ADS)

Vala, J.

2007-09-01

Diffusion in multi-component alloys can be characterized by the vacancy mechanism for substitutional components, by the existence of sources and sinks for vacancies and by the motion of atoms of interstitial components. The description of diffusive and massive phase transformation of a multi-component system is based on the thermodynamic extremal principle by Onsager; the finite thickness of the interface between both phases is respected. The resulting system of partial differential equations of evolution with integral terms for unknown mole fractions (and additional variables in case of non-ideal sources and sinks for vacancies), can be analyzed using the method of lines and the finite difference technique (or, alternatively, the finite element one) together with the semi-analytic and numerical integration formulae and with certain iteration procedure, making use of the spectral properties of linear operators. The original software code for the numerical evaluation of solutions of such systems, written in MATLAB, offers a chance to simulate various real processes of diffusional phase transformation. Some results for the (nearly) steady-state real processes in substitutional alloys have been published yet. The aim of this paper is to demonstrate that the same approach can handle both substitutional and interstitial components even in case of a general system of evolution.

S-Lagrangian dynamics of many-body systems and behavior of social groups: Dominance and hierarchy formation

NASA Astrophysics Data System (ADS)

Sandler, U.

2017-11-01

In this paper, we extend our generalized Lagrangian dynamics (i.e., S-Lagrangian dynamics, which can be applied equally to physical and non-physical systems as per Sandler (2014)) to many-body systems. Unlike common Lagrangian dynamics, this is not a trivial task. For many-body systems with S-dependent Lagrangians, the Lagrangian and the corresponding Hamiltonian or energy become vector functions, conjugated momenta become second-order tensors, and the system inevitably develops a hierarchical structure, even if all bodies initially have similar status and Lagrangians. As an application of our theory, we consider dominance and hierarchy formation, which is present in almost all communities of living species. As a biological basis for this application, we assume that the primary motivation of a groups activity is to attempt to cope with stress arising as pressure from the environment and from intrinsic unmet needs of individuals. It has been shown that the S-Lagrangian approach to a group's evolution naturally leads to formation of linear or despotic dominance hierarchies, depending on differences between individuals in coping with stress. That is, individuals that cope more readily with stress take leadership roles during the evolution. Experimental results in animal groups which support our assumption and findings are considered.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Cross-field Current Instability for Substorm Expansions

NASA Technical Reports Server (NTRS)

Lui, Anthony

1997-01-01

The funding provided by the above-referenced NASA grant has enabled us: (1) to investigate the quasi-linear evolution of the IWI [Lui et al., 1993] and that of the generalized MTSI/IWI [Yoon and Lui, 1993], (2) to carry out the linear analysis of the LHDI to elucidate the difference between it and the MTSI/PM instability [Yoon et al., 1994], (3) to conduct some preliminary nonlocal analyses of the MTSI [Lui et al., 1995] and the IWI [Yoon and Lui, 1996] modes, (4) to study low-frequency shear-driven instability and its nonlinear evolution, which might compete with the CCI [Yoon et al., 1996], and (5) to study the evolution of current sheet during late substorm growth phase by means of 2-D Hall-MHD simulation in order to obtain a better understanding of the current sheet equilibrium crucial for CCI theory [Yoon and Lui, 1997].

δ M formalism: a new approach to cosmological perturbation theory in anisotropic inflation

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.; Abolhasani, A. A.

2018-03-01

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the δ M formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in almost the same way that the so-called δ N formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, δ N, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as δ N it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

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

Hollenstein, Lukas; Jain, Rajeev Kumar; Urban, Federico R., E-mail: lukas.hollenstein@cea.fr, E-mail: jain@cp3.dias.sdu.dk, E-mail: furban@ulb.ac.be

2013-01-01

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizeablemore » conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios. Even at scales well beyond a Mpc, any departure from flux freezing behaviour is inhibited.« less

Temporal evolution of age data under transient pumping conditions

NASA Astrophysics Data System (ADS)

Leray, S.; de Dreuzy, J.-R.; Aquilina, L.; Vergnaud-Ayraud, V.; Labasque, T.; Bour, O.; Le Borgne, T.

2014-04-01

While most age data derived from tracers have been analyzed in steady-state flow conditions, we determine their temporal evolution when starting a pumping. Our study is based on a model made up of a shallowly dipping aquifer overlain by a less permeable aquitard characteristic of the crystalline aquifer of Plœmeur (Brittany, France). Under a pseudo transient flow assumption (instantaneous shift between two steady-state flow fields), we solve the transport equation with a backward particle-tracking method and determine the temporal evolution of the concentrations at the pumping well of CFC-11, CFC-12, CFC-113 and SF6. Apparent ages evolve because of the modifications of the flow pattern and because of the non-linear evolution of the tracer atmospheric concentrations. To identify the respective role of these two causes, we propose two successive analyses. We first convolute residence time distributions initially arising at different times at the same sampling time. We secondly convolute one residence time distribution at various sampling times. We show that flow pattern modifications control the apparent ages evolution in the first pumping year when the residence time distribution is modified from a piston-like distribution to a much broader distribution. In the first pumping year, the apparent age evolution contains transient information that can be used to better constrain hydrogeological systems and slightly compensate for the small number of tracers. Later, the residence time distribution hardly evolves and apparent ages only evolve because of the tracer atmospheric concentrations. In this phase, apparent age time-series do not reflect any evolution in the flow pattern.

Translation invariant time-dependent massive gravity: Hamiltonian analysis

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

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Baryonic Force for Accelerated Cosmic Expansion and Generalized U1b Gauge Symmetry in Particle-Cosmology

NASA Astrophysics Data System (ADS)

Khan, Mehbub; Hao, Yun; Hsu, Jong-Ping

2018-01-01

Based on baryon charge conservation and a generalized Yang-Mills symmetry for Abelian (and non-Abelian) groups, we discuss a new baryonic gauge field and its linear potential for two point-like baryon charges. The force between two point-like baryons is repulsive, extremely weak and independent of distance. However, for two extended baryonic systems, we have a dominant linear force α r. Thus, only in the later stage of the cosmic evolution, when two baryonic galaxies are separated by an extremely large distance, the new repulsive baryonic force can overcome the gravitational attractive force. Such a model provides a gauge-field-theoretic understanding of the late-time accelerated cosmic expansion. The baryonic force can be tested by measuring the accelerated Wu-Doppler frequency shifts of supernovae at different distances.

Barrier island morphodynamic classification based on lidar metrics for north Assateague Island, Maryland

USGS Publications Warehouse

Brock, John C.; Krabill, William; Sallenger, Asbury H.

2004-01-01

In order to reap the potential of airborne lidar surveys to provide geological information useful in understanding coastal sedimentary processes acting on various time scales, a new set of analysis methods are needed. This paper presents a multi-temporal lidar analysis of north Assateague Island, Maryland, and demonstrates the calculation of lidar metrics that condense barrier island morphology and morphological change into attributed linear features that may be used to analyze trends in coastal evolution. The new methods proposed in this paper are also of significant practical value, because lidar metric analysis reduces large volumes of point elevations into linear features attributed with essential morphological variables that are ideally suited for inclusion in Geographic Information Systems. A morphodynamic classification of north Assategue Island for a recent 10 month time period that is based on the recognition of simple patterns described by lidar change metrics is presented. Such morphodynamic classification reveals the relative magnitude and the fine scale alongshore variation in the importance of coastal changes over the study area during a defined time period. More generally, through the presentation of this morphodynamic classification of north Assateague Island, the value of lidar metrics in both examining large lidar data sets for coherent trends and in building hypotheses regarding processes driving barrier evolution is demonstrated

Phase field benchmark problems for dendritic growth and linear elasticity

DOE PAGES

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.; ...

2018-03-26

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

Phase field benchmark problems for dendritic growth and linear elasticity

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

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

A geomorphic process law for detachment-limited hillslopes

NASA Astrophysics Data System (ADS)

Turowski, Jens

2015-04-01

Geomorphic process laws are used to assess the shape evolution of structures at the Earth's surface over geological time scales, and are routinely used in landscape evolution models. There are two currently available concepts on which process laws for hillslope evolution rely. In the transport-limited concept, the evolution of a hillslope is described by a linear or a non-linear diffusion equation. In contrast, in the threshold slope concept, the hillslope is assumed to collapse to a slope equal to the internal friction angle of the material when the load due to the relief exists the material strength. Many mountains feature bedrock slopes, especially in the high mountains, and material transport along the slope is limited by the erosion of the material from the bedrock. Here, I suggest a process law for detachment-limited or threshold-dominated hillslopes, in which the erosion rate is a function of the applied stress minus the surface stress due to structural loading. The process law leads to the prediction of an equilibrium form that compares well to the shape of many mountain domes.

Evolution of lower hybrid turbulence in the ionosphere

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

Ganguli, G.; Crabtree, C.; Mithaiwala, M.

2015-11-15

Three-dimensional evolution of the lower hybrid turbulence driven by a spatially localized ion ring beam perpendicular to the ambient magnetic field in space plasmas is analyzed. It is shown that the quasi-linear saturation model breaks down when the nonlinear rate of scattering by thermal electron is larger than linear damping rates, which can occur even for low wave amplitudes. The evolution is found to be essentially a three-dimensional phenomenon, which cannot be accurately explained by two-dimensional simulations. An important feature missed in previous studies of this phenomenon is the nonlinear conversion of electrostatic lower hybrid waves into electromagnetic whistler andmore » magnetosonic waves and the consequent energy loss due to radiation from the source region. This can result in unique low-amplitude saturation with extended saturation time. It is shown that when the nonlinear effects are considered the net energy that can be permanently extracted from the ring beam is larger. The results are applied to anticipate the outcome of a planned experiment that will seed lower hybrid turbulence in the ionosphere and monitor its evolution.« less

Petrological evidence for non-linear increase of magmatic intrusion rates before eruption at open vent mafic volcanoe

NASA Astrophysics Data System (ADS)

Ruth, D. C. S.; Costa Rodriguez, F.

2015-12-01

The most active volcanoes on earth erupt in a yearly to decadal time scales, typically erupt mafic magmas and are open-vent systems with prominent degassing plumes (e.g. Mayon, Arenal, Llaima, Etna). Here we investigate the plumbing systems, dynamics, and processes that drive eruptions at these systems. These are key questions for improving hazard evaluation, and better understanding the unrest associated with these types of volcanoes. The petrology and geochemistry from six historical eruptions (1947-2006) of Mayon volcano (Philippines) shows that all lavas are basaltic andesite with phenocrysts of plagioclase + orthopyroxene (Opx) + clinopyroxene. Opx crystals show a variety of compositions and zoning patterns (reverse, normal or complex) with Mg# (= 100 *Mg/[Mg+Fe]) varying from 67 to 81. The simplest interpretation is that the low Mg# parts of the crystals resided on an upper crustal and crystal rich reservoir that was intruded by more primitive magmas from which the high Mg# parts of the crystals grew. Modelling Mg-Fe diffusion in Opx shows that times since magma injection and eruption range from a few days up to 3.5 years in all of the investigated eruptions. The longest diffusion times are shorter than the repose times between the eruptions, which implies that crystal recycling between eruptive events is negligible. This is a surprising result that shows that for each eruption a different part of the evolved crystal-rich plumbing system is activated. This can be due to random intrusion location or an irreversibility of the plumbing system that prevents multiple eruptions from the same crystal-rich part. Moreover, we find that the number of intrusions markedly increases before each eruption in a non-linear manner. Such an increased rate of intrusions with time might reflect non-linear rheological properties of the crystal-rich system, of the enclosing rocks, or the non-linear evolution of crystal-melt reaction-dissolution fronts during magma intrusions.

Helicity Evolution at Small x

NASA Astrophysics Data System (ADS)

Sievert, Michael; Kovchegov, Yuri; Pitonyak, Daniel

2017-01-01

We construct small- x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of ln2(1 / x) in the polarization-dependent evolution along with the powers of ln(1 / x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-Nc and large-Nc &Nf limits. After solving the large-Nc equations numerically we obtain the following small- x asymptotics for the flavor-singlet g1 structure function along with quarks hPDFs and helicity TMDs (in absence of saturation effects): g1S(x ,Q2) ΔqS(x ,Q2) g1L S(x ,kT2) (1/x) > αh (1/x) 2.31√{αsNc/2 π. We also give an estimate of how much of the proton's spin may be at small x and what impact this has on the so-called ``spin crisis.'' Work supported by the U.S. DOE, Office of Science, Office of Nuclear Physics under Award Number DE-SC0004286 (YK), the RIKEN BNL Research Center, and TMD Collaboration (DP), and DOE Contract No. DE-SC0012704 (MS).

Ludwig Edinger: the vertebrate series and comparative neuroanatomy.

PubMed

Patton, Paul

2015-01-01

At the end of the nineteenth century, Ludwig Edinger completed the first comparative survey of the microscopic anatomy of vertebrate brains. He is regarded as the founder of the field of comparative neuroanatomy. Modern commentators have misunderstood him to have espoused an anti-Darwinian linear view of brain evolution, harkening to the metaphysics of the scala naturae. This understanding arises, in part, from an increasingly contested view of nineteenth-century morphology in Germany. Edinger did espouse a progressionist, though not strictly linear, view of forebrain evolution, but his work also provided carefully documented evidence that brain stem structures vary in complexity independently from one another and across species in a manner that is not compatible with linear progress. This led Edinger to reject progressionism for all brain structures other than the forebrain roof, based on reasoning not too dissimilar from those his successors used to dismiss it for the forebrain roof.

Instability, finite amplitude pulsation and mass-loss in models of massive OB-type stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Glatzel, Wolfgang

2017-11-01

Variability and mass-loss are common phenomena in massive OB-type stars. It is argued that they are caused by violent strange mode instabilities identified in corresponding stellar models. We present a systematic linear stability analysis with respect to radial perturbations of massive OB-type stars with solar chemical composition and masses between 23 and 100 M⊙. For selected unstable stellar models, we perform non-linear simulations of the evolution of the instabilities into the non-linear regime. Finite amplitude pulsations with periods in the range between hours and 100 d are found to be the final result of the instabilities. The pulsations are associated with a mean acoustic luminosity which can be the origin of a pulsationally driven wind. Corresponding mass-loss rates lie in the range between 10-9 and 10-4 M⊙ yr-1 and may thus affect the evolution of massive stars.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Pursuing optimal electric machines transient diagnosis: The adaptive slope transform

NASA Astrophysics Data System (ADS)

Pons-Llinares, Joan; Riera-Guasp, Martín; Antonino-Daviu, Jose A.; Habetler, Thomas G.

2016-12-01

The aim of this paper is to introduce a new linear time-frequency transform to improve the detection of fault components in electric machines transient currents. Linear transforms are analysed from the perspective of the atoms used. A criterion to select the atoms at every point of the time-frequency plane is proposed, taking into account the characteristics of the searched component at each point. This criterion leads to the definition of the Adaptive Slope Transform, which enables a complete and optimal capture of the different components evolutions in a transient current. A comparison with conventional linear transforms (Short-Time Fourier Transform and Wavelet Transform) is carried out, showing their inherent limitations. The approach is tested with laboratory and field motors, and the Lower Sideband Harmonic is captured for the first time during an induction motor startup and subsequent load oscillations, accurately tracking its evolution.

Proton structure functions at small x

DOE PAGES

Hentschinski, Martin

2015-11-03

Proton structure functions are measured in electron-proton collision through inelastic scattering of virtual photons with virtuality Q on protons; x denotes the momentum fraction carried by the struck parton. Proton structure functions are currently described with excellent accuracy in terms of scale dependent parton distribution functions, defined in terms of collinear factorization and DGLAP evolution in Q. With decreasing x however, parton densities increase and are ultimately expected to saturate. In this regime DGLAP evolution will finally break down and non-linear evolution equations w.r.t x are expected to take over. In the first part of the talk we present recentmore » result on an implementation of physical DGLAP evolution. Unlike the conventional description in terms of parton distribution functions, the former describes directly the Q dependence of the measured structure functions. It is therefore physical insensitive to factorization scheme and scale ambiguities. It therefore provides a more stringent test of DGLAP evolution and eases the manifestation of (non-linear) small x effects. It however requires a precise measurement of both structure functions F 2 and F L, which will be only possible at future facilities, such as an Electron Ion Collider. In the second part we present a recent analysis of the small x region of the combined HERA data on the structure function F 2. We demonstrate that (linear) next-to-leading order BFKL evolution describes the effective Pomeron intercept, determined from the combined HERA data, once a resummation of collinear enhanced terms is included and the renormalization scale is fixed using the BLM optimal scale setting procedure. We also provide a detailed description of the Q and x dependence of the full structure functions F 2 in the small x region, as measured at HERA. As a result, predictions for the structure function F L are found to be in agreement with the existing HERA data.« less

Linear and non-linear perturbations in dark energy models

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

Escamilla-Rivera, Celia; Casarini, Luciano; Fabris, Júlio C.

2016-11-01

In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state w ( z ). In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected w ( z ) parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard ΛCDM model.

The non-linear power spectrum of the Lyman alpha forest

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

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo

2015-12-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate themore » comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.« less

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Multi-scaling allometric analysis for urban and regional development

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2017-01-01

The concept of allometric growth is based on scaling relations, and it has been applied to urban and regional analysis for a long time. However, most allometric analyses were devoted to the single proportional relation between two elements of a geographical system. Few researches focus on the allometric scaling of multielements. In this paper, a process of multiscaling allometric analysis is developed for the studies on spatio-temporal evolution of complex systems. By means of linear algebra, general system theory, and by analogy with the analytical hierarchy process, the concepts of allometric growth can be integrated with the ideas from fractal dimension. Thus a new methodology of geo-spatial analysis and the related theoretical models emerge. Based on the least squares regression and matrix operations, a simple algorithm is proposed to solve the multiscaling allometric equation. Applying the analytical method of multielement allometry to Chinese cities and regions yields satisfying results. A conclusion is reached that the multiscaling allometric analysis can be employed to make a comprehensive evaluation for the relative levels of urban and regional development, and explain spatial heterogeneity. The notion of multiscaling allometry may enrich the current theory and methodology of spatial analyses of urban and regional evolution.

A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials.

PubMed

Giorgio, Ivan; Andreaus, Ugo; Scerrato, Daria; dell'Isola, Francesco

2016-10-01

In this paper, the phenomena of resorption and growth of bone tissue and resorption of the biomaterial inside a bicomponent system are studied by means of a numerical method based on finite elements. The material behavior is described by a poro-viscoelastic model with infiltrated voids. The mechanical stimulus that drives these processes is a linear combination of density of strain energy and viscous dissipation. The external excitation is represented by a bending load slowly variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency, of type of the stimulus and of the effective porosity on the time evolution of the mass densities of considered system.

Generation of squeezing in a driven many-body system

NASA Astrophysics Data System (ADS)

Hebbe Madhusudhana, Bharath; Boguslawski, Matthew; Anquez, Martin; Robbins, Bryce; Barrios, Maryrose; Hoang, Thai; Chapman, Michael

2016-05-01

In a spin-1 Bose-Einstein condensate, the non-linear spin-dependent collisional interactions can create entanglement and squeezing. Typically, the condensate is initialized at an unstable fixed point of the phase space, and subsequent free evolution under a time-independent Hamiltonian creates the squeezed state. Alternatively, it is possible to generate squeezing by driving the system localized at a stable fixed point. Here, we demonstrate that periodic modulation of the Hamiltonian can generate highly squeezed states. Our measurements show -5 dB of squeezing, limited by the detection, but calculations indicate that a theoretical potential of -20 dB of squeezing. We discuss the advantages of this method compared with the typical techniques.

Reduced nonlinear prognostic model construction from high-dimensional data

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Design feasibility study of a divertor component reinforced with fibrous metal matrix composite laminate

NASA Astrophysics Data System (ADS)

You, Jeong-Ha

2005-01-01

Fibrous metal matrix composites possess advanced mechanical properties compared to conventional alloys. It is expected that the application of these composites to a divertor component will enhance the structural reliability. A possible design concept would be a system consisting of tungsten armour, copper composite interlayer and copper heat sink where the composite interlayer is locally inserted into the highly stressed domain near the bond interface. For assessment of the design feasibility of the composite divertor concept, a non-linear multi-scale finite element analysis was performed. To this end, a micro-mechanics algorithm was implemented into a finite element code. A reactor-relevant heat flux load was assumed. Focus was placed on the evolution of stress state, plastic deformation and ductile damage on both macro- and microscopic scales. The structural response of the component and the micro-scale stress evolution of the composite laminate were investigated.

Discovering urban mobility patterns with PageRank based traffic modeling and prediction

NASA Astrophysics Data System (ADS)

Wang, Minjie; Yang, Su; Sun, Yi; Gao, Jun

2017-11-01

Urban transportation system can be viewed as complex network with time-varying traffic flows as links to connect adjacent regions as networked nodes. By computing urban traffic evolution on such temporal complex network with PageRank, it is found that for most regions, there exists a linear relation between the traffic congestion measure at present time and the PageRank value of the last time. Since the PageRank measure of a region does result from the mutual interactions of the whole network, it implies that the traffic state of a local region does not evolve independently but is affected by the evolution of the whole network. As a result, the PageRank values can act as signatures in predicting upcoming traffic congestions. We observe the aforementioned laws experimentally based on the trajectory data of 12000 taxies in Beijing city for one month.

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Non-modal analysis of the diocotron instability: Cylindrical geometry

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

Mikhailenko, V. V.; Lee, Hae June; Mikhailenko, V. S.

2013-04-15

The temporal evolution of the linear diocotron instability of the cylindrical annular plasma column is investigated by employing the extension of the shearing modes methodology to the cylindrical geometry. It was obtained that the spatial time-dependent distortion of the electron density initial perturbations by shear flows leads to the non-modal evolution of the potential, which was referred to as the manifestation of the continuous spectrum. The evolution process leads toward the convergence to the phase-locking configuration of the mutually growing normal modes.

The red/infrared evolution in galaxies - Effect of the stars on the asymptotic giant branch

NASA Technical Reports Server (NTRS)

Chokshi, Arati; Wright, Edward L.

1987-01-01

The effect of including the asymptotic giant branch (AGB) population in a spectral synthesis model of galaxy evolution is examined. Stars on the AGB are luminous enough and also evolve rapidly enough to affect the evolution of red and infrared colors in galaxies. The validity of using infrared colors as distance indicators to galaxies is then investigated in detail. It is found that for z of 1 or less infrared colors of model galaxies behave linearly with redshift.

Some simple solutions of Schrödinger's equation for a free particle or for an oscillator

NASA Astrophysics Data System (ADS)

Andrews, Mark

2018-05-01

For a non-relativistic free particle, we show that the evolution of some simple initial wave functions made up of linear segments can be expressed in terms of Fresnel integrals. Examples include the square wave function and the triangular wave function. The method is then extended to wave functions made from quadratic elements. The evolution of all these initial wave functions can also be found for the harmonic oscillator by a transformation of the free evolutions.

Left Right Patterning, Evolution and Cardiac Development

PubMed Central

Dykes, Iain M.

2018-01-01

Many aspects of heart development are determined by the left right axis and as a result several congenital diseases have their origins in aberrant left-right patterning. Establishment of this axis occurs early in embryogenesis before formation of the linear heart tube yet impacts upon much later morphogenetic events. In this review I discuss the differing mechanisms by which left-right polarity is achieved in the mouse and chick embryos and comment on the evolution of this system. I then discus three major classes of cardiovascular defect associated with aberrant left-right patterning seen in mouse mutants and human disease. I describe phenotypes associated with the determination of atrial identity and venous connections, looping morphogenesis of the heart tube and finally the asymmetric remodelling of the embryonic branchial arch arterial system to form the leftward looped arch of aorta and associated great arteries. Where appropriate, I consider left right patterning defects from an evolutionary perspective, demonstrating how developmental processes have been modified in species over time and illustrating how comparative embryology can aide in our understanding of congenital heart disease. PMID:29755990

The co-evolution of microstructure features in self-ion irradiated HT9 at very high damage levels

NASA Astrophysics Data System (ADS)

Getto, Elizabeth Margaret

The objective of this study was to understand the co-evolution of microstructure features in self-ion irradiated HT9 at very high damage levels. HT9 (heat 84425) was pre-implanted with 10 atom parts per million helium and then irradiated with 5 MeV Fe++ in the temperature range of 440-480°C to 188 dpa. A damage dependence study from 75 to 650 dpa was performed at the peak swelling temperature of 460°C. The swelling, dislocation and precipitate evolution was determined using Analytic Electron Microscopes in both Conventional Transmission electron microscopy (CTEM) and Scanning Transmission Electron Microscopy (STEM) modes. Void swelling reached a nominally linear rate of 0.03%/dpa from 188 to 650 dpa at 460°C. G phase precipitates were observed by 75 dpa and grew linearly up to 650 dpa. M 2X was observed by 250 dpa and peaked in volume fraction at 450 dpa. Dislocation loop evolution was observed up to 650 dpa including a step change in diameter between 375 and 450 dpa; which correlated with nucleation and growth of M2X. The experimental results were interpreted using a rate theory model, the Radiation Induced Microstructure Evolution (RIME), in the damage range from 188 to 650 dpa. A simple system of voids and dislocations was modeled in which the dislocations measured from experiment were used as input, or the dislocations were allowed to evolve dynamically, resulting in swelling that was overestimated by 63% relative to that observed experimentally. G phase had limited effect on the void or dislocation behavior. The behavior of M2X within the microstructure was characterized as a direct effect as a coherent sink, and as an indirect effect in consuming carbon from the matrix, which had the largest impact on both void and dislocation behavior. A slowly monotonically increasing swelling rate was observed both experimentally and computationally, with swelling rates of ˜0.025%/dpa and ˜0.036%/dpa before and after 450 dpa. The agreement in void behavior between experiment and model when all effects (loops, network, G phase, M2X formation and growth, and removal of carbon) are accounted for demonstrates the importance of characterizing the evolution of the full microstructure over a large dpa range.

Computational power and generative capacity of genetic systems.

PubMed

Igamberdiev, Abir U; Shklovskiy-Kordi, Nikita E

2016-01-01

Semiotic characteristics of genetic sequences are based on the general principles of linguistics formulated by Ferdinand de Saussure, such as the arbitrariness of sign and the linear nature of the signifier. Besides these semiotic features that are attributable to the basic structure of the genetic code, the principle of generativity of genetic language is important for understanding biological transformations. The problem of generativity in genetic systems arises to a possibility of different interpretations of genetic texts, and corresponds to what Alexander von Humboldt called "the infinite use of finite means". These interpretations appear in the individual development as the spatiotemporal sequences of realizations of different textual meanings, as well as the emergence of hyper-textual statements about the text itself, which underlies the process of biological evolution. These interpretations are accomplished at the level of the readout of genetic texts by the structures defined by Efim Liberman as "the molecular computer of cell", which includes DNA, RNA and the corresponding enzymes operating with molecular addresses. The molecular computer performs physically manifested mathematical operations and possesses both reading and writing capacities. Generativity paradoxically resides in the biological computational system as a possibility to incorporate meta-statements about the system, and thus establishes the internal capacity for its evolution. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Linear grammar as a possible stepping-stone in the evolution of language.

PubMed

Jackendoff, Ray; Wittenberg, Eva

2017-02-01

We suggest that one way to approach the evolution of language is through reverse engineering: asking what components of the language faculty could have been useful in the absence of the full complement of components. We explore the possibilities offered by linear grammar, a form of language that lacks syntax and morphology altogether, and that structures its utterances through a direct mapping between semantics and phonology. A language with a linear grammar would have no syntactic categories or syntactic phrases, and therefore no syntactic recursion. It would also have no functional categories such as tense, agreement, and case inflection, and no derivational morphology. Such a language would still be capable of conveying certain semantic relations through word order-for instance by stipulating that agents should precede patients. However, many other semantic relations would have to be based on pragmatics and discourse context. We find evidence of linear grammar in a wide range of linguistic phenomena: pidgins, stages of late second language acquisition, home signs, village sign languages, language comprehension (even in fully syntactic languages), aphasia, and specific language impairment. We also find a full-blown language, Riau Indonesian, whose grammar is arguably close to a pure linear grammar. In addition, when subjects are asked to convey information through nonlinguistic gesture, their gestures make use of semantically based principles of linear ordering. Finally, some pockets of English grammar, notably compounds, can be characterized in terms of linear grammar. We conclude that linear grammar is a plausible evolutionary precursor of modern fully syntactic grammar, one that is still active in the human mind.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Cancer heterogeneity: converting a limitation into a source of biologic information.

PubMed

Rübben, Albert; Araujo, Arturo

2017-09-08

Analysis of spatial and temporal genetic heterogeneity in human cancers has revealed that somatic cancer evolution in most cancers is not a simple linear process composed of a few sequential steps of mutation acquisitions and clonal expansions. Parallel evolution has been observed in many early human cancers resulting in genetic heterogeneity as well as multilineage progression. Moreover, aneuploidy as well as structural chromosomal aberrations seems to be acquired in a non-linear, punctuated mode where most aberrations occur at early stages of somatic cancer evolution. At later stages, the cancer genomes seem to get stabilized and acquire only few additional rearrangements. While parallel evolution suggests positive selection of driver mutations at early stages of somatic cancer evolution, stabilization of structural aberrations at later stages suggests that negative selection takes effect when cancer cells progressively lose their tolerance towards additional mutation acquisition. Mixing of genetically heterogeneous subclones in cancer samples reduces sensitivity of mutation detection. Moreover, driver mutations present only in a fraction of cancer cells are more likely to be mistaken for passenger mutations. Therefore, genetic heterogeneity may be considered a limitation negatively affecting detection sensitivity of driver mutations. On the other hand, identification of subclones and subclone lineages in human cancers may lead to a more profound understanding of the selective forces which shape somatic cancer evolution in human cancers. Identification of parallel evolution by analyzing spatial heterogeneity may hint to driver mutations which might represent additional therapeutic targets besides driver mutations present in a monoclonal state. Likewise, stabilization of cancer genomes which can be identified by analyzing temporal genetic heterogeneity might hint to genes and pathways which have become essential for survival of cancer cell lineages at later stages of cancer evolution. These genes and pathways might also constitute patient specific therapeutic targets.

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

PubMed Central

Iijima, Leo; Suzuki, Shingo; Hashimoto, Tomomi; Oyake, Ayana; Kobayashi, Hisaka; Someya, Yuki; Narisawa, Dai; Yomo, Tetsuya

2015-01-01

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution. PMID:26177190

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process.

PubMed

Kishimoto, Toshihiko; Ying, Bei-Wen; Tsuru, Saburo; Iijima, Leo; Suzuki, Shingo; Hashimoto, Tomomi; Oyake, Ayana; Kobayashi, Hisaka; Someya, Yuki; Narisawa, Dai; Yomo, Tetsuya

2015-07-01

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.

Comparison of buried sand ridges and regressive sand ridges on the outer shelf of the East China Sea

NASA Astrophysics Data System (ADS)

Wu, Ziyin; Jin, Xianglong; Zhou, Jieqiong; Zhao, Dineng; Shang, Jihong; Li, Shoujun; Cao, Zhenyi; Liang, Yuyang

2017-06-01

Based on multi-beam echo soundings and high-resolution single-channel seismic profiles, linear sand ridges in U14 and U2 on the East China Sea (ECS) shelf are identified and compared in detail. Linear sand ridges in U14 are buried sand ridges, which are 90 m below the seafloor. It is presumed that these buried sand ridges belong to the transgressive systems tract (TST) formed 320-200 ka ago and that their top interface is the maximal flooding surface (MFS). Linear sand ridges in U2 are regressive sand ridges. It is presumed that these buried sand ridges belong to the TST of the last glacial maximum (LGM) and that their top interface is the MFS of the LGM. Four sub-stage sand ridges of U2 are discerned from the high-resolution single-channel seismic profile and four strikes of regressive sand ridges are distinguished from the submarine topographic map based on the multi-beam echo soundings. These multi-stage and multi-strike linear sand ridges are the response of, and evidence for, the evolution of submarine topography with respect to sea-level fluctuations since the LGM. Although the difference in the age of formation between U14 and U2 is 200 ka and their sequences are 90 m apart, the general strikes of the sand ridges are similar. This indicates that the basic configuration of tidal waves on the ECS shelf has been stable for the last 200 ka. A basic evolutionary model of the strata of the ECS shelf is proposed, in which sea-level change is the controlling factor. During the sea-level change of about 100 ka, five to six strata are developed and the sand ridges develop in the TST. A similar story of the evolution of paleo-topography on the ECS shelf has been repeated during the last 300 ka.

Toroidal Geometry Stabilizing a Latitudinal Ring of Point Vortices on a Torus

NASA Astrophysics Data System (ADS)

Sakajo, Takashi; Shimizu, Yuuki

2018-06-01

We carry out the linear stability analysis of a polygonal ring configuration of N point vortices, called an N-ring, along the line of latitude θ _0 on a torus with the aspect ratio α . Deriving a criterion for the stability depending on the parameters N, θ _0 and α , we reveal how the aspect ratio α contributes to the stability of the N-ring. While the N-ring necessarily becomes unstable when N is sufficiently large for fixed α , the stability is closely associated with the geometric property of the torus for variable α ; for low aspect ratio α ˜ 1, N=7 is a critical number determining the stability of the N-ring when it is located along a certain range of latitudes, which is an analogous result to those in a plane and on a sphere. On the other hand, the stability is determined by the sign of curvature for high aspect ratio α ≫ 1. That is to say, the N-ring is neutrally stable if it is located on the inner side of the toroidal surface with a negative curvature, while the N-ring on its outer side with a positive curvature is unstable. Furthermore, based on the linear stability analysis, we describe nonlinear evolution of the N-ring when it becomes unstable. It is difficult to deal with this problem, since the evolution equation of the N point vortices is formulated as a Hamiltonian system with N degrees of freedom, which is in general non-integrable. Thus, we reduce the Hamiltonian system to a simple integrable system by introducing a cyclic symmetry. Owing to this reduction, we successfully find some periodic orbits in the reduced system, whose local bifurcations and global transitions for variable α are characterized in terms of the fundamental group of the torus.

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Kelvin-Helmholtz instability of counter-rotating discs

NASA Astrophysics Data System (ADS)

Quach, Dan; Dyda, Sergei; Lovelace, Richard V. E.

2015-01-01

Observations of galaxies and models of accreting systems point to the occurrence of counter-rotating discs where the inner part of the disc (r < r0) is corotating and the outer part is counter-rotating. This work analyses the linear stability of radially separated co- and counter-rotating thin discs. The strong instability found is the supersonic Kelvin-Helmholtz instability. The growth rates are of the order of or larger than the angular rotation rate at the interface. The instability is absent if there is no vertical dependence of the perturbation. That is, the instability is essentially three dimensional. The non-linear evolution of the instability is predicted to lead to a mixing of the two components, strong heating of the mixed gas, and vertical expansion of the gas, and annihilation of the angular momenta of the two components. As a result, the heated gas will free-fall towards the disc's centre over the surface of the inner disc.

Nonlinear dynamics near the stability margin in rotating pipe flow

NASA Technical Reports Server (NTRS)

Yang, Z.; Leibovich, S.

1991-01-01

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Evolution from MEMS-based Linear Drives to Bio-based Nano Drives

NASA Astrophysics Data System (ADS)

Fujita, Hiroyuki

The successful extension of semiconductor technology to fabricate mechanical parts of the sizes from 10 to 100 micrometers opened wide ranges of possibilities for micromechanical devices and systems. The fabrication technique is called micromachining. Micromachining processes are based on silicon integrated circuits (IC) technology and used to build three-dimensional structures and movable parts by the combination of lithography, etching, film deposition, and wafer bonding. Microactuators are the key devices allowing MEMS to perform physical functions. Some of them are driven by electric, magnetic, and fluidic forces. Some others utilize actuator materials including piezoelectric (PZT, ZnO, quartz) and magnetostrictive materials (TbFe), shape memory alloy (TiNi) and bio molecular motors. This paper deals with the development of MEMS based microactuators, especially linear drives, following my own research experience. They include an electrostatic actuator, a superconductive levitated actuator, arrayed actuators, and a bio-motor-driven actuator.

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

Resettable binary latch mechanism for use with paraffin linear motors

NASA Technical Reports Server (NTRS)

Maus, Daryl; Tibbitts, Scott

1991-01-01

A new resettable Binary Latch Mechanism was developed utilizing a paraffin actuator as the motor. This linear actuator alternately latches between extended and retracted positions, maintaining either position with zero power consumption. The design evolution and kinematics of the latch mechanism are presented, as well as the development problems and lessons that were learned.

Thin film flow along a periodically-stretched elastic beam

NASA Astrophysics Data System (ADS)

Boamah Mensah, Chris; Chini, Greg; Jensen, Oliver

2017-11-01

Motivated by an application to pulmonary alveolar micro-mechanics, a system of partial differential equations is derived that governs the motion of a thin liquid film lining both sides of an inertia-less elastic substrate. The evolution of the film mass distribution is described by invoking the usual lubrication approximation while the displacement of the substrate is determined by employing a kinematically nonlinear Euler-Bernoulli beam formulation. In the parameter regime of interest, the axial strain can be readily shown to be a linear function of arc-length specified completely by the motion of ends of the substrate. In contrast, the normal force balance on the beam yields an equation for the substrate curvature that is fully coupled to the time-dependent lubrication equation. Linear analyses of both a stationary and periodically-stretched flat substrate confirm the potential for buckling instabilities and reveal an upper bound on the dimensionless axial stiffness for which the coupled thin-film/inertial-less-beam model is well-posed. Numerical simulations of the coupled system are used to explore the nonlinear development of the buckling instabilities.

The inherent dynamics of a molecular liquid: geodesic pathways through the potential energy landscape of a liquid of linear molecules.

PubMed

Jacobson, Daniel; Stratt, Richard M

2014-05-07

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation-molecules largely thread their way through narrow channels available in the potential energy landscape.

The inherent dynamics of a molecular liquid: Geodesic pathways through the potential energy landscape of a liquid of linear molecules

NASA Astrophysics Data System (ADS)

Jacobson, Daniel; Stratt, Richard M.

2014-05-01

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.

Formation of organized nanostructures from unstable bilayers of thin metallic liquids

NASA Astrophysics Data System (ADS)

Khenner, Mikhail; Yadavali, Sagar; Kalyanaraman, Ramki

2011-12-01

Dewetting of pulsed-laser irradiated, thin (<20 nm), optically reflective metallic bilayers on an optically transparent substrate with a reflective support layer is studied within the lubrication equations model. A steady-state bilayer film thickness (h) dependent temperature profile is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Large thermocapillary forces are observed along the plane of the liquid-liquid and liquid-gas interfaces due to this h-dependent temperature, which, in turn, is strongly influenced by the h-dependent laser light reflection and absorption. Consequently the dewetting is a result of the competition between thermocapillary and intermolecular forces. A linear analysis of the dewetting length scales established that the non-isothermal calculations better predict the experimental results as compared to the isothermal case within the bounding Hamaker coefficients. Subsequently, a computational non-linear dynamics study of the dewetting pathway was performed for Ag/Co and Co/Ag bilayer systems to predict the morphology evolution. We found that the systems evolve towards formation of different morphologies, including core-shell, embedded, or stacked nanostructure morphologies.

Interaction between mantle and crustal detachments: a non-linear system controlling lithospheric extension

NASA Astrophysics Data System (ADS)

Rosenbaum, G.; Regenauer-Lieb, K.; Weinberg, R. F.

2009-12-01

We use numerical modelling to investigate the development of crustal and mantle detachment faults during lithospheric extension. Our models simulate a wide range of rift systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles, which grow in response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation at different levels of the lithosphere. Crustal detachment faults are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW/m2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate (60-70 mW/m2) heat flow. Results show a non-linear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometime unexpected switches in extension modes (e.g. from diffuse rifting to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this non-linearity to result from the interference of doming wavelengths. Disharmony of crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonious crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged rifting history prior to continental breakup.

Detailed analysis of evolution of the state of polarization in all-fiber polarization transformers.

PubMed

Zhu, Xiushan; Jain, Ravinder K

2006-10-30

We present a detailed analysis of key attributes and performance characteristics of controllably-spun birefringent-fiber-based all-fiber waveplates or "all fiber polarization transformers" (AFPTs), first proposed and demonstrated by Huang [11]; these AFPTs consist essentially of a long carefully-designed "spin-twisted" high-birefringence fiber, fabricated by slowly varying the spin rate of a birefringent fiber preform (either from very fast to very slow or vice versa) while the fiber is being drawn. The evolution of the eigenstate from a linear polarization state to a circular polarization state, induced by slow variation of the intrinsic structure from linear anisotropy at the unspun end to circular anisotropy at the fast-spun end, enables the AFPT to behave like an all-fiber quarter-wave plate independent of the wavelength of operation. Power coupling between local eigenstates causes unique evolution of the polarization state along the fiber, and has been studied to gain insight into - as well as to understand detailed characteristics of -- the polarization transformation behavior. This has been graphically illustrated via plots of the relative power in these local eigenstates as a function of distance along the length of the fiber and plots of the extinction ratio of the output state of polarization (SOP) as a function of distance and the normalized spin rate. Deeper understanding of such polarization transformers has been further elucidated by quantitative calculations related to two crucial requirements for fabricating practical AFPT devices. Our calculations have also indicated that the polarization mode dispersion behaviour of the AFPT is much smaller than that of the original birefringent fiber. Finally, a specific AFPT was experimentally investigated at two widely-separated wavelengths (1310 nm and 1550 nm) of interest in telecommunications systems applications, further demonstrating and elucidating the broadband character of such AFPTs.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

Evolutionary dynamics of general group interactions in structured populations

NASA Astrophysics Data System (ADS)

Li, Aming; Broom, Mark; Du, Jinming; Wang, Long

2016-02-01

The evolution of populations is influenced by many factors, and the simple classical models have been developed in a number of important ways. Both population structure and multiplayer interactions have been shown to significantly affect the evolution of important properties, such as the level of cooperation or of aggressive behavior. Here we combine these two key factors and develop the evolutionary dynamics of general group interactions in structured populations represented by regular graphs. The traditional linear and threshold public goods games are adopted as models to address the dynamics. We show that for linear group interactions, population structure can favor the evolution of cooperation compared to the well-mixed case, and we see that the more neighbors there are, the harder it is for cooperators to persist in structured populations. We further show that threshold group interactions could lead to the emergence of cooperation even in well-mixed populations. Here population structure sometimes inhibits cooperation for the threshold public goods game, where depending on the benefit to cost ratio, the outcomes are bistability or a monomorphic population of defectors or cooperators. Our results suggest, counterintuitively, that structured populations are not always beneficial for the evolution of cooperation for nonlinear group interactions.

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

Guo, Z.; Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083; Lin, P.

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy lawmore » (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.« less

Quasistatic elastoplasticity via Peridynamics: existence and localization

NASA Astrophysics Data System (ADS)

Kružík, Martin; Mora-Corral, Carlos; Stefanelli, Ulisse

2018-04-01

Peridynamics is a nonlocal continuum mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years. We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive Γ -convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero.

Spectral effects in the propagation of chirped laser pulses in uniform underdense plasma

NASA Astrophysics Data System (ADS)

Pathak, Naveen; Zhidkov, Alexei; Hosokai, Tomonao; Kodama, Ryosuke

2018-01-01

Propagation of linearly chirped and linearly polarized, powerful laser pulses in uniform underdense plasma with their duration exceeding the plasma wave wavelength is examined via 3D fully relativistic particle-in-cell simulations. Spectral evolution of chirped laser pulses, determined by Raman scattering, essentially depends on the nonlinear electron evacuation from the first wake bucket via modulation of the known parameter /n e ( r ) ω0 2 γ . Conversely, the relative motion of different spectral components inside a pulse changes the evolution of the pulse length and, therefore, the ponderomotive forces at the pulse rear. Such longitudinal dynamics of the pulse length provoke a parametric resonance in the laser wake with continuous electron self-injection for any chirped pulses. However, the total charge of accelerated electrons and their energy distribution essentially depends on the chirp. Besides, negatively chirped laser pulses are shown to be useful for spatially resolved measurements of the plasma density profiles and for rough estimations of the laser pulse intensity evolution in underdense plasma.

3D-MHD Simulations of the Madison Dynamo Experiment

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Forest, C. B.; Wright, J. C.; O'Connell, R.

2003-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations are used to predict behavior of the experiment. The code solves the self-consistent full evolution of the magnetic and velocity fields. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James [Proc. R. Soc. Lond. A 425. 407-429 (1989)]. Initial results indicate that saturation of the magnetic field occurs so that the resulting perturbed backreaction of the induced magnetic field changes the velocity field such that it would no longer be linearly unstable, suggesting non-linear terms are necessary for explaining the resulting state. Saturation and self-excitation depend in detail upon the magnetic Prandtl number.

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

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

Tamanini, Nicola; Wright, Matthew, E-mail: nicola.tamanini@cea.fr, E-mail: matthew.wright.13@ucl.ac.uk

We investigate the cosmological dynamics of the recently proposed extended chameleon models at both background and linear perturbation levels. Dynamical systems techniques are employed to fully characterize the evolution of the universe at the largest distances, while structure formation is analysed at sub-horizon scales within the quasi-static approximation. The late time dynamical transition from dark matter to dark energy domination can be well described by almost all extended chameleon models considered, with no deviations from ΛCDM results at both background and perturbation levels. The results obtained in this work confirm the cosmological viability of extended chameleons as alternative dark energymore » models.« less

Complex Networks Dynamics Based on Events-Phase Synchronization and Intensity Correlation Applied to The Anomaly Patterns and Extremes in The Tropical African Climate System

NASA Astrophysics Data System (ADS)

Oluoch, K.; Marwan, N.; Trauth, M.; Loew, A.; Kurths, J.

2012-04-01

The African continent lie almost entirely within the tropics and as such its (tropical) climate systems are predominantly governed by the heterogeneous, spatial and temporal variability of the Hadley and Walker circulations. The variabilities in these meridional and zonal circulations lead to intensification or suppression of the intensities, durations and frequencies of the Inter-tropical Convergence Zone (ICTZ) migration, trade winds and subtropical high-pressure regions and the continental monsoons. The above features play a central role in determining the African rainfall spatial and temporal variability patterns. The current understanding of these climate features and their influence on the rainfall patterns is not sufficiently understood. Like many real-world systems, atmospheric-oceanic processes exhibit non-linear properties that can be better explored using non-linear (NL) methods of time-series analysis. Over the recent years, the complex network approach has evolved as a powerful new player in understanding spatio-temporal dynamics and evolution of complex systems. Together with NL techniques, it is continuing to find new applications in many areas of science and technology including climate research. We would like to use these two powerful methods to understand the spatial structure and dynamics of African rainfall anomaly patterns and extremes. The method of event synchronization (ES) developed by Quiroga et al., 2002 and first applied to climate networks by Malik et al., 2011 looks at correlations with a dynamic time lag and as such, it is a more intuitive way to correlate a complex and heterogeneous system like climate networks than a fixed time delay most commonly used. On the other hand, the short comings of ES is its lack of vigorous test statistics for the significance level of the correlations, and the fact that only the events' time indices are synchronized while all information about how the relative intensities propagate within network framework is lost. The new method we present is motivated by the ES and borrows ideas from signal processing where a signal is represented by its intensity and frequency. Even though the anomaly signals are not periodic, the idea of phase synchronization is not far fetched. It brings into one umbrella, the traditionally known linear Intensity correlation methods like Pearson correlation, spear-man's rank or non-linear ones like mutual information with the ES for non-linear temporal synchronization. The intensity correlation is only performed where there is a temporal synchronization. The former just measures how constant the intensity differences are. In other words, how monotonic are the two functions. The overall measure of correlation and synchronization is the product of the two coefficients. Complex networks constructed by this technique has all the advantages inherent in each of the techniques it borrows. But, it is more superior and able to uncover many known and unknown dynamical features in rainfall field or any variable of interest. The main aim of this work is to develop a method that can identify the footprints of coherent or incoherent structures within the ICTZ, the African and the Indian monsoons and the ENSO signal on the tropical African continent and their temporal evolution.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

NASA Astrophysics Data System (ADS)

Bénisti, Didier

2018-01-01

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.

Modeling coding-sequence evolution within the context of residue solvent accessibility.

PubMed

Scherrer, Michael P; Meyer, Austin G; Wilke, Claus O

2012-09-12

Protein structure mediates site-specific patterns of sequence divergence. In particular, residues in the core of a protein (solvent-inaccessible residues) tend to be more evolutionarily conserved than residues on the surface (solvent-accessible residues). Here, we present a model of sequence evolution that explicitly accounts for the relative solvent accessibility of each residue in a protein. Our model is a variant of the Goldman-Yang 1994 (GY94) model in which all model parameters can be functions of the relative solvent accessibility (RSA) of a residue. We apply this model to a data set comprised of nearly 600 yeast genes, and find that an evolutionary-rate ratio ω that varies linearly with RSA provides a better model fit than an RSA-independent ω or an ω that is estimated separately in individual RSA bins. We further show that the branch length t and the transition-transverion ratio κ also vary with RSA. The RSA-dependent GY94 model performs better than an RSA-dependent Muse-Gaut 1994 (MG94) model in which the synonymous and non-synonymous rates individually are linear functions of RSA. Finally, protein core size affects the slope of the linear relationship between ω and RSA, and gene expression level affects both the intercept and the slope. Structure-aware models of sequence evolution provide a significantly better fit than traditional models that neglect structure. The linear relationship between ω and RSA implies that genes are better characterized by their ω slope and intercept than by just their mean ω.

Effects of resonant magnetic perturbation on the triggering and the evolution of double-tearing mode

NASA Astrophysics Data System (ADS)

Wang, L.; Lin, W. B.; Wang, X. Q.

2018-02-01

The effects of resonant magnetic perturbation on the triggering and the evolution of the double-tearing mode are investigated by using nonlinear magnetohydrodynamics simulations in a slab geometry. It is found that the double-tearing mode can be destabilized by boundary magnetic perturbation. Moreover, the mode has three typical development stages before it reaches saturation: the linear stable stage, the linear-growth stage, and the exponential-growth stage. The onset and growth of the double-tearing mode significantly depend on the boundary magnetic perturbations, particularly in the early development stage of the mode. The influences of the magnetic perturbation amplitude on the mode for different separations of the two rational surfaces are also discussed.

Angular Size Test on the Expansion of the Universe

NASA Astrophysics Data System (ADS)

López-Corredoira, Martín

Assuming the standard cosmological model to be correct, the average linear size of the galaxies with the same luminosity is six times smaller at z = 3.2 than at z = 0; and their average angular size for a given luminosity is approximately proportional to z-1. Neither the hypothesis that galaxies which formed earlier have much higher densities nor their luminosity evolution, merger ratio, and massive outflows due to a quasar feedback mechanism are enough to justify such a strong size evolution. Also, at high redshift, the intrinsic ultraviolet surface brightness would be prohibitively high with this evolution, and the velocity dispersion much higher than observed. We explore here another possibility of overcoming this problem: considering different cosmological scenarios, which might make the observed angular sizes compatible with a weaker evolution. One of the explored models, a very simple phenomenological extrapolation of the linear Hubble law in a Euclidean static universe, fits quite well the angular size versus redshift dependence, also approximately proportional to z-1 with this cosmological model. There are no free parameters derived ad hoc, although the error bars allow a slight size/luminosity evolution. The supernova Ia Hubble diagram can also be explained in terms of this model without any ad-hoc-fitted parameter. NB: I do not argue here that the true universe is static. My intention is just to discuss which intellectual theoretical models fit better some data of the observational cosmology.

Turbulence closure for mixing length theories

NASA Astrophysics Data System (ADS)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

Estimating Traffic Accidents in Turkey Using Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Akgüngör, Ali Payıdar; Korkmaz, Ersin

2017-06-01

Estimating traffic accidents play a vital role to apply road safety procedures. This study proposes Differential Evolution Algorithm (DEA) models to estimate the number of accidents in Turkey. In the model development, population (P) and the number of vehicles (N) are selected as model parameters. Three model forms, linear, exponential and semi-quadratic models, are developed using DEA with the data covering from 2000 to 2014. Developed models are statistically compared to select the best fit model. The results of the DE models show that the linear model form is suitable to estimate the number of accidents. The statistics of this form is better than other forms in terms of performance criteria which are the Mean Absolute Percentage Errors (MAPE) and the Root Mean Square Errors (RMSE). To investigate the performance of linear DE model for future estimations, a ten-year period from 2015 to 2024 is considered. The results obtained from future estimations reveal the suitability of DE method for road safety applications.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Streamflow droughts in major watershed regions of the conterminous U.S.: Understanding evolution of historic patterns

NASA Astrophysics Data System (ADS)

Pournasiri Poshtiri, M.; Pal, I.

2015-12-01

Climate non-stationarity affects regional hydrological extremes. This research looks into historic patterns of streamflow drought indicators and their evolution for major watershed regions in the conterminous U.S. (CONUS). The results indicate general linear and non-linear drying trends, particularly in the last four decades, as opposed to wetting trends reported in previous studies. Regional differences in the trends are notable, and echo the local climatic changes documented in the recent National Climate Assessment (NCA). A reversal of linear trends is seen for some northern regions after 1980s. Patterns in return periods and corresponding return values of the indicators are also examined, which suggests changing risk conditions that are important for water-resources decision-making. Persistent or flash drought conditions in a river can lead to chronic or short-term water scarcity—a main driver of societal and cross-boundary conflicts. Thus, this research identifies "hotspot" locations where suitable adaptive management measures are most needed.

Concepts in solid tumor evolution.

PubMed

Sidow, Arend; Spies, Noah

2015-04-01

Evolutionary mechanisms in cancer progression give tumors their individuality. Cancer evolution is different from organismal evolution, however, and we discuss where concepts from evolutionary genetics are useful or limited in facilitating an understanding of cancer. Based on these concepts we construct and apply the simplest plausible model of tumor growth and progression. Simulations using this simple model illustrate the importance of stochastic events early in tumorigenesis, highlight the dominance of exponential growth over linear growth and differentiation, and explain the clonal substructure of tumors. Copyright © 2015 Elsevier Ltd. All rights reserved.

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

Capela, Fabio; Ramazanov, Sabir, E-mail: fc403@cam.ac.uk, E-mail: Sabir.Ramazanov@ulb.ac.be

At large scales and for sufficiently early times, dark matter is described as a pressureless perfect fluid—dust— non-interacting with Standard Model fields. These features are captured by a simple model with two scalars: a Lagrange multiplier and another playing the role of the velocity potential. That model arises naturally in some gravitational frameworks, e.g., the mimetic dark matter scenario. We consider an extension of the model by means of higher derivative terms, such that the dust solutions are preserved at the background level, but there is a non-zero sound speed at the linear level. We associate this Modified Dust withmore » dark matter, and study the linear evolution of cosmological perturbations in that picture. The most prominent effect is the suppression of their power spectrum for sufficiently large cosmological momenta. This can be relevant in view of the problems that cold dark matter faces at sub-galactic scales, e.g., the missing satellites problem. At even shorter scales, however, perturbations of Modified Dust are enhanced compared to the predictions of more common particle dark matter scenarios. This is a peculiarity of their evolution in radiation dominated background. We also briefly discuss clustering of Modified Dust. We write the system of equations in the Newtonian limit, and sketch the possible mechanism which could prevent the appearance of caustic singularities. The same mechanism may be relevant in light of the core-cusp problem.« less

Transport and Dynamics in Toroidal Fusion Systems

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

Schnack, Dalton D

2006-05-16

This document reports the successful completion of the OFES Theory Milestone for FY2005, namely, Perform parametric studies to better understand the edge physics regimes of laboratory experiments. Simulate at increased resolution (up to 20 toroidal modes), with density evolution, late into the nonlinear phase and compare results from different types of edge modes. Simulate a single case including a study of heat deposition on nearby material walls. The linear stability properties and nonlinear evolution of Edge Localized Modes (ELMs) in tokamak plasmas are investigated through numerical computation. Data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/) is used for themore » magnetohydrodynamic (MHD) equilibria, but edge parameters are varied to reveal important physical effects. The equilibrium with very low magnetic shear produces an unstable spectrum that is somewhat insensitive to dissipation coefficient values. Here, linear growth rates from the non-ideal NIMROD code (http://nimrodteam.org) agree reasonably well with ideal, i.e. non-dissipative, results from the GATO global linear stability code at low toroidal mode number (n) and with ideal results from the ELITE edge linear stability code at moderate to high toroidal mode number. Linear studies with a more realistic sequence of MHD equilibria (based on DIII-D discharge 86166) produce more significant discrepancies between the ideal and non-ideal calculations. The maximum growth rate for the ideal computations occurs at toroidal mode index n=10, whereas growth rates in the non-ideal computations continue to increase with n unless strong anisotropic thermal conduction is included. Recent modeling advances allow drift effects associated with the Hall electric field and gyroviscosity to be considered. A stabilizing effect can be observed in the preliminary results, but while the distortion in mode structure is readily apparent at n=40, the growth rate is only 13% less than the non-ideal MHD result. Computations performed with a non-local kinetic closure for parallel electron thermal conduction that is valid over all collisionality regimes identify thermal diffusivity ratios of {chi}{sub ||}/{chi}{sub {perpendicular}} ~ 10{sup 7} - 10{sup 8} as appropriate when using collisional heat flux modeling for these modes. Adding significant parallel viscosity proves to have little effect. Nonlinear ELM computations solve the resistive MHD model with toroidal resolution 0{<=}n{<=}21, including anisotropic thermal conduction, temperature-dependent resistivity, and number density evolution. The computations are based on a realistic equilibrium with high pedestal temperature from the linear study. When the simulated ELM grows to appreciable amplitude, ribbon-like thermal structures extend from the separatrix to the wall as the spectrum broadens about a peak at n=13. Analysis of the results finds the heat flux on the wall to be very nonuniform with greatest intensity occurring in spots on the top and bottom of the chamber. Net thermal energy loss occurs on a time-scale of 100 {micro}s, and the instantaneous loss rate exceeds 1 GW.« less

Investigating the unification of LOFAR-detected powerful AGN in the Boötes field

NASA Astrophysics Data System (ADS)

Morabito, Leah K.; Williams, W. L.; Duncan, Kenneth J.; Röttgering, H. J. A.; Miley, George; Saxena, Aayush; Barthel, Peter; Best, P. N.; Bruggen, M.; Brunetti, G.; Chyży, K. T.; Engels, D.; Hardcastle, M. J.; Harwood, J. J.; Jarvis, Matt J.; Mahony, E. K.; Prandoni, I.; Shimwell, T. W.; Shulevski, A.; Tasse, C.

2017-08-01

Low radio frequency surveys are important for testing unified models of radio-loud quasars and radio galaxies. Intrinsically similar sources that are randomly oriented on the sky will have different projected linear sizes. Measuring the projected linear sizes of these sources provides an indication of their orientation. Steep-spectrum isotropic radio emission allows for orientation-free sample selection at low radio frequencies. We use a new radio survey of the Boötes field at 150 MHz made with the Low-Frequency Array (LOFAR) to select a sample of radio sources. We identify 60 radio sources with powers P > 1025.5 W Hz-1 at 150 MHz using cross-matched multiwavelength information from the AGN and Galaxy Evolution Survey, which provides spectroscopic redshifts and photometric identification of 16 quasars and 44 radio galaxies. When considering the radio spectral slope only, we find that radio sources with steep spectra have projected linear sizes that are on average 4.4 ± 1.4 larger than those with flat spectra. The projected linear sizes of radio galaxies are on average 3.1 ± 1.0 larger than those of quasars (2.0 ± 0.3 after correcting for redshift evolution). Combining these results with three previous surveys, we find that the projected linear sizes of radio galaxies and quasars depend on redshift but not on power. The projected linear size ratio does not correlate with either parameter. The LOFAR data are consistent within the uncertainties with theoretical predictions of the correlation between the quasar fraction and linear size ratio, based on an orientation-based unification scheme.

Evolution of Linear Mitochondrial Genomes in Medusozoan Cnidarians

PubMed Central

Kayal, Ehsan; Bentlage, Bastian; Collins, Allen G.; Pirro, Stacy; Lavrov, Dennis V.

2012-01-01

In nearly all animals, mitochondrial DNA (mtDNA) consists of a single circular molecule that encodes several subunits of the protein complexes involved in oxidative phosphorylation as well as part of the machinery for their expression. By contrast, mtDNA in species belonging to Medusozoa (one of the two major lineages in the phylum Cnidaria) comprises one to several linear molecules. Many questions remain on the ubiquity of linear mtDNA in medusozoans and the mechanisms responsible for its evolution, replication, and transcription. To address some of these questions, we determined the sequences of nearly complete linear mtDNA from 24 species representing all four medusozoan classes: Cubozoa, Hydrozoa, Scyphozoa, and Staurozoa. All newly determined medusozoan mitochondrial genomes harbor the 17 genes typical for cnidarians and map as linear molecules with a high degree of gene order conservation relative to the anthozoans. In addition, two open reading frames (ORFs), polB and ORF314, are identified in cubozoan, schyphozoan, staurozoan, and trachyline hydrozoan mtDNA. polB belongs to the B-type DNA polymerase gene family, while the product of ORF314 may act as a terminal protein that binds telomeres. We posit that these two ORFs are remnants of a linear plasmid that invaded the mitochondrial genomes of the last common ancestor of Medusozoa and are responsible for its linearity. Hydroidolinan hydrozoans have lost the two ORFs and instead have duplicated cox1 at each end of their mitochondrial chromosome(s). Fragmentation of mtDNA occurred independently in Cubozoa and Hydridae (Hydrozoa, Hydroidolina). Our broad sampling allows us to reconstruct the evolutionary history of linear mtDNA in medusozoans. PMID:22113796

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Nonlinear Evolution of Counter-Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1-D PIC Simulations

NASA Astrophysics Data System (ADS)

Chen, Huayue; Gao, Xinliang; Lu, Quanming; Sun, Jicheng; Wang, Shui

2018-02-01

Nonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1-D particle-in-cell simulation model, we have investigated the nonlinear evolution of parallel counter-propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter-propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high-k modes in this plasma system. Compared with excited whistler mode waves, these high-k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

A Comparison of the CHILD and Landlab Computational Landscape Evolution Models and Examples of Best Practices in Numerical Modeling of Surface Processes

NASA Astrophysics Data System (ADS)

Gasparini, N. M.; Hobley, D. E. J.; Tucker, G. E.; Istanbulluoglu, E.; Adams, J. M.; Nudurupati, S. S.; Hutton, E. W. H.

2014-12-01

Computational models are important tools that can be used to quantitatively understand the evolution of real landscapes. Commonalities exist among most landscape evolution models, although they are also idiosyncratic, in that they are coded in different languages, require different input values, and are designed to tackle a unique set of questions. These differences can make applying a landscape evolution model challenging, especially for novice programmers. In this study, we compare and contrast two landscape evolution models that are designed to tackle similar questions, but the actual model designs are quite different. The first model, CHILD, is over a decade-old and is relatively well-tested, well-developed and well-used. It is coded in C++, operates on an irregular grid and was designed more with function rather than user-experience in mind. In contrast, the second model, Landlab, is relatively new and was designed to be accessible to a wide range of scientists, including those who have not previously used or developed a numerical model. Landlab is coded in Python, a relatively easy language for the non-proficient programmer, and has the ability to model landscapes described on both regular and irregular grids. We present landscape simulations from both modeling platforms. Our goal is to illustrate best practices for implementing a new process module in a landscape evolution model, and therefore the simulations are applicable regardless of the modeling platform. We contrast differences and highlight similarities between the use of the two models, including setting-up the model and input file for different evolutionary scenarios, computational time, and model output. Whenever possible, we compare model output with analytical solutions and illustrate the effects, or lack thereof, of a uniform vs. non-uniform grid. Our simulations focus on implementing a single process, including detachment-limited or transport-limited fluvial bedrock incision and linear or non-linear diffusion of material on hillslopes. We also illustrate the steps necessary to couple processes together, for example, detachment-limited fluvial bedrock incision with linear diffusion on hillslopes. Trade-offs exist between the two modeling platforms, and these are primarily in speed and ease-of-use.

A mechanistic stress model of protein evolution accounts for site-specific evolutionary rates and their relationship with packing density and flexibility

PubMed Central

2014-01-01

Background Protein sites evolve at different rates due to functional and biophysical constraints. It is usually considered that the main structural determinant of a site’s rate of evolution is its Relative Solvent Accessibility (RSA). However, a recent comparative study has shown that the main structural determinant is the site’s Local Packing Density (LPD). LPD is related with dynamical flexibility, which has also been shown to correlate with sequence variability. Our purpose is to investigate the mechanism that connects a site’s LPD with its rate of evolution. Results We consider two models: an empirical Flexibility Model and a mechanistic Stress Model. The Flexibility Model postulates a linear increase of site-specific rate of evolution with dynamical flexibility. The Stress Model, introduced here, models mutations as random perturbations of the protein’s potential energy landscape, for which we use simple Elastic Network Models (ENMs). To account for natural selection we assume a single active conformation and use basic statistical physics to derive a linear relationship between site-specific evolutionary rates and the local stress of the mutant’s active conformation. We compare both models on a large and diverse dataset of enzymes. In a protein-by-protein study we found that the Stress Model outperforms the Flexibility Model for most proteins. Pooling all proteins together we show that the Stress Model is strongly supported by the total weight of evidence. Moreover, it accounts for the observed nonlinear dependence of sequence variability on flexibility. Finally, when mutational stress is controlled for, there is very little remaining correlation between sequence variability and dynamical flexibility. Conclusions We developed a mechanistic Stress Model of evolution according to which the rate of evolution of a site is predicted to depend linearly on the local mutational stress of the active conformation. Such local stress is proportional to LPD, so that this model explains the relationship between LPD and evolutionary rate. Moreover, the model also accounts for the nonlinear dependence between evolutionary rate and dynamical flexibility. PMID:24716445

Non-linear thermal evolution of the crystal structure and phase transitions of LaFeO{sub 3} investigated by high temperature X-ray diffraction

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

Selbach, Sverre M.; Tolchard, Julian R.; Fossdal, Anita

2012-12-15

The crystal structure, anisotropic thermal expansion and structural phase transition of the perovskite LaFeO{sub 3} has been studied by high-temperature X-ray diffraction from room temperature to 1533 K. The structural evolution of the orthorhombic phase with space group Pbnm and the rhombohedral phase with R3{sup Macron }c structure of LaFeO{sub 3} is reported in terms of lattice parameters, thermal expansion coefficients, atomic positions, octahedral rotations and polyhedral volumes. Non-linear lattice expansion across the antiferromagnetic to paramagnetic transition of LaFeO{sub 3} at T{sub N}=735 K was compared to the corresponding behavior of the ferroelectric antiferromagnet BiFeO{sub 3} to gain insight tomore » the magnetoelectric coupling in BiFeO{sub 3}, which is also multiferroic. The first order phase transition of LaFeO{sub 3} from Pbnm to R3{sup Macron }c was observed at 1228{+-}9 K, and a subsequent transition to Pm3{sup Macron }m was extrapolated to occur at 2140{+-}30 K. The stability of the Pbnm and R3{sup Macron }c polymorphs of LaFeO{sub 3} is discussed in terms of the competing enthalpy and entropy of the two crystal polymorphs and the thermal evolution of the polyhedral volume ratio V{sub A}/V{sub B}. - Graphical abstract: Aniostropic thermal evolution of the lattice parameters and phase transition of LaFeO{sub 3}. Highlights: Black-Right-Pointing-Pointer The crystal structure of LaFeO{sub 3} is studied by HTXRD from RT to 1533 K. Black-Right-Pointing-Pointer A non-linear expansion across the Neel temperature is observed for LaFeO{sub 3}. Black-Right-Pointing-Pointer The ratio V{sub A}/V{sub B} is used to rationalize the thermal evolution of the structure.« less

Evidence for the Concerted Evolution between Short Linear Protein Motifs and Their Flanking Regions

PubMed Central

Chica, Claudia; Diella, Francesca; Gibson, Toby J.

2009-01-01

Background Linear motifs are short modules of protein sequences that play a crucial role in mediating and regulating many protein–protein interactions. The function of linear motifs strongly depends on the context, e.g. functional instances mainly occur inside flexible regions that are accessible for interaction. Sometimes linear motifs appear as isolated islands of conservation in multiple sequence alignments. However, they also occur in larger blocks of sequence conservation, suggesting an active role for the neighbouring amino acids. Results The evolution of regions flanking 116 functional linear motif instances was studied. The conservation of the amino acid sequence and order/disorder tendency of those regions was related to presence/absence of the instance. For the majority of the analysed instances, the pairs of sequences conserving the linear motif were also observed to maintain a similar local structural tendency and/or to have higher local sequence conservation when compared to pairs of sequences where one is missing the linear motif. Furthermore, those instances have a higher chance to co–evolve with the neighbouring residues in comparison to the distant ones. Those findings are supported by examples where the regulation of the linear motif–mediated interaction has been shown to depend on the modifications (e.g. phosphorylation) at neighbouring positions or is thought to benefit from the binding versatility of disordered regions. Conclusion The results suggest that flanking regions are relevant for linear motif–mediated interactions, both at the structural and sequence level. More interestingly, they indicate that the prediction of linear motif instances can be enriched with contextual information by performing a sequence analysis similar to the one presented here. This can facilitate the understanding of the role of these predicted instances in determining the protein function inside the broader context of the cellular network where they arise. PMID:19584925

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

Ten reasons why a thermalized system cannot be described by a many-particle wave function

NASA Astrophysics Data System (ADS)

Drossel, Barbara

2017-05-01

It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of statistical mechanics. The usual attempts to resolve this conflict for instance by appealing to decoherence or eigenstate thermalization are riddled with problems. This paper considers theoretical physics of thermalized systems as it is done in practice and shows that all approaches to thermalized systems presuppose in some form limits to linear superposition and deterministic time evolution. These considerations include, among others, the classical limit, extensivity, the concepts of entropy and equilibrium, and symmetry breaking in phase transitions and quantum measurement. As a conclusion, the paper suggests that the irreversibility and stochasticity of statistical mechanics should be taken as a real property of nature. It follows that a gas of a macroscopic number N of atoms in thermal equilibrium is best represented by a collection of N wave packets of a size of the order of the thermal de Broglie wave length, which behave quantum mechanically below this scale but classically sufficiently far beyond this scale. In particular, these wave packets must localize again after scattering events, which requires stochasticity and indicates a connection to the measurement process.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

PubMed

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.; Bagheri Harouni, M.

2014-04-01

In this paper, we study the interaction between a Λ-type three-level atom and two quantized electromagnetic fields which are simultaneously injected in a bichromatic cavity surrounded by a Kerr medium in the presence of field-field interaction (parametric down conversion) and detuning parameters. By applying a canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions which may be prepared for the atom and the field, the time evolution of the state vector of the entire system is analytically evaluated. Then, the dynamics of the atom is studied through the evolution of the atomic population inversion. In addition, two different measures of entanglement between the tripartite system (three entities make the system: two field modes and one atom), i.e., von Neumann and linear entropy are investigated. Also, two kinds of entropic uncertainty relations, from which entropy squeezing can be obtained, are discussed. In each case, the influences of the detuning parameters and Kerr medium on the above nonclassicality features are analyzed in detail via numerical results. It is illustrated that the amount of the above-mentioned physical phenomena can be tuned by choosing the evolved parameters, appropriately.

Lack of phonotactic preferences of female frogs and its consequences for signal evolution.

PubMed

Velásquez, Nelson A; Valdés, Jose Luis; Vásquez, Rodrigo A; Penna, Mario

2015-09-01

Sexual selection is one of the main evolutionary forces that drive signal evolution. In previous studies, we have found out that males of Pleurodema thaul, a frog with an extensive latitudinal distribution in Chile, emits advertisement calls that show remarkable variation among populations. In addition, this variation is related to intense inter-male acoustic competition (intra-sexual selection) occurring within each population. However, the extent to which female preferences contribute to the signal divergence observed is unclear. To study the responsiveness of females in each population, we stimulated females with synthetic calls designed with the acoustic structure of their own population and subsequently responsive females were subjected to a two-choice experiment, where they were stimulated with synthetic calls of their own population versus a call of a foreign population. Females do not show phonotactic preferences for calls of their own or foreign populations as measured with both linear and circular variables. The lack of phonotactic preferences suggests an absence of participation of inter-sexual selection processes in the divergence of the acoustic signals of P. thaul, highlighting the importance of intra-sexual selection for the evolution of these signals. These results concur with studies in other vertebrates emphasizing the relevance of interactions among males for the evolution of acoustic communication systems. Copyright © 2015. Published by Elsevier B.V.

Stellar dynamics around a massive black hole - II. Resonant relaxation

NASA Astrophysics Data System (ADS)

Sridhar, S.; Touma, Jihad R.

2016-06-01

We present a first-principles theory of resonant relaxation (RR) of a low-mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert to include the Keplerian field of a black hole of mass M•. Specializing to a Keplerian stellar system of mass M ≪ M•, we use the orbit-averaging method of Sridhar & Touma to derive a kinetic equation for RR. This describes the collisional evolution of a system of N ≫ 1 Gaussian rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 post-Newtonian (PN) and 1.5 PN relativistic effects of the MBH and an arbitrary external potential. In general geometries, RR is driven by both apsidal and nodal resonances, so the distinction between scalar RR and vector RR disappears. The system passes through a sequence of quasi-steady secular collisionless equilibria, driven by irreversible two-ring correlations that accrue through gravitational interactions, both direct and collective. This correlation function is related to a `wake function', which is the linear response of the system to the perturbation of a chosen ring. The wake function is easier to appreciate, and satisfies a simpler equation, than the correlation function. We discuss general implications for the interplay of secular dynamics and non-equilibrium statistical mechanics in the evolution of Keplerian stellar systems towards secular thermodynamic equilibria, and set the stage for applications to the RR of axisymmetric discs in Paper III.

Effects of resolved boundary layer turbulence on near-ground rotation in simulated quasi-linear convective systems (QLCSs)

NASA Astrophysics Data System (ADS)

Nowotarski, C. J.

2017-12-01

Though most strong to violent tornadoes are associated with supercell thunderstorms, quasi-linear convective systems (QLCSs) pose a risk of tornadoes, often at times and locations where supercell tornadoes are less common. Because QLCS low-level mesocyclones and tornado signatures tend to be less coherent, forecasting such tornadoes remains particularly difficult. The majority of simulations of such storms rely on horizontally homogeneous base states lacking resolved boundary layer turbulence and surface fluxes. Previous work has suggested that heterogeneities associated with boundary layer turbulence in the form of horizontal convective rolls can influence the evolution and characteristics of low-level mesocyclones in supercell thunderstorms. This study extends methods for generating boundary layer convection to idealized simulations of QLCSs. QLCS simulations with resolved boundary layer turbulence will be compared against a control simulation with a laminar boundary layer. Effects of turbulence, the resultant heterogeneity in the near-storm environment, and surface friction on bulk storm characteristics and the intensity, morphology, and evolution of low-level rotation will be presented. Although maximum surface vertical vorticity values are similar, when boundary layer turbulence is included, a greater number of miso- and meso-scale vortices develop along the QLCS gust front. The source of this vorticity is analyzed using Eulerian decomposition of vorticity tendency terms and trajectory analysis to delineate the relative importance of surface friction and baroclinicity in generating QLCS vortices. The role of anvil shading in suppressing boundary layer turbulence in the near-storm environment and subsequent effects on QLCS vortices will also be presented. Finally, implications of the results regarding inclusion of more realistic boundary layers in future idealized simulations of deep convection will be discussed.

Payoff non-linearity sways the effect of mistakes on the evolution of reciprocity.

PubMed

Kurokawa, Shun

2016-09-01

The existence of cooperation is considered to require explanation, and reciprocity is a potential explanatory mechanism. Animals sometimes fail to cooperate even when they attempt to do so, and a reciprocator has an Achilles' heel: it is vulnerable to error (the interaction between two reciprocators can lead to an endless vendetta.). However, the strategy favored by natural selection is determined also by its interaction with other strategies. The relationship between two reciprocators leading to a collapse of cooperation through error does not straightforwardly imply that mistakes make the conditions under which reciprocity evolves stringent. Hence, mistakes may facilitate the evolution of reciprocity. However, it has been shown through the analysis of the interaction between reciprocators and unconditional defectors that the existence of mistakes makes the conditions for reciprocators stable against invasion by an unconditional defector more stringent, which indicates that mistakes discourage the evolution of reciprocity. However, this result is based on the assumption that the effects of cooperation are additive (payoff is linear), while the game played by real animals does not always display this feature. In such cases, the result may be swayed. In this paper, we remove this assumption, reexamining whether mistakes disturb the evolution of reciprocity. Using the analysis of an evolutionarily stable strategy (ESS), we show that when extra fitness costs are present in cases where mutual cooperation is established, mistakes can facilitate the evolution of reciprocity; whereas, when the effect of cooperation is additive, mistakes always disturb the evolution of reciprocity, as has been shown previously. Copyright © 2016. Published by Elsevier Inc.

Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration

NASA Astrophysics Data System (ADS)

Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J.

2002-02-01

This is the first paper in a two-part series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a Hele-Shaw cell with arbitrary density and viscosity contrast between the components. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid (NSCH model [Lowengrub and Truskinovsky, Proc. R. Soc. London, Ser. A 454, 2617 (1998)]) to flow in a Hele-Shaw cell. The system takes into account the chemical diffusivity between different components of a fluid mixture and the reactive stresses induced by inhomogeneity. In one of the systems we consider (HSCH), the binary fluid may be compressible due to diffusion. In the other system (BHSCH), a Boussinesq approximation is used and the fluid is incompressible. In this paper, we motivate, present and calibrate the HSCH/BHSCH equations so as to yield the classical sharp interface model as a limiting case. We then analyze their equilibria, one dimensional evolution and linear stability. In the second paper [paper II, Phys. Fluids 14, 514 (2002)], we analyze the behavior of the models in the fully nonlinear regime. In the BHSCH system, the equilibrium concentration profile is obtained using the classical Maxwell construction [Rowlinson and Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1979)] and does not depend on the orientation of the gravitational field. We find that the equilibria in the HSCH model are somewhat surprising as the gravitational field actually affects the internal structure of an isolated interface by driving additional stratification of light and heavy fluids over that predicted in the Boussinesq case. A comparison of the linear growth rates indicates that the HSCH system is slightly more diffusive than the BHSCH system. In both, linear convergence to the sharp interface growth rates is observed in a parameter controlling the interface thickness. In addition, we identify the effect that each of the parameters, in the HSCH/BHSCH models, has on the linear growth rates. We then show how this analysis may be used to suggest a set of modified parameters which, when used in the HSCH/BHSCH systems, yield improved agreement with the sharp interface model at a finite interface thickness. Evidence of this improved agreement may be found in paper II.

Design, construction, and evaluation of new high resolution medical imaging detector/systems

NASA Astrophysics Data System (ADS)

Jain, Amit

Increasing need of minimally invasive endovascular image guided interventional procedures (EIGI) for accurate and successful treatment of vascular disease has set a quest for better image quality. Current state of the art detectors are not up to the mark for these complex procedures due to their inherent limitations. Our group has been actively working on the design and construction of a high resolution, region of interest CCD-based X-ray imager for some time. As a part of that endeavor, a Micro-angiographic fluoroscope (MAF) was developed to serve as a high resolution, ROI X-ray imaging detector in conjunction with large lower resolution full field of view (FOV) state-of-the-art x-ray detectors. The newly developed MAF is an indirect x-ray imaging detector capable of providing real-time images with high resolution, high sensitivity, no lag and low instrumentation noise. It consists of a CCD camera coupled to a light image intensifier (LII) through a fiber optic taper. The CsI(Tl) phosphor serving as the front end is coupled to the LII. For this work, the MAF was designed and constructed. The linear system cascade theory was used to evaluate the performance theoretically. Linear system metrics such as MTF and DQE were used to gauge the detector performance experimentally. The capabilities of the MAF as a complete system were tested using generalized linear system metrics. With generalized linear system metrics the effects of finite size focal spot, geometric magnification and the presence of scatter are included in the analysis and study. To minimize the effect of scatter, an anti-scatter grid specially designed for the MAF was also studied. The MAF was compared with the flat panel detector using signal-to-noise ratio and the two dimensional linear system metrics. The signal-to-noise comparison was carried out to point out the effect of pixel size and Point Spread Function of the detector. The two dimensional linear system metrics were used to investigate the comparative performance of both the detectors in similar simulated clinical neuro-vascular conditions. The last part of this work presents a unique quality of the MAF: operation in single photon mode. The successful operation of the MAF was demonstrated with considerable improvement in spatial and contrast resolution over conventional energy integrating mode. The work presented shows the evolution of a high resolution, high sensitivity, and region of interest x-ray imaging detector as an attractive and capable x-ray imager for the betterment of complex EIGI procedures. The capability of single photon counting mode imaging provides the potential for additional uses of the MAF including the possibility of use in dual modality imaging with radionuclide sources as well as x-rays.

A first continuous 4-aminoantipyrine (4-AAP)-based screening system for directed esterase evolution.

PubMed

Lülsdorf, Nina; Vojcic, Ljubica; Hellmuth, Hendrik; Weber, Thomas T; Mußmann, Nina; Martinez, Ronny; Schwaneberg, Ulrich

2015-06-01

Esterases hydrolyze ester bonds with an often high stereoselectivity as well as regioselectivity and are therefore industrially employed in the synthesis of pharmaceuticals, in food processing, and in laundry detergents. Continuous screening systems based on p-nitrophenyl- (e.g., p-nitrophenyl acetate) or umbelliferyl-esters are commonly used in directed esterase evolution campaigns. Ongoing challenges in directed esterase evolution are screening formats which offer a broad substrate spectrum, especially for complex aromatic substrates. In this report, a novel continuous high throughput screening system for indirect monitoring of esterolytic activity was developed and validated by detection of phenols employing phenyl benzoate as substrate and p-nitrobenzyl esterase (pNBEBL from Bacillus licheniformis) as catalyst. The released phenol directly reacts with 4-aminoantipyrine yielding the red compound 1,5-dimethyl-4-(4-oxo-cyclohexa-2,5-dienylidenamino)-2-phenyl-1,2-dihydro-pyrazol-3-one. In this continuous B. licheniformis esterase activity detection system (cBLE-4AAP), the product formation is followed through an increase in absorbance at 509 nm. The cBLE-4AAP screening system was optimized in 96-well microtiter plate format in respect to standard deviation (5 %), linear detection range (15 to 250 μM), lower detection limit (15 μM), and pH (7.4 to 10.4). The cBLE-4AAP screening system was validated by screening a random epPCR pNBEBL mutagenesis library (2000 clones) for improved esterase activity at elevated temperatures. Finally, the variant T3 (Ser378Pro) was identified which nearly retains its specific activity at room temperature (WT 1036 U/mg and T3 929 U/mg) and shows compared to WT a 4.7-fold improved residual activity after thermal treatment (30 min incubation at 69.4 °C; WT 170 U/mg to T3 804 U/mg).

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, M.; Zlotnik, S.; Fernandez, M.; Verges, J.; Jiménez-Munt, I.; Torne, M.

2015-12-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model proposed by Vergés and Fernàndez (2012) suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model of double-polarity subduction is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle and the problem is driven by Rayleigh-Taylor instability. The main factors to be studied are the interaction between the two plates, the poloidal and toroidal mantle fluxes, the velocity variations of slabs, the stress distribution and the variations in the trench morphology.

Modeling the Long-term Planform Evolution of Meandering Rivers in Confined Alluvial Valleys: Etsch-Adige River, NE Italy.

NASA Astrophysics Data System (ADS)

Zen, S.; Bogoni, M.; Zolezzi, G.; Lanzoni, S.; Scorpio, V.

2016-12-01

We combine the use of a morphodynamic model for river meander planform evolution with a geological dataset to investigate the influence of external confinements on the long-term evolution of a meandering river flowing in an Alpine valley. The analysis focuses on a 100 km reach of the Adige River, NE Italy, which had several sinuous/meandering sections before being extensively channelized in the 1800s. Geological surveys and historical maps revealed that many sections of the study reach impinge on the borders of the valley during its evolution. Moreover, a marked spatial heterogeneity in floodplain vertical accretion rates likely reflects preferential positions of the river channel in the floodplain. Valley confinements are represented by bedrock outcrops and by alluvial fans created by lateral tributaries, and were extracted from the geological and historical maps to build the computational domain for the meander morphodynamic model. The model predicts the long-term planform evolution of a meandering river based on a linear solution of the 2D De St Venant-Exner differential system and can manage changes in floodplain erodibility. Model applications allow to isolate the effects of valley bedrock and of alluvial fans in constraining the lateral channel migration. Modeled river channel persistence maps are compared with the available geological information. The present work allows further insights into the role of external confinements to river meander belts, which have been conducted so far mostly assuming the channel to evolve in unconfined floodplains. Future research shall incorporate model components for floodplain vertical accretion rates and for the advancement of alluvial fans occurring at the same time scale considered for meander evolution.

NLO evolution of 3-quark Wilson loop operator

DOE PAGES

Balitsky, I.; Grabovsky, A. V.

2015-01-07

It is well known that high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to fast quark-antiquark pair. Moreover, the energy dependence of the scattering amplitude is governed by the evolution equation of this color dipole with respect to rapidity. Similarly, the energy dependence of scattering of a baryon can be described in terms of evolution of a three-Wilson-lines operator with respect to the rapidity of the Wilson lines. We calculate the evolution of the 3-quark Wilson loop operator in themore » next-to-leading order (NLO) and present a quasi-conformal evolution equation for a composite 3-Wilson-lines operator. Thus we also obtain the linearized version of that evolution equation describing the amplitude of the odderon exchange at high energies.« less

Enhancement of ultracold molecule formation by local control in the nanosecond regime

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

Carini, J. L.; Kallush, S.; Kosloff, R.

2015-02-01

We describe quantum simulations of ultracold 87Rb 2 molecule formation using photoassociation (PA) with nanosecond-time-scale pulses of frequency chirped light. In particular, we compare the case of a linear chirp to one where the frequency evolution is optimized by local control (LC) of the phase, and find that LC can provide a significant enhancement. The resulting optimal frequency evolution corresponds to a rapid jump from the PA absorption resonance to a downward transition to a bound level of the lowest triplet state. We also consider the case of two frequencies and investigate interference effects. The assumed chirp parameters should bemore » achievable with nanosecond pulse shaping techniques and are predicted to provide a significant enhancement over recent experiments with linear chirps.« less

Secular evolution of asteroid families: the role of Ceres

NASA Astrophysics Data System (ADS)

Novaković, Bojan; Tsirvoulis, Georgios; Marò, Stefano; Đošović, Vladimir; Maurel, Clara

2016-01-01

We consider the role of the dwarf planet Ceres on the secular dynamics of the asteroid main belt. Specifically, we examine the post impact evolution of asteroid families due to the interaction of their members with the linear nodal secular resonance with Ceres. First, we find the location of this resonance and identify which asteroid families are crossed by its path. Next, we summarize our results for three asteroid families, namely (1726) Hoffmeister, (1128) Astrid and (1521) Seinajoki which have irregular distributions of their members in the proper elements space, indicative of the effect of the resonance. We confirm this by performing a set of numerical simulations, showcasing that the perturbing action of Ceres through its linear nodal secular resonance is essential to reproduce the actual shape of the families.

The evolution of males: support for predictions from sex allocation theory using mating arrays of sagittaria latifolia (alismataceae).

PubMed

Perry, Laura E; Dorken, Marcel E

2011-10-01

Investment in male function should often yield diminishing fitness returns, subjecting the evolution of male phenotypes to substantial constraints. In plants, the subdivision of male function via the gradual presentation of pollen might minimize these constraints by preventing the saturation of receptive stigmas. Here, we report on an investigation of (1) patterns of investment in male function by plants in hermaphroditic (monoecious) and dioecious populations of Sagittaria latifolia, and (2) patterns of siring success by males versus hermaphrodites in experimental mating arrays. We show that in natural populations, males from dioecious populations had greater investment in male function than hermaphrodites in monoecious populations. However, as a proportion of total flower production, males presented substantially fewer flowers at once than hermaphrodites. In comparison with hermaphrodites, therefore, males prolonged the period over which they presented pollen. In mating arrays comprised of females, males, and hermaphrodites, siring success by males increased linearly with flower production. This finding is consistent with the existence of a linear gain curve for male function in S. latifolia and supports the idea that the gradual deployment of male function enables plants to avoid diminishing returns on the investment in male function. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Characterization of linear interfacial waves in a turbulent gas-liquid pipe flow

NASA Astrophysics Data System (ADS)

Ayati, A. A.; Farias, P. S. C.; Azevedo, L. F. A.; de Paula, I. B.

2017-06-01

The evolution of interfacial waves on a stratified flow was investigated experimentally for air-water flow in a horizontal pipe. Waves were introduced in the liquid level of stratified flow near the pipe entrance using an oscillating plate. The mean height of liquid layer and the fluctuations superimposed on this mean level were captured using high speed cameras. Digital image processing techniques were used to detect instantaneous interfaces along the pipe. The driving signal of the oscillating plate was controlled by a D/A board that was synchronized with acquisitions. This enabled to perform phase-locked acquisitions and to use ensemble average procedures. Thereby, it was possible to measure the temporal and spatial evolution of the disturbances introduced in the flow. In addition, phase-locked measurements of the velocity field in the liquid layer were performed using standard planar Particle Image Velocimetry (PIV). The velocity fields were extracted at a fixed streamwise location, whereas the measurements of the liquid level were performed at several locations along the pipe. The assessment of the setup was important for validation of the methodology proposed in this work, since it aimed at providing results for further comparisons with theoretical models and numerical simulations. Therefore, the work focuses on validation and characterization of interfacial waves within the linear regime. Results show that under controlled conditions, the wave development can be well captured and reproduced. In addition, linear waves were observed for liquid level oscillations lower than about 1.5% of the pipe diameter. It was not possible to accurately define an amplitude threshold for the appearance of nonlinear effects because it strongly depended on the wave frequency. According to the experimental findings, longer waves display characteristics similar to linear waves, while short ones exhibit a more complex evolution, even for low amplitudes.

Implications for future activity of Grímsvötn volcano, Iceland, from compositional time series of historical tephra

NASA Astrophysics Data System (ADS)

Carpentier, Marion; Sigmarsson, Olgeir; Larsen, Gudrun

2014-05-01

The nature of future eruptions of active volcanoes is hard to predict. Improved understanding of the past volcanic activity is probably the best way to infer future eruptive scenarios. The most active volcano in Iceland, Grímsvötn, last erupted in 2011 with consequences for habitants living close to the volcano and aviation in the North-Atlantic. In an effort to better understand the magmatic system of the volcano, we have investigated the compositions of 23 selected tephra layers representing the last 8 centuries of volcanic activity at Grímsvötn. The tephra was collected in the ablation area of outlet glaciers from Vatnajökull ice cap. The ice-conserved tephra are less prone to alteration than those exposed in soil sections. Major element analyses are indistinguishable and of quartz-normative tholeiite composition, and Sr and Nd isotope ratios are constant. In contrast, both trace element concentrations (Th range from 0.875 ppm to 1.37 ppm and Ni from 28.5 ppm to 56.6 ppm) in the basalts and Pb isotopes show small but significant variations. The high-precision analyses of Pb isotope ratios allow the identification of tephra samples (3 in total) with more radiogenic ratios than the bulk of the samples. The tephra of constant isotope ratios show linear increase in incompatible element concentrations with time. The rate of increasing concentrations permits exploring possible future scenarios assuming that the magmatic system beneath the volcano follows the established historical evolution. Assuming similar future behaviour of the magma system beneath Grímsvötn volcano, the linear increase in e.g. Th concentration suggests that the volcano is likely to principally produce basalts for the next 500-1000 years. Evolution of water concentration will most likely follow those of incompatible elements with consequent increases in explosiveness of future Grímsvötn eruptions.

Large-scale geomorphology: Classical concepts reconciled and integrated with contemporary ideas via a surface processes model

NASA Astrophysics Data System (ADS)

Kooi, Henk; Beaumont, Christopher

1996-02-01

Linear systems analysis is used to investigate the response of a surface processes model (SPM) to tectonic forcing. The SPM calculates subcontinental scale denudational landscape evolution on geological timescales (1 to hundreds of million years) as the result of simultaneous hillslope transport, modeled by diffusion, and fluvial transport, modeled by advection and reaction. The tectonically forced SPM accommodates the large-scale behavior envisaged in classical and contemporary conceptual geomorphic models and provides a framework for their integration and unification. The following three model scales are considered: micro-, meso-, and macroscale. The concepts of dynamic equilibrium and grade are quantified at the microscale for segments of uniform gradient subject to tectonic uplift. At the larger meso- and macroscales (which represent individual interfluves and landscapes including a number of drainage basins, respectively) the system response to tectonic forcing is linear for uplift geometries that are symmetric with respect to baselevel and which impose a fully integrated drainage to baselevel. For these linear models the response time and the transfer function as a function of scale characterize the model behavior. Numerical experiments show that the styles of landscape evolution depend critically on the timescales of the tectonic processes in relation to the response time of the landscape. When tectonic timescales are much longer than the landscape response time, the resulting dynamic equilibrium landscapes correspond to those envisaged by Hack (1960). When tectonic timescales are of the same order as the landscape response time and when tectonic variations take the form of pulses (much shorter than the response time), evolving landscapes conform to the Penck type (1972) and to the Davis (1889, 1899) and King (1953, 1962) type frameworks, respectively. The behavior of the SPM highlights the importance of phase shifts or delays of the landform response and sediment yield in relation to the tectonic forcing. Finally, nonlinear behavior resulting from more general uplift geometries is discussed. A number of model experiments illustrate the importance of "fundamental form," which is an expression of the conformity of antecedent topography with the current tectonic regime. Lack of conformity leads to models that exhibit internal thresholds and a complex response.

Solubility of polyethers in hydrocarbons at low temperatures. A model for potential genetic backbones on warm titans.

PubMed

McLendon, Christopher; Opalko, F Jeffrey; Illangkoon, Heshan I; Benner, Steven A

2015-03-01

Ethers are proposed here as the repeating backbone linking units in linear genetic biopolymers that might support Darwinian evolution in hydrocarbon oceans. Hydrocarbon oceans are found in our own solar system as methane mixtures on Titan. They may be found as mixtures of higher alkanes (propane, for example) on warmer hydrocarbon-rich planets in exosolar systems ("warm Titans"). We report studies on the solubility of several short polyethers in propane over its liquid range (from 85 to 231 K, or -188 °C to -42 °C). These show that polyethers are reasonably soluble in propane at temperatures down to ca. 200 K. However, their solubilities drop dramatically at still lower temperatures and become immeasurably low below 170 K, still well above the ∼ 95 K in Titan's oceans. Assuming that a liquid phase is essential for any living system, and genetic biopolymers must dissolve in that biosolvent to support Darwinism, these data suggest that we must look elsewhere to identify linear biopolymers that might support genetics in Titan's surface oceans. However, genetic molecules with polyether backbones may be suitable to support life in hydrocarbon oceans on warm Titans, where abundant organics and environments lacking corrosive water might make it easier for life to originate.

Continued Rapid Uplift at Laguna del Maule Volcanic Field (Chile) from 2007 through 2014

NASA Astrophysics Data System (ADS)

Le Mével, H.; Feigl, K. L.; Cordova, L.; DeMets, C.; Lundgren, P.

2014-12-01

The current rate of uplift at Laguna del Maule (LdM) volcanic field in Chile is among the highest ever observed geodetically for a volcano that is not actively erupting. Using data from interferometric synthetic aperture radar (InSAR) and the Global Positioning System (GPS) recorded at five continuously operating stations, we measure the deformation field with dense sampling in time (1/day) and space (1/hectare). These data track the temporal evolution of the current unrest episode from its inception (sometime between 2004 and 2007) to vertical velocities faster than 200 mm/yr that continue through (at least) July 2014. Building on our previous work, we evaluate the temporal evolution by analyzing data from InSAR (ALOS, TerraSAR-X, TanDEM-X) and GPS [http://dx.doi.org/ 10.1093/gji/ggt438]. In addition, we consider InSAR data from (ERS, ENVISAT, COSMO-Skymed, and UAVSAR), as well as constraints from magneto-telluric (MT), seismic, and gravity surveys. The goal is to test the hypothesis that a recent magma intrusion is feeding a large, existing magma reservoir. What will happen next? To address this question, we analyze the temporal evolution of deformation at other large silicic systems such as Yellowstone, Long Valley, and Three Sisters, during well-studied episodes of unrest. We consider several parameterizations, including piecewise linear, parabolic, and Gaussian functions of time. By choosing the best-fitting model, we expect to constrain the time scales of such episodes and elucidate the processes driving them.

Isotopic anomalies - Chemical memory of Galactic evolution

NASA Technical Reports Server (NTRS)

Clayton, Donald D.

1988-01-01

New mechanisms for the chemical memory of isotopic anomalies are proposed which are based on the temporal change during the chemical evolution of the Galaxy of the isotopic composition of the mean ejecta from stars. Because of the differing temporal evolution of primary and secondary products of nucleosynthesis, the isotopic composition of the bulk interstellar medium changes approximately linearly with time, and thus any dust component having an age different from that of average dust will be isotopically anomalous. Special attention is given to C, O, Mg, Si, and isotopically heavy average-stellar condensates of SiC.

Gene family evolution: an in-depth theoretical and simulation analysis of non-linear birth-death-innovation models.

PubMed

Karev, Georgy P; Wolf, Yuri I; Berezovskaya, Faina S; Koonin, Eugene V

2004-09-09

The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution. In this work, we extend our previous analysis of stochastic BDIMs. In addition to the previously examined rational BDIMs, we introduce potentially more realistic logistic BDIMs, in which birth/death rates are limited for the largest families, and show that their properties are similar to those of models that include no such limitation. We show that the mean time required for the formation of the largest gene families detected in eukaryotic genomes is limited by the mean number of duplications per gene and does not increase indefinitely with the model degree. Instead, this time reaches a minimum value, which corresponds to a non-linear rational BDIM with the degree of approximately 2.7. Even for this BDIM, the mean time of the largest family formation is orders of magnitude greater than any realistic estimates based on the timescale of life's evolution. We employed the embedding chains technique to estimate the expected number of elementary evolutionary events (gene duplications and deletions) preceding the formation of gene families of the observed size and found that the mean number of events exceeds the family size by orders of magnitude, suggesting a highly dynamic process of genome evolution. The variance of the time required for the formation of the largest families was found to be extremely large, with the coefficient of variation > 1. This indicates that some gene families might grow much faster than the mean rate such that the minimal time required for family formation is more relevant for a realistic representation of genome evolution than the mean time. We determined this minimal time using Monte Carlo simulations of family growth from an ensemble of simultaneously evolving singletons. In these simulations, the time elapsed before the formation of the largest family was much shorter than the estimated mean time and was compatible with the timescale of evolution of eukaryotes. The analysis of stochastic BDIMs presented here shows that non-linear versions of such models can well approximate not only the size distribution of gene families but also the dynamics of their formation during genome evolution. The fact that only higher degree BDIMs are compatible with the observed characteristics of genome evolution suggests that the growth of gene families is self-accelerating, which might reflect differential selective pressure acting on different genes.

Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points

NASA Astrophysics Data System (ADS)

Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

2017-01-01

Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (~100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

Kinematics and Flow Evolution of a Flexible Wing in Stall Flutter

NASA Astrophysics Data System (ADS)

Farnsworth, John; Akkala, James; Buchholz, James; McLaughlin, Thomas

2014-11-01

Large amplitude stall flutter limit cycle oscillations were observed on an aspect ratio six finite span NACA0018 flexible wing model at a free stream velocity of 23 m/s and an initial angle of attack of six degrees. The wing motion was characterized by periodic oscillations of predominately a torsional mode at a reduced frequency of k = 0.1. The kinematics were quantified via stereoscopic tracking of the wing surface with high speed camera imaging and direct linear transformation. Simultaneously acquired accelerometer measurements were used to track the wing motion and trigger the collection of two-dimensional particle image velocimetry field measurements to the phase angle of the periodic motion. Aerodynamically, the flutter motion is driven by the development and shedding of a dynamic stall vortex system, the evolution of which is characterized and discussed. This work was supported by the AFOSR Flow Interactions and Control Portfolio monitored by Dr. Douglas Smith and the AFOSR/ASEE Summer Faculty Fellowship Program (JA and JB).

Nonlinear simulation of the fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, Malik; Faganello, Matteo; Berk, Herbert; Garbet, Xavier; Benkadda, Sadruddin; PIIM Team; IFS Team; IRFM Team

2014-10-01

We propose to extend the Odblom-Breizman precessional fishbone model to account for both the MagnetoHydroDynamic (MHD) nonlinearity at the q = 1 surface and the nonlinear response of the energetic particles contained within the q = 1 surface. This electromagnetic mode, whose excitation, damping and frequency chirping are determined by the self-consistent interaction between an energetic trapped particle population and the bulk plasma evolution, can induce effective transport and losses for the energetic particles, being them alpha-particles in next-future fusion devices or heated particles in present Tokamaks. The model is reduced to its simplest form, assuming a reduced MHD description for the bulk plasma and a two-dimensional phase-space evolution (gyro and bounce averaged) for deeply trapped energetic particles. Numerical simulations have been performed in order to characterize the mode chirping and saturation, in particular looking at the interplay between the development of phase-space structures and the system dissipation associated to the MHD non-linearities at the resonance locations.

Experimental study on the formation of subaqueous barchan dunes in closed conduits

NASA Astrophysics Data System (ADS)

Alvarez, Carlos A.; Franklin, Erick

2018-06-01

The present paper reports the formation of subaqueous barchan dunes by analyzing the temporal evolution of their main geometrical characteristics (width W, length L and horn lengths Lh). After certain time, the dunes reach an equilibrium state and it is possible to study the relation between W versus L, and the dependence of the dune velocity on L. The barchan dunes were formed from spherical glass and zirconium beads. An initial conical heap of beads was placed on the bottom wall of a rectangular channel and it was entrained by a water turbulent flow. The evolution of the dunes was filmed with a CCD camera placed above the channel and mounted on a traveling system. Our results show that after a characteristic time the dune shape does not change and it travels with a roughly constant velocity. Once the equilibrium state is reach, W and L are measured, showing linear dependence. Furthermore, we show that the dune velocity Vd scales with the inverse of the dune length.

Correlating Oxygen Evolution Catalysts Activity and Electronic Structure by a High-Throughput Investigation of Ni1-y-zFeyCrzOx

PubMed Central

Schwanke, Christoph; Stein, Helge Sören; Xi, Lifei; Sliozberg, Kirill; Schuhmann, Wolfgang; Ludwig, Alfred; Lange, Kathrin M.

2017-01-01

High-throughput characterization by soft X-ray absorption spectroscopy (XAS) and electrochemical characterization is used to establish a correlation between electronic structure and catalytic activity of oxygen evolution reaction (OER) catalysts. As a model system a quasi-ternary materials library of Ni1-y-zFeyCrzOx was synthesized by combinatorial reactive magnetron sputtering, characterized by XAS, and an automated scanning droplet cell. The presence of Cr was found to increase the OER activity in the investigated compositional range. The electronic structure of NiII and CrIII remains unchanged over the investigated composition spread. At the Fe L-edge a linear combination of two spectra was observed. These spectra were assigned to FeIII in Oh symmetry and FeIII in Td symmetry. The ratio of FeIII Oh to FeIII Td increases with the amount of Cr and a correlation between the presence of the FeIII Oh and a high OER activity is found. PMID:28287134

Correlating Oxygen Evolution Catalysts Activity and Electronic Structure by a High-Throughput Investigation of Ni1-y-zFeyCrzOx

NASA Astrophysics Data System (ADS)

Schwanke, Christoph; Stein, Helge Sören; Xi, Lifei; Sliozberg, Kirill; Schuhmann, Wolfgang; Ludwig, Alfred; Lange, Kathrin M.

2017-03-01

High-throughput characterization by soft X-ray absorption spectroscopy (XAS) and electrochemical characterization is used to establish a correlation between electronic structure and catalytic activity of oxygen evolution reaction (OER) catalysts. As a model system a quasi-ternary materials library of Ni1-y-zFeyCrzOx was synthesized by combinatorial reactive magnetron sputtering, characterized by XAS, and an automated scanning droplet cell. The presence of Cr was found to increase the OER activity in the investigated compositional range. The electronic structure of NiII and CrIII remains unchanged over the investigated composition spread. At the Fe L-edge a linear combination of two spectra was observed. These spectra were assigned to FeIII in Oh symmetry and FeIII in Td symmetry. The ratio of FeIII Oh to FeIII Td increases with the amount of Cr and a correlation between the presence of the FeIII Oh and a high OER activity is found.

Stick-slip friction and ageing in Velcro®

NASA Astrophysics Data System (ADS)

Mariani, Lisa; Angiolillo, Paul

2014-03-01

The mesoscopic hook and loop system of Velcro® provides a model of stick-slip friction that exhibits behavior reminiscent of results seen in nanoscale model systems. The friction is linearly dependent on contact area and independent of driving velocity. Morever, there is a power law dependence of the friction on loading, with exponent between 1/4 and 1/3. Furthermore, the evolution of stick-slip to more smooth sliding, as controlled by contact area, is also noted. These transition predictions follow power law profiles, as well, with respect to increasing contact area. Thus, the hook-and-loop system shows to be a good mesoscale model system of stick-slip friction and provides a link between nanoscale and macroscale friction. Through an investigation into the ageing of the hooks in the system, the data suggests that the hooks age during the shearing regime and take a characteristic time to return to initial attachment strength. Additionally, there does not appear to be a significant affect of ageing on the kinetic friction experienced by the system.

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

NASA Technical Reports Server (NTRS)

McKinley, David P.

2006-01-01

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

[Prediction and evolution of B cell epitopes of hemagglutinin in human-infecting H6N1 avian influenza virus].

PubMed

Yang, Jianke; Yuan, Jian; Gao, Jiguang; Zhu, Xiaolei; Lin, Aiqin

2015-01-01

To predict B cell epitopes of hemagglutinin (HA) of human-infecting H6N1 avian influenza virus and analyze their evolutionary characteristics. The dataset was downloaded from GISAID and GenBank databases. And the linear and conformational B cell epitopes of HA were predicted separately by various bioinformatic software. Furthermore, the conservation, adaptation and other evolutionary characteristics were also analyzed by some bioinformatic means. Four linear epitopes (A, B, C and D) and two conformational epitopes (E and F) were obtained after consideration of multiple factors. And the C epitope and sites ( 41, 157, 186, 187) mutated easily, but the other epitopes were very conservative and the D epitope was the most conservative. Interestingly, the site 157 was identified under positive selection, suggesting that it may be a particularly important site to make the virus evade the attack from the host immune system. The HA of human-infecting H6N1 avian influenza virus has five conservative B cell epitopes (three linear and two conformational) and one site under positive selection. The findings would facilitate the vaccine development, virus control and pathogenesis understanding.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Effects of Phase Transformations and Dynamic Material Strength on Hydrodynamic Instability Evolution in Metals

NASA Astrophysics Data System (ADS)

Opie, Saul

Hydrodynamic phenomena such as the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities can be described by exponential/linear growth of surface perturbations at a bimaterial interface when subjected to constant/impulsive acceleration. A challenge in designing systems to mitigate or exploit these effects is the lack of accurate material models at large dynamic strain rates and pressures. In particular, little stress-strain constitutive information at large strain rates and pressures is available for transient material phases formed at high pressures, and the continuum effect the phase transformation process has on the instability evolution. In this work, a phase-aware isotropic strength model is developed and partially validated with a novel RM-based instability experiment in addition to existing data from the literature. With the validated material model additional simulations are performed to provide insight into to the role that robust material constitutive behavior (e.g., pressure, temperature, rate dependence) has on RM instability and how RM instability experiments can be used to characterize and validated expected material behavior. For phase aware materials, particularly iron in this work, the simulations predict a strong dependence on the Atwood number that single phase materials do not have. At Atwood numbers close to unity, and pressures in the high pressure stability region, the high pressure phase dominates the RM evolution. However, at Atwood numbers close to negative one, the RM evolution is only weakly affected by the high-pressure phase even for shocks well above the phase transformation threshold. In addition to RM evolution this work looks at the closely related shock front perturbation evolution. Existing analytical models for isentropic processes in gases and liquids are modified for metal equation of states and plastic behavior for the first time. It is found that the presence of a volume collapsing phase transformation with increased pressure causes shock front perturbations to decay sooner, while plastic strength has the opposite effect which is significantly different from the effect viscosity has. These results suggest additional experimental setups to validate material models, or relevant material parameters that can be optimized for system design objectives, e.g., minimize feed through perturbations in inertial confinement fusion capsules.

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

Geologic Evolution of North America: Geologic features suggest that the continent has grown and differentiated through geologic time.

PubMed

Engel, A E

1963-04-12

The oldest decipherable rock complexes within continents (more than 2.5 billion years old) are largely basaltic volcanics and graywacke. Recent and modern analogs are the island arcs formed along and adjacent to the unstable interface of continental and oceanic crusts. The major interfacial reactions (orogenies) incorporate pre-existing sial, oceanic crust, and mantle into crust of a more continental type. Incipient stages of continental evolution, more than 3 billion years ago, remain obscure. They may involve either a cataclysmic granite-forming event or a succession of volcanic-sedimentary and granite-forming cycles. Intermediate and recent stages of continental evolution, as indicated by data for North America, involve accretion of numerous crustal interfaces with fragments of adjacent continental crust and their partial melting, reinjection, elevation, unroofing, and stabilization. Areas of relict provinces defined by ages of granites suggest that continental growth is approximately linear. But the advanced differentiation found in many provinces and the known overlaps permit wide deviation from linearity in the direction of a more explosive early or intermediate growth.

Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

NASA Astrophysics Data System (ADS)

Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

2017-06-01

The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

Intrinsic subpicosecond magnetization reversal driven by femtosecond laser pulses in GdFeCo amorphous films

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

Li, Shufa; Gao, Ruixin; Cheng, Chuyuan

2013-12-09

Ultrafast magnetization dynamics in GdFeCo films triggered by femtosecond laser pulses with and without an external field applied is studied experimentally for different excitation fluence. It is found that subpicosecond magnetization reversal occurs simultaneously in the ultrafast dynamics of both saturation and remnant magnetization states and almost identical within 13 ps, whereas relatively slow magnetization reversal across compensation point appears only in the dynamics of saturation magnetization state. It shows the subpicosecond magnetization reversal is external field independent, and originates from intrinsic magnetic evolution in ferrimagnetic system. The intrinsic subpicosecond reversal is qualitatively explained by linear reversal.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Linear analysis of time dependent properties of Child-Langmuir flow

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

Rokhlenko, A.

We continue our analysis of the time dependent behavior of the electron flow in the Child-Langmuir system, removing an approximation used earlier. We find a modified set of oscillatory decaying modes with frequencies of the same order as the inverse of the electron transient time. This range (typically MHz) allows simple experimental detection and maybe exploitation. We then study the time evolution of the current in response to a slow change of the anode voltage where the same modes of oscillations appear too. The cathode current in this case is systematically advanced or retarded depending on the direction of themore » voltage change.« less

Physics division annual report 2006.

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

Glover, J.; Physics

2008-02-28

This report highlights the activities of the Physics Division of Argonne National Laboratory in 2006. The Division's programs include the operation as a national user facility of ATLAS, the Argonne Tandem Linear Accelerator System, research in nuclear structure and reactions, nuclear astrophysics, nuclear theory, investigations in medium-energy nuclear physics as well as research and development in accelerator technology. The mission of nuclear physics is to understand the origin, evolution and structure of baryonic matter in the universe--the core of matter, the fuel of stars, and the basic constituent of life itself. The Division's research focuses on innovative new ways tomore » address this mission.« less

Small-Scale Tropopause Dynamics and TOMS Total Ozone

NASA Technical Reports Server (NTRS)

Stanford, John L.

2002-01-01

This project used Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) along-track ozone retrievals, in conjunction with ancillary meteorological fields and modeling studies, for high resolution investigations of upper troposphere and lower stratosphere dynamics. Specifically, high resolution along-track (Level 2) EP TOMS data were used to investigate the beautiful fine-scale structure in constituent and meteorological fields prominent in the evolution of highly non-linear baroclinic storm systems. Comparison was made with high resolution meteorological models. The analyses provide internal consistency checks and validation of the EP TOMS data which are vital for monitoring ozone depletion in both polar and midlatitude regions.

Linear analysis of time dependent properties of Child-Langmuir flow

NASA Astrophysics Data System (ADS)

Rokhlenko, A.

2013-01-01

We continue our analysis of the time dependent behavior of the electron flow in the Child-Langmuir system, removing an approximation used earlier. We find a modified set of oscillatory decaying modes with frequencies of the same order as the inverse of the electron transient time. This range (typically MHz) allows simple experimental detection and maybe exploitation. We then study the time evolution of the current in response to a slow change of the anode voltage where the same modes of oscillations appear too. The cathode current in this case is systematically advanced or retarded depending on the direction of the voltage change.

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

PubMed

Goldobin, D S; Pimenova, A V; Kovalevskaya, K V; Lyubimov, D V; Lyubimova, T P

2015-05-01

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

Dynamical systems for modeling evolution of the magnetic field of the Sun, stars and planets

NASA Astrophysics Data System (ADS)

Popova, E.

2016-12-01

The magnetic activity of the Sun, stars and planets are connected with a dynamo process based on the combined action of the differential rotation and the alpha-effect. Application of this concept allows us to get different types of solutions which can describe the magnetic activity of celestial bodies. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the spherical shell where dynamo process operates. It was shown the possibility of coexistence of quiasi-biennial oscillations, 22-year cycle, and grand minima of magnetic activity which is consistent with the observational data for the solar activity. We obtained different regimes (oscillations, vacillations, dynamo-bursts) depending on a value of the dynamo-number, the meridional circulation, and thickness of the spherical shell. We discuss features of these regimes and compare them with the observed features of the magnetic fields of the Sun, stars and Earth. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

Simulation of linear and nonlinear Landau damping of lower hybrid waves

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

Qi, Lei; Wang, X. Y.; Lin, Y.

2013-06-15

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k{sub ∥}/k,T{sub i}/T{sub e}, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear dampingmore » rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.« less

A Korteweg-de Vries description of dark solitons in polariton superfluids

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Horikis, T. P.; Kevrekidis, P. G.; Rodrigues, A. S.

2017-12-01

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed of a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture.

Structural Rheology of the Smectic Phase

PubMed Central

Fujii, Shuji; Komura, Shigeyuki; Lu, Chun-Yi David

2014-01-01

In this review article, we discuss the rheological properties of the thermotropic smectic liquid crystal 8CB with focal conic domains (FCDs) from the viewpoint of structural rheology. It is known that the unbinding of the dislocation loops in the smectic phase drives the smectic-nematic transition. Here we discuss how the unbinding of the dislocation loops affects the evolution of the FCD size, linear and nonlinear rheological behaviors of the smectic phase. By studying the FCD formation from the perpendicularly oriented smectic layers, we also argue that dislocations play a key role in the structural development in layered systems. Furthermore, similarities in the rheological behavior between the FCDs in the smectic phase and the onion structures in the lyotropic lamellar phase suggest that these systems share a common physical origin for the elasticity. PMID:28788123

Electric-field-induced association of colloidal particles

NASA Astrophysics Data System (ADS)

Fraden, Seth; Hurd, Alan J.; Meyer, Robert B.

1989-11-01

Dilute suspensions of micron diameter dielectric spheres confined to two dimensions are induced to aggregate linearly by application of an electric field. The growth of the average cluster size agrees well with the Smoluchowski equation, but the evolution of the measured cluster size distribution exhibits significant departures from theory at large times due to the formation of long linear clusters which effectively partition space into isolated one-dimensional strips.

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

Grenon, Cedric; Lake, Kayll

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.

Friction surfacing and linear friction welding

NASA Astrophysics Data System (ADS)

Nicholas, E. D.

The paper describes the development of the friction-surfacing and linear-friction welding technologies, with particular attention given to the equipment evolution and the application of the processes and advanced materials (such as intermetallics, metal-matrix composites (MMCs), ODS alloys, and powder metallurgy alloys) for the aerospace industry. The use of friction surfacing to modify the surface material with MMCs, to repair defects by plugging, and manufacture/reprocess materials is described.

Novel Approaches to Manipulating Bacterial Pathogen Biofilms: Whole-Systems Design Philosophy and Steering Microbial Evolution.

PubMed

Penn, Alexandra S

2016-01-01

Understanding and manipulating bacterial biofilms is crucial in medicine, ecology and agriculture and has potential applications in bioproduction, bioremediation and bioenergy. Biofilms often resist standard therapies and the need to develop new means of intervention provides an opportunity to fundamentally rethink our strategies. Conventional approaches to working with biological systems are, for the most part, "brute force", attempting to effect control in an input and effort intensive manner and are often insufficient when dealing with the inherent non-linearity and complexity of living systems. Biological systems, by their very nature, are dynamic, adaptive and resilient and require management tools that interact with dynamic processes rather than inert artefacts. I present an overview of a novel engineering philosophy which aims to exploit rather than fight those properties, and hence provide a more efficient and robust alternative. Based on a combination of evolutionary theory and whole-systems design, its essence is what I will call systems aikido; the basic principle of aikido being to interact with the momentum of an attacker and redirect it with minimal energy expenditure, using the opponent's energy rather than one's own. In more conventional terms, this translates to a philosophy of equilibrium engineering, manipulating systems' own self-organisation and evolution so that the evolutionarily or dynamically stable state corresponds to a function which we require. I illustrate these ideas with a description of a proposed manipulation of environmental conditions to alter the stability of co-operation in the context of Pseudomonas aeruginosa biofilm infection of the cystic fibrosis lung.

Life Cycle of Midlatitude Deep Convective Systems in a Lagrangian Framework

NASA Technical Reports Server (NTRS)

Feng, Zhe; Dong, Xiquan; Xie, Baike; McFarlane, Sally A.; Kennedy, Aaron; Lin, Bing; Minnis, Patrick

2012-01-01

Deep Convective Systems (DCSs) consist of intense convective cores (CC), large stratiform rain (SR) regions, and extensive non-precipitating anvil clouds (AC). This study focuses on the evolution of these three components and the factors that affect convective AC production. An automated satellite tracking method is used in conjunction with a recently developed multi-sensor hybrid classification to analyze the evolution of DCS structure in a Lagrangian framework over the central United States. Composite analysis from 4221 tracked DCSs during two warm seasons (May-August, 2010-2011) shows that maximum system size correlates with lifetime, and longer-lived DCSs have more extensive SR and AC. Maximum SR and AC area lag behind peak convective intensity and the lag increases linearly from approximately 1-hour for short-lived systems to more than 3-hours for long-lived ones. The increased lag, which depends on the convective environment, suggests that changes in the overall diabatic heating structure associated with the transition from CC to SR and AC could prolong the system lifetime by sustaining stratiform cloud development. Longer-lasting systems are associated with up to 60% higher mid-tropospheric relative humidity and up to 40% stronger middle to upper tropospheric wind shear. Regression analysis shows that the areal coverage of thick AC is strongly correlated with the size of CC, updraft strength, and SR area. Ambient upper tropospheric wind speed and wind shear also play an important role for convective AC production where for systems with large AC (radius greater than 120-km) they are 24% and 20% higher, respectively, than those with small AC (radius=20 km).

The initial instability and finite-amplitude stability of alternate bars in straight channels

USGS Publications Warehouse

Nelson, J.M.

1990-01-01

The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed. ?? 1990.

Water and the Earth System in the Anthropocene: Evolution of Socio-Hydrology

NASA Astrophysics Data System (ADS)

Sivapalan, M.; Bloeschl, G.

2014-12-01

Over the past century, hydrological science has evolved through distinct eras as judged by ideas, information sources, technological advances and societal influences: Empirical Era which was data based with little theory, Systems Era that focused on input-output relationships, Process Era with a focus on processes, and the Geosciences Era where hydrology was considered an Earth System science. We argue that as the human footprint on earth becomes increasingly dominant, we are moving into a Co-evolution Era. Co-evolution implies that the components of the Earth system are intimately intertwined at many time scales - fast scales of immediate feedbacks that translate into slow scale interdependencies and trends. These involve feedbacks between the atmosphere, biota, soils and landforms, mediated by water flow and transport processes. The human factor is becoming a key component of this coupled system. While there is a long tradition of considering effects of water on humans, and vice versa, the new thrust on socio-hydrology has a number of defining characteristics that sets it apart from traditional approaches: - Capturing feedbacks of human-natural water system in a dynamic way (slow and fast processes) to go beyond prescribing human factors as mere boundary conditions. These feedbacks will be essential to understand how the system may evolve in the future into new, perhaps previously unobserved, states. - Quantifying system dynamics in a generalizable way. So far, water resources assessment has been context dependent, tied to local conditions. While for immediate decision making this is undoubtedly essential, for more scientific inquiry, a more uniform knowledge base is indispensable. - Not necessarily predictive. The coupled human-nature system is inherently non-linear, which may prohibit predictability in the traditional sense. The socio-hydrologic approach may still be predictive in a statistical sense and, perhaps even more importantly, it may yet reveal possible futures not predicted by traditional forecasts, yet essential for long-term decision making. Guided by these overarching arguments, and a review of recent progress, we will present a structured overview of socio-hydrology, framing the theoretical, observational and methodological challenges that lie ahead and ways to address them.

Re-Evaluating Clonal Dominance in Cancer Evolution.

PubMed

Burrell, Rebecca A; Swanton, Charles

2016-05-01

Tumours are composed of genetically heterogeneous subclones which may diverge early during tumour growth. However, our strategies for treating and assessing outcome for patients are overwhelmingly based upon the classical linear paradigm for cancer evolution. Increasing numbers of studies are finding that minor subclones can determine clinical disease course, and that temporal and spatial heterogeneity needs to be considered in disease management. In this article we review evidence for cancer clonal heterogeneity, evaluating the importance of tumour subclones and their growth through both Darwinian and neutral evolution. Major shifts in current clinical practice and trial designs, aimed at understanding cancer evolution on a patient-by-patient basis, may be necessary to achieve more successful treatment of heterogeneous metastatic disease. Copyright © 2016 Elsevier Inc. All rights reserved.

Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space.

PubMed

Peng, Yulian; Chen, Bo; Peng, Xi; Zhou, Meiling; Zhang, Liping; Li, Dongdong; Deng, Dongmei

2016-08-22

The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Quantum linear magnetoresistance in NbTe2

NASA Astrophysics Data System (ADS)

Chen, Hongxiang; Li, Zhilin; Fan, Xiao; Guo, Liwei; Chen, Xiaolong

2018-07-01

NbTe2 is a quasi-2D layered semimetal with charge density wave ground state showing a distorted-1T structure at room temperature. Here we report the anisotropic magneto-transport properties of NbTe2. An anomalous linear magnetoresistance up to 30% at 3 K in 9 T was observed, which can be well explained by a quantum linear magnetoresistance model. Our results reveal that a large quasi-2D Fermi surface and small Fermi pockets with linearly dispersive bands coexist in NbTe2. The comparison with the isostructural TaTe2 provides more information about the band structure evolution with charge density wave transitions in NbTe2 and TaTe2.

Comparison of the linear bias models in the light of the Dark Energy Survey

NASA Astrophysics Data System (ADS)

Papageorgiou, A.; Basilakos, S.; Plionis, M.

2018-05-01

The evolution of the linear and scale independent bias, based on the most popular dark matter bias models within the Λ cold dark matter (ΛCDM) cosmology, is confronted to that of the Dark Energy Survey (DES) luminous red galaxies (LRGs). Applying a χ2 minimization procedure between models and data, we find that all the considered linear bias models reproduce well the LRG bias data. The differences among the bias models are absorbed in the predicted mass of the dark-matter halo in which LRGs live and which ranges between ˜6 × 1012 and 1.4 × 1013 h-1 M⊙, for the different bias models. Similar results, reaching however a maximum value of ˜2 × 1013 h-1 M⊙, are found by confronting the SDSS (2SLAQ) Large Red Galaxies clustering with theoretical clustering models, which also include the evolution of bias. This later analysis also provides a value of Ωm = 0.30 ± 0.01, which is in excellent agreement with recent joint analyses of different cosmological probes and the reanalysis of the Planck data.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

Mineralization of surfactants by the microbiota of submerged plant detritus.

PubMed

Federle, T W; Ventullo, R M

1990-02-01

In wetlands and canopied bodies of water, plant detritus is an important source of carbon and energy. Detrital materials possess a large surface area for sorption of dissolved organics and are colonized by a large and diverse microbiota. To examine the biodegradation of surfactants by these microorganisms, submerged oak leaves were obtained from a laundromat wastewater pond, its overflow, and a pristine control pond. Leaves were cut into disks and incubated in sterile water amended with 50 mug of C-labeled linear alkylbenzene sulfonate (LAS), linear alcohol ethoxylate, stearyltrimethyl ammonium chloride, distearyldimethyl ammonium chloride, benzoic acid, or mixed amino acids per liter. Sorption of the test compounds to the detritus and evolution of CO(2) were followed with time. All of the compounds sorbed to the detritus to various degrees, with LAS and stearyltrimethyl ammonium chloride the most sorptive and benzoic acid the least. All compounds were mineralized without a lag. With leaves from the laundromat wastewater pond, half-lives were 12.6 days for LAS, 8.4 days for linear alcohol ethoxylate, 14.2 days for stearyltrimethyl ammonium chloride, 1.0 days for benzoic acid, and 2.7 days for mixed amino acids. Mineralization of LAS and linear alcohol ethoxylate by control pond leaves was slower and exhibited an S-shaped rather than a typical first-order pattern. This study shows that detritus represents a significant site of surfactant removal in detritus-rich systems.

Evolution of diffraction and self-diffraction phenomena in thin films of Gelite Bloom/Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Cano-Lara, Miroslava; Severiano-Carrillo, Israel; Trejo-Durán, Mónica; Alvarado-Méndez, Edgar

2017-09-01

In this work, we present a study of non-linear optical response in thin films elaborated with Gelite Bloom and extract of Hibiscus Sabdariffa. Non-linear refraction and absorption effects were studied experimentally (Z-scan technique) and numerically, by considering the transmittance as non-linear absorption and refraction contribution. We observe large phase shifts to far field, and diffraction due to self-phase modulation of the sample. Diffraction and self-diffraction effects were observed as time function. The aim of studying non-linear optical properties in thin films is to eliminate thermal vortex effects that occur in liquids. This is desirable in applications such as non-linear phase contrast, optical limiting, optics switches, etc. Finally, we find good agreement between experimental and theoretical results.

Probabilistic model of ligaments and tendons: quasistatic linear stretching.

PubMed

Bontempi, M

2009-03-01

Ligaments and tendons have a significant role in the musculoskeletal system and are frequently subjected to injury. This study presents a model of collagen fibers, based on the study of a statistical distribution of fibers when they are subjected to quasistatic linear stretching. With respect to other methodologies, this model is able to describe the behavior of the bundle using less ad hoc hypotheses and is able to describe all the quasistatic stretch-load responses of the bundle, including the yield and failure regions described in the literature. It has two other important results: the first is that it is able to correlate the mechanical behavior of the bundle with its internal structure, and it suggests a methodology to deduce the fibers population distribution directly from the tensile-test data. The second is that it can follow fibers' structure evolution during the stretching and it is possible to study the internal adaptation of fibers in physiological and pathological conditions.

Probabilistic model of ligaments and tendons: Quasistatic linear stretching

NASA Astrophysics Data System (ADS)

Bontempi, M.

2009-03-01

Ligaments and tendons have a significant role in the musculoskeletal system and are frequently subjected to injury. This study presents a model of collagen fibers, based on the study of a statistical distribution of fibers when they are subjected to quasistatic linear stretching. With respect to other methodologies, this model is able to describe the behavior of the bundle using less ad hoc hypotheses and is able to describe all the quasistatic stretch-load responses of the bundle, including the yield and failure regions described in the literature. It has two other important results: the first is that it is able to correlate the mechanical behavior of the bundle with its internal structure, and it suggests a methodology to deduce the fibers population distribution directly from the tensile-test data. The second is that it can follow fibers’ structure evolution during the stretching and it is possible to study the internal adaptation of fibers in physiological and pathological conditions.

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Suboptimal distributed control and estimation: application to a four coupled tanks system

NASA Astrophysics Data System (ADS)

Orihuela, Luis; Millán, Pablo; Vivas, Carlos; Rubio, Francisco R.

2016-06-01

The paper proposes an innovative estimation and control scheme that enables the distributed monitoring and control of large-scale processes. The proposed approach considers a discrete linear time-invariant process controlled by a network of agents that may both collect information about the evolution of the plant and apply control actions to drive its behaviour. The problem makes full sense when local observability/controllability is not assumed and the communication between agents can be exploited to reach system-wide goals. Additionally, to reduce agents bandwidth requirements and power consumption, an event-based communication policy is studied. The design procedure guarantees system stability, allowing the designer to trade-off performance, control effort and communication requirements. The obtained controllers and observers are implemented in a fully distributed fashion. To illustrate the performance of the proposed technique, experimental results on a quadruple-tank process are provided.

Optical solitons in nematic liquid crystals: model with saturation effects

NASA Astrophysics Data System (ADS)

Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego; de la Vega, Constanza Sánchez F.

2018-04-01

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

Nonlinear Simulation of DIII-D Plasma and Poloidal Systems Using DINA and Simulink

NASA Astrophysics Data System (ADS)

Walker, M. L.; Leuer, J. A.; Deranian, R. D.; Humphreys, D. A.; Khayrutdinov, R. R.

2002-11-01

Hardware-in-the-loop simulation capability was developed previously for poloidal shape control testing using Matlab Simulink [1]. This has been upgraded by replacing a linearized plasma model with the DINA nonlinear plasma evolution code [2]. In addition to its use for shape control studies, this new capability will allow study of current profile control using the DINA model of electron cyclotron current drive (ECCD) and current profile information soon to be available from the Plasma Control System (PCS) real time EFIT [3] calculation. We describe the incorporation of DINA into the Simulink DIII-D tokamak systems model and results of validating this combined model against DIII-D data. \\vspace0.1em [1] J.A. Leuer, et al., 18th IEEE/NPSS SOFE (1999), p. 531. [2] R.R. Khayrutdinov, V.E. Lukash, J. Comput. Phys. 109, 193 (1993). [3] J.R. Ferron, et al., Nucl. Fusion 38, 1055 (1988).

A non-linear irreversible thermodynamic perspective on organic pigment proliferation and biological evolution

NASA Astrophysics Data System (ADS)

Michaelian, K.

2013-12-01

The most important thermodynamic work performed by life today is the dissipation of the solar photon flux into heat through organic pigments in water. From this thermodynamic perspective, biological evolution is thus just the dispersal of organic pigments and water throughout Earth's surface, while adjusting the gases of Earth's atmosphere to allow the most intense part of the solar spectrum to penetrate the atmosphere and reach the surface to be intercepted by these pigments. The covalent bonding of atoms in organic pigments provides excited levels compatible with the energies of these photons. Internal conversion through vibrational relaxation to the ground state of these excited molecules when in water leads to rapid dissipation of the solar photons into heat, and this is the major source of entropy production on Earth. A non-linear irreversible thermodynamic analysis shows that the proliferation of organic pigments on Earth is a direct consequence of the pigments catalytic properties in dissipating the solar photon flux. A small part of the energy of the photon goes into the production of more organic pigments and supporting biomass, while most of the energy is dissipated and channeled into the hydrological cycle through the latent heat of vaporization of surface water. By dissipating the surface to atmosphere temperature gradient, the hydrological cycle further increases the entropy production of Earth. This thermodynamic perspective of solar photon dissipation by life has implications to the possibility of finding extra-terrestrial life in our solar system and the Universe.

Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

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

Makin, M. I.; Hill, Charles D.; Greentree, Andrew D.

2009-10-15

The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two-level system which can be tuned in resonance with the cavity. Here, we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where intercavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread overmore » many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.« less

Discrete dynamic modeling of cellular signaling networks.

PubMed

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, Mireia; Zlotnik, Sergio; Fernandez, Manel; Vergés, Jaume; Jiménez-Munt, Ivone; Torne, Montserrat

2016-04-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle in opposite direction and the problem is driven by Rayleigh-Taylor instability. We study the influence of the boundary conditions in the model evolution, and the slab deformation produced by the proximity between both plates. Moreover the case of asymmetric friction on the lateral sides of slabs is also considered. Simulations of single subduction models are used as a reference, to compare results and understand the influence of the second plate. We observe slight differences in the trench retreat velocity and the slab morphology near the contact area when plates are spaced less than 100 km.

Secular resonances with Ceres and Vesta

NASA Astrophysics Data System (ADS)

Tsirvoulis, Georgios; Novaković, Bojan

2016-12-01

In this work we explore dynamical perturbations induced by the massive asteroids Ceres and Vesta on main-belt asteroids through secular resonances. First we determine the location of the linear secular resonances with Ceres and Vesta in the main belt, using a purely numerical technique. Then we use a set of numerical simulations of fictitious asteroids to investigate the importance of these secular resonances in the orbital evolution of main-belt asteroids. We found, evaluating the magnitude of the perturbations in the proper elements of the test particles, that in some cases the strength of these secular resonances is comparable to that of known non-linear secular resonances with the giant planets. Finally we explore the asteroid families that are crossed by the secular resonances we studied, and identified several cases where the latter seem to play an important role in their post-impact evolution.

The evolution of kicked stellar-mass black holes in star cluster environments

NASA Astrophysics Data System (ADS)

Webb, Jeremy J.; Leigh, Nathan W. C.; Singh, Abhishek; Ford, K. E. Saavik; McKernan, Barry; Bellovary, Jillian

2018-03-01

We consider how dynamical friction acts on black holes that receive a velocity kick while located at the centre of a gravitational potential, analogous to a star cluster, due to either a natal kick or the anisotropic emission of gravitational waves during a black hole-black hole merger. Our investigation specifically focuses on how well various Chandrasekhar-based dynamical friction models can predict the orbital decay of kicked black holes with mbh ≲ 100 M⊙ due to an inhomogeneous background stellar field. In general, the orbital evolution of a kicked black hole follows that of a damped oscillator where two-body encounters and dynamical friction serve as sources of damping. However, we find models for approximating the effects of dynamical friction do not accurately predict the amount of energy lost by the black hole if the initial kick velocity vk is greater than the stellar velocity dispersion σ. For all kick velocities, we also find that two-body encounters with nearby stars can cause the energy evolution of a kicked BH to stray significantly from standard dynamical friction theory as encounters can sometimes lead to an energy gain. For larger kick velocities, we find the orbital decay of a black hole departs from classical theory completely as the black hole's orbital amplitude decays linearly with time as opposed to exponentially. Therefore, we have developed a linear decay formalism, which scales linearly with black hole mass and v_k/σ in order to account for the variations in the local gravitational potential.

Analysis of Blockade in Charge Transport Across Polymeric Heterojunctions as a Function of Thermal Annealing: A Different Perspective

NASA Astrophysics Data System (ADS)

Rathi, Sonika; Chauhan, Gayatri; Gupta, Saral K.; Srivastava, Ritu; Singh, Amarjeet

2017-02-01

A blend of poly(3-hexylthiophene-2,5diyl) (P3HT) and [6,6]-phenyl C61 butyric acid methyl ester (PCBM) is popularly used as an active medium in polymeric solar devices. According to the most recent understanding, the blend is a three-phase system contrary to its earlier understanding of two-phase bicontinuous network. We have synthesized a P3HT-PCBM based layered heterostructure system by spin coating and thermal vacuum evaporations. Current density ( J) was measured as a function of applied electric field ( E) across the system bound between two metal electrodes. J- E relations were analyzed into the backdrop of space charge limited current model and Schottky model. The later was used to predict dc-dielectric constants from the linear slopes of ln ( J) versus E 1/2. The curves were not monotonously linear, but observe a knee-bend separating into two linear segments for each curve. Thermal annealing from 40°C to 80°C was used as an activation tool for driving changes in the internal morphology via inter-diffusion of polymers and current measurements were performed at room temperature after each annealing. At the last stage of annealing the two linear slopes were highly distinct. The presence of sharp knee-bend results in approximately 20 times jump in dielectric constant as a function of electric field. Such high jumps in dielectric constant illustrate the potential for switching applications and charge storage. The high dielectric constants can be understood in terms of space charge polarization due to isolated domains which hindrance to charge transport. The high dielectric constants were confirmed by another experiment of capacitance measurements of a different set of similar samples. A study of thermal evolution of internal morphology was also carried out using x-ray diffraction and scanning electron microscopy techniques to correlate the morphological changes with the transport properties.

Simple estimation of linear 1+1 D tsunami run-up

NASA Astrophysics Data System (ADS)

Fuentes, M.; Campos, J. A.; Riquelme, S.

2016-12-01

An analytical expression is derived concerning the linear run-up for any given initial wave generated over a sloping bathymetry. Due to the simplicity of the linear formulation, complex transformations are unnecessay, because the shoreline motion is directly obtained in terms of the initial wave. This analytical result not only supports maximum run-up invariance between linear and non-linear theories, but also the time evolution of shoreline motion and velocity. The results exhibit good agreement with the non-linear theory. The present formulation also allows computing the shoreline motion numerically from a customised initial waveform, including non-smooth functions. This is useful for numerical tests, laboratory experiments or realistic cases in which the initial disturbance might be retrieved from seismic data rather than using a theoretical model. It is also shown that the real case studied is consistent with the field observations.

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

Krasnov, Kirill; Shtanov, Yuri, E-mail: kirill.krasnov@nottingham.ac.uk, E-mail: shtanov@bitp.kiev.ua

We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energymore » density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity.« less

A reassessment of the Archean-Mesoproterozoic tectonic development of the southeastern Chhattisgarh Basin, Central India through detailed aeromagnetic analysis

NASA Astrophysics Data System (ADS)

Sridhar, M.; Ramesh Babu, V.; Markandeyulu, A.; Raju, B. V. S. N.; Chaturvedi, A. K.; Roy, M. K.

2017-08-01

We constrained the geological framework over polydeformed Paleoproterozoic Sonakhan Greenstone Belt and addressed the tectonic evolution of Singhora basin in the fringes of Bastar Craton, central India by utilizing aeromagnetic data interpretation, 2.5D forward modelling and 3D magnetic susceptibility inversions. The Sonakhan Greenstone Belt exposes volcano-sedimentary sequences of the Sonakhan Group within NNW-SSE to NW-SE trending linear belts surrounded by granite gneisses, which are unconformably overlain by sedimentary rocks of Chhattisgarh Basin. The orientations of aeromagnetic anomalies are coincident with geological trends and appear to correlate with lithology and geologic structure. Regional magnetic anomalies and lineaments reveal both NNW-SSE and NE-SW trends. Prominent E-W trending linear, high amplitude magnetic anomalies are interpreted as the Trans-Chhattisgarh Aeromagnetic Lineament (TCAL). NW-SE trending aeromagnetic signatures related to Sonakhan Greenstone Belt extends below the Singhora sedimentary rocks and forms the basement in the west. The analysis suggests that TCAL is a block fault with northern block down-thrown and affected the basement rocks comprising the Sonakhan Greenstone Belt and Samblapur Granitoids. The episode of faulting represented by the TCAL is pre-Singhora sedimentation and played a vital role in basin evolution. The basement configuration image generated by estimates of depth to magnetic basement suggests a complex pattern of NNE-SSW to NE-SW trending depressions separated by a linear N-S trending basement ridge. It is inferred from the 3D magnetic susceptibility inversion that the thickness of sediments is more towards the eastern basin margin and the N-S ridge is a manifestation of post sedimentary faulting. Results of 2.5D modelling of a WNW-ESE profile across the Singhora Basin combined with results from 3D inversion suggest suggests the basin subsidence was controlled by NE-SW trending regional faults in an active system. The basin geometry evolved by E-W block faulting overprinted by NE-SW trending pre- to syn-depositional normal faults generating NE-SW depression, which are affected by N-S trend post-sedimentary faulting. Though the present work relates the basin evolution with the initiation of rift basin, it warrants further work to establish the deformation within the basin pertaining to the proximal thrust and uplift along the craton fringe.

Spin-electron acoustic soliton and exchange interaction in separate spin evolution quantum plasmas

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

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru

Separate spin evolution quantum hydrodynamics is generalized to include the Coulomb exchange interaction, which is considered as interaction between the spin-down electrons being in quantum states occupied by one electron. The generalized model is applied to study the non-linear spin-electron acoustic waves. Existence of the spin-electron acoustic soliton is demonstrated. Contributions of concentration, spin polarization, and exchange interaction to the properties of the spin electron acoustic soliton are studied.

Evolution of metastasis revealed by mutational landscapes of chemically induced skin cancers | Office of Cancer Genomics

Cancer.gov

Human tumors show a high level of genetic heterogeneity, but the processes that influence the timing and route of metastatic dissemination of the subclones are unknown. Here we have used whole-exome sequencing of 103 matched benign, malignant and metastatic skin tumors from genetically heterogeneous mice to demonstrate that most metastases disseminate synchronously from the primary tumor, supporting parallel rather than linear evolution as the predominant model of metastasis.

Conditional and unconditional Gaussian quantum dynamics

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio

2016-07-01

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.

Using the Cn2 and wind profiler method with wide-field laser-guide-stars adaptive optics to quantify the frozen-flow decay

NASA Astrophysics Data System (ADS)

Guesalaga, Andrés; Neichel, Benoit; Cortés, Angela; Béchet, Clémentine; Guzmán, Dani

2014-05-01

We use the spatio-temporal cross-correlations of slopes from five Shack-Hartmann wavefront sensors to analyse the temporal evolution of the atmospheric turbulence layers at different altitudes. The focus is on the verification of the frozen-flow assumption. The data come from the Gemini South Multiconjugate Adaptive Optics System (GeMS). First, we present the Cn2 and wind profiling technique. This method provides useful information for the operation of the adaptive optics system, such as the number of existing turbulence layers, their associated velocities, altitudes and strengths, and also a mechanism to estimate the dome-seeing contribution to the total turbulence. Next, by identifying the turbulence layers, we show that it is possible to estimate the rate of decay in time of the correlation among turbulence measurements. We reduce on-sky data obtained during the 2011, 2012 and 2013 campaigns. The first results suggest that the rate of temporal decorrelation can be expressed in terms of a single parameter that is independent of the layer altitude and turbulence strength. Finally, we show that the decay rate of the frozen-flow contribution increases linearly with the layer speed. The observed evolution of the decay rate confirms the potential interest of the predictive control for wide-field adaptive optics systems.

Analytical approach to Eigen-emittance evolution in storage rings

NASA Astrophysics Data System (ADS)

Nash, Boaz

This dissertation develops the subject of beam evolution in storage rings with nearly uncoupled symplectic linear dynamics. Linear coupling and dissipative/diffusive processes are treated perturbatively. The beam distribution is assumed Gaussian and a function of the invariants. The development requires two pieces: the global invariants and the local stochastic processes which change the emittances, or averages of the invariants. A map based perturbation theory is described, providing explicit expressions for the invariants near each linear resonance, where small perturbations can have a large effect. Emittance evolution is determined by the damping and diffusion coefficients. The discussion is divided into the cases of uniform and non-uniform stochasticity, synchrotron radiation an example of the former and intrabeam scattering the latter. For the uniform case, the beam dynamics is captured by a global diffusion coefficent and damping decrement for each eigen-invariant. Explicit expressions for these quantities near coupling resonances are given. In many cases, they are simply related to the uncoupled values. Near a sum resonance, it is found that one of the damping decrements becomes negative, indicating an anti-damping instability. The formalism is applied to a number of examples, including synchrobetatron coupling caused by a crab cavity, a case of current interest where there is concern about operation near half integer betatron tune. In the non-uniform case, the moment evolution is computed directly, which is illustrated through the example of intrabeam scattering. Our approach to intrabeam scattering damping and diffusion has the advantage of not requiring a loosely-defined Coulomb Logarithm. It is found that in some situations there is a small difference between our results and the standard approaches such as Bjorken-Mtingwa, which is illustrated by comparison of the two approaches and with a measurement of Au evolution in RHIC. Finally, in combining IBS with the global invariants some general statements about IBS equilibrium can be made. Specifically, it is emphasized that no such equilibrium is possible in a non-smooth lattice, even below transition. Near enough to a synchrobetatron coupling resonance, it is found that even for a smooth ring, no IBS equilibrium occurs.

A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements

NASA Astrophysics Data System (ADS)

Vincenzo, F.; Matteucci, F.; Spitoni, E.

2017-04-01

We present a theoretical method for solving the chemical evolution of galaxies by assuming an instantaneous recycling approximation for chemical elements restored by massive stars and the delay time distribution formalism for delayed chemical enrichment by Type Ia Supernovae. The galaxy gas mass assembly history, together with the assumed stellar yields and initial mass function, represents the starting point of this method. We derive a simple and general equation, which closely relates the Laplace transforms of the galaxy gas accretion history and star formation history, which can be used to simplify the problem of retrieving these quantities in the galaxy evolution models assuming a linear Schmidt-Kennicutt law. We find that - once the galaxy star formation history has been reconstructed from our assumptions - the differential equation for the evolution of the chemical element X can be suitably solved with classical methods. We apply our model to reproduce the [O/Fe] and [Si/Fe] versus [Fe/H] chemical abundance patterns as observed at the solar neighbourhood by assuming a decaying exponential infall rate of gas and different delay time distributions for Type Ia Supernovae; we also explore the effect of assuming a non-linear Schmidt-Kennicutt law, with the index of the power law being k = 1.4. Although approximate, we conclude that our model with the single-degenerate scenario for Type Ia Supernovae provides the best agreement with the observed set of data. Our method can be used by other complementary galaxy stellar population synthesis models to predict also the chemical evolution of galaxies.

A three-dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete

NASA Astrophysics Data System (ADS)

Zárate, Francisco; Cornejo, Alejandro; Oñate, Eugenio

2018-07-01

This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301-314, 2015). Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple four-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

Generic phylogeny, historical biogeography and character evolution of the cosmopolitan aquatic plant family Hydrocharitaceae.

PubMed

Chen, Ling-Yun; Chen, Jin-Ming; Gituru, Robert Wahiti; Wang, Qing-Feng

2012-03-10

Hydrocharitaceae is a fully aquatic monocot family, consists of 18 genera with approximately 120 species. The family includes both fresh and marine aquatics and exhibits great diversity in form and habit including annual and perennial life histories; submersed, partially submersed and floating leaf habits and linear to orbicular leaf shapes. The family has a cosmopolitan distribution and is well represented in the Tertiary fossil record in Europe. At present, the historical biogeography of the family is not well understood and the generic relationships remain controversial. In this study we investigated the phylogeny and biogeography of Hydrocharitaceae by integrating fossils and DNA sequences from eight genes. We also conducted ancestral state reconstruction for three morphological characters. Phylogenetic analyses produced a phylogeny with most branches strongly supported by bootstrap values greater than 95 and Bayesian posterior probability values of 1.0. Stratiotes is the first diverging lineage with the remaining genera in two clades, one clade consists of Lagarosiphon, Ottelia, Blyxa, Apalanthe, Elodea and Egeria; and the other consists of Hydrocharis-Limnobium, Thalassia, Enhalus, Halophila, Najas, Hydrilla, Vallisneria, Nechamandra and Maidenia. Biogeographic analyses (DIVA, Mesquite) and divergence time estimates (BEAST) resolved the most recent common ancestor of Hydrocharitaceae as being in Asia during the Late Cretaceous and Palaeocene (54.7-72.6 Ma). Dispersals (including long-distance dispersal and migrations through Tethys seaway and land bridges) probably played major roles in the intercontinental distribution of this family. Ancestral state reconstruction suggested that in Hydrocharitaceae evolution of dioecy is bidirectional, viz., from dioecy to hermaphroditism, and from hermaphroditism to dioecy, and that the aerial-submerged leaf habit and short-linear leaf shape are the ancestral states. Our study has shed light on the previously controversial generic phylogeny of Hydrocharitaceae. The study has resolved the historical biogeography of this family and supported dispersal as the most likely explanation for the intercontinental distribution. We have also provided valuable information for understanding the evolution of breeding system and leaf phenotype in aquatic monocots.

Shifting of the resonance location for planets embedded in circumstellar disks

NASA Astrophysics Data System (ADS)

Marzari, F.

2018-03-01

Context. In the early evolution of a planetary system, a pair of planets may be captured in a mean motion resonance while still embedded in their nesting circumstellar disk. Aims: The goal is to estimate the direction and amount of shift in the semimajor axis of the resonance location due to the disk gravity as a function of the gas density and mass of the planets. The stability of the resonance lock when the disk dissipates is also tested. Methods: The orbital evolution of a large number of systems is numerically integrated within a three-body problem in which the disk potential is computed as a series of expansion. This is a good approximation, at least over a limited amount of time. Results: Two different resonances are studied: the 2:1 and the 3:2. In both cases the shift is inwards, even if by a different amount, when the planets are massive and carve a gap in the disk. For super-Earths, the shift is instead outwards. Different disk densities, Σ, are considered and the resonance shift depends almost linearly on Σ. The gas dissipation leads to destabilization of a significant number of resonant systems, in particular if it is fast. Conclusions: The presence of a massive circumstellar disk may significantly affect the resonant behavior of a pair of planets by shifting the resonant location and by decreasing the size of the stability region. The disk dissipation may explain some systems found close to a resonance but not locked in it.

The Mass Evolution of Protostellar Disks and Envelopes in the Perseus Molecular Cloud

NASA Astrophysics Data System (ADS)

Andersen, Bridget; Stephens, Ian; Dunham, Michael; Pokhrel, Riwaj; Jørgensen, Jes; Frimann, Søren

2018-01-01

In the standard picture for low-mass star formation, a dense molecular cloud undergoes gravitational collapse to form a protostellar system consisting of a new central star, a circumstellar disk, and a surrounding envelope of remaining material. The mass distribution of the system evolves as matter accretes from the large-scale envelope through the disk and onto the protostar. While this general picture is supported by simulations and indirect observational measurements, the specific timescales related to disk growth and envelope dissipation remain poorly constrained. We present a rigorous test of a method introduced by Jørgensen et al. (2009) to obtain observational mass measurements of disks and envelopes around embedded protostars from unresolved (resolution of ~1000 AU) observations. Using data from the recent Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) survey, we derive disk and envelope mass estimates for 59 protostellar systems in the Perseus molecular cloud. We compare our results to independent disk mass measurements from the VLA Nascent Disk and Multiplicity (VANDAM) survey and find a strong linear correlation. Then, leveraging the size and uniformity of our sample, we find no significant trend in protostellar mass distribution as a function of age, as approximated from bolometric temperatures. These results may indicate that the disk mass of a protostar is set near the onset of the Class 0 protostellar stage and remains roughly constant throughout the Class I protostellar stage.

First-principles study of oxygen evolution reaction on Co doped NiFe-layered double hydroxides

NASA Astrophysics Data System (ADS)

Yu, Jie; Perdew, John; Yan, Qimin

The conversion of solar energy to renewable fuels is a grand challenge. One of the crucial steps for this energy conversion process is the discovery of efficient catalysts with lower overpotential for the oxygen evolution reaction (OER). Layered double hydroxides (LDH) with earth abundant elements such as Ni and Fe have been found as promising OER catalysts and shown to be active for water oxidation. Doping is one of the feasible ways to even lower the overpotential of host materials and breaks the linear scaling law. In this talk we'll present our study on the reaction mechanism of OER on pure and Co-doped NiFe-LDH systems in alkaline solution. We study the absorption energetics of reaction intermediate states and calculate the thermodynamic reaction energy using density functional theory with the PBE +U and the newly developed SCAN functionals. It is shown that the NiFe-LDH system with Co dopants has lower overpotential and higher activity compared with the undoped system. The improvement in activity is related to the presence of Co states in the electronic structure. The work provides a clear clue for the further improvement of the OER activity of LDH systems by chemical doping. The work was supported as part of the Center for the Computational Design of Functional Layered Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science.

Detecting nonlinear dynamics of functional connectivity

NASA Astrophysics Data System (ADS)

LaConte, Stephen M.; Peltier, Scott J.; Kadah, Yasser; Ngan, Shing-Chung; Deshpande, Gopikrishna; Hu, Xiaoping

2004-04-01

Functional magnetic resonance imaging (fMRI) is a technique that is sensitive to correlates of neuronal activity. The application of fMRI to measure functional connectivity of related brain regions across hemispheres (e.g. left and right motor cortices) has great potential for revealing fundamental physiological brain processes. Primarily, functional connectivity has been characterized by linear correlations in resting-state data, which may not provide a complete description of its temporal properties. In this work, we broaden the measure of functional connectivity to study not only linear correlations, but also those arising from deterministic, non-linear dynamics. Here the delta-epsilon approach is extended and applied to fMRI time series. The method of delays is used to reconstruct the joint system defined by a reference pixel and a candidate pixel. The crux of this technique relies on determining whether the candidate pixel provides additional information concerning the time evolution of the reference. As in many correlation-based connectivity studies, we fix the reference pixel. Every brain location is then used as a candidate pixel to estimate the spatial pattern of deterministic coupling with the reference. Our results indicate that measured connectivity is often emphasized in the motor cortex contra-lateral to the reference pixel, demonstrating the suitability of this approach for functional connectivity studies. In addition, discrepancies with traditional correlation analysis provide initial evidence for non-linear dynamical properties of resting-state fMRI data. Consequently, the non-linear characterization provided from our approach may provide a more complete description of the underlying physiology and brain function measured by this type of data.

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator systems might reflect the importance of group selection and competition between ensembles of cooperating replicators. Reviewers This article was reviewed by Viswanadham Sridhara (nominated by Claus Wilke), Puushottam Dixit (nominated by Sergei Maslov), and Nick Grishin. For the complete reviews, see the Reviewers’ Reports section. PMID:23937956

Anisotropies in the linear polarization of vacancy photoluminescence in diamond induced by crystal rotations and strong magnetic fields

NASA Astrophysics Data System (ADS)

Braukmann, D.; Popov, V. P.; Glaser, E. R.; Kennedy, T. A.; Bayer, M.; Debus, J.

2018-03-01

We study the linear polarization properties of the photoluminescence of ensembles of neutral and negatively charged nitrogen vacancies and neutral vacancies in diamond crystals as a function of their symmetry and their response to strong external magnetic fields. The linear polarization degree, which exceeds 10% at room temperature, and rotation of the polarization plane of their zero-phonon lines significantly depend on the crystal rotation around specific axes demonstrating anisotropic angular evolutions. The sign of the polarization plane rotation is changed periodically through the crystal rotation, which indicates a switching between electron excited states of orthogonal linear polarizations. At external magnetic fields of up to 10 T, the angular dependencies of the linear polarization degree experience a remarkable phase shift. Moreover, the rotation of the linear polarization plane increases linearly with rising magnetic field at 6 K and room temperature, for the negatively charged nitrogen vacancies, which is attributed to magneto-optical Faraday rotation.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

ARPES study of the evolution of band structure and charge density wave properties in RTe3 ( R=Y , La, Ce, Sm, Gd, Tb, and Dy)

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

Hussain, Zahid; Brouet, Veronique; Yang, Wanli

2008-01-16

We present a detailed angle-resolved photoemission spectroscopy (ARPES) investigation of the RTe3 family, which sets this system as an ideal"textbook" example for the formation of a nesting driven charge density wave (CDW). This family indeed exhibits the full range of phenomena that can be associated to CDWinstabilities, from the opening of large gaps on the best nested parts of Fermi surface (up to 0.4 eV), to the existence of residual metallic pockets. ARPES is the best suited technique to characterize these features, thanks to its unique ability to resolve the electronic structure in k space. An additional advantage of RTe3more » is that theband structure can be very accurately described by a simple two dimensional tight-binding (TB) model, which allows one to understand and easily reproduce many characteristics of the CDW. In this paper, we first establish the main features of the electronic structure by comparing our ARPES measurements with the linear muffin-tinorbital band calculations. We use this to define the validity and limits of the TB model. We then present a complete description of the CDW properties and of their strong evolution as a function of R. Using simple models, we are able to reproduce perfectly the evolution of gaps in k space, the evolution of the CDW wave vector with R, and the shape of the residual metallic pockets. Finally, we give an estimation of the CDWinteraction parameters and find that the change in the electronic density of states n (EF), due to lattice expansion when different R ions are inserted, has the correct order of magnitude to explain the evolution of the CDW properties.« less

Quantum Entanglement Growth under Random Unitary Dynamics

NASA Astrophysics Data System (ADS)

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan

2017-07-01

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

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

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Hydrogen atom initiated chemistry. [chemical evolution in planetary atmospheres

NASA Technical Reports Server (NTRS)

Hong, J. H.; Becker, R. S.

1979-01-01

H Atoms have been created by the photolysis of H2S. These then initiated reactions in mixtures involving acetylene-ammonia-water and ethylene-ammonia-water. In the case of the acetylene system, the products consisted of two amino acids, ethylene and a group of primarily cyclic thio-compounds, but no free sulfur. In the case of the ethylene systems, seven amino acids, including an aromatic one, ethane, free sulfur, and a group of solely linear thio-compounds were produced. Total quantum yields for the production of amino acids were about 3 x 10 to the -5th and about 2 x 10 to the -4th with ethylene and acetylene respectively as carbon substrates. Consideration is given of the mechanism for the formation of some of the products and implications regarding planetary atmosphere chemistry, particularly that of Jupiter, are explored.

Monte Carlo wave-function description of losses in a one-dimensional Bose gas and cooling to the ground state by quantum feedback

NASA Astrophysics Data System (ADS)

Schemmer, M.; Johnson, A.; Photopoulos, R.; Bouchoule, I.

2017-04-01

The effect of atom losses on a homogeneous one-dimensional Bose gas lying within the quasicondensate regime is investigated using a Monte Carlo wave-function approach. The evolution of the system is calculated, conditioned by the loss sequence, namely, the times of individual losses and the position of the removed atoms. We describe the gas within the linearized Bogoliubov approach. For each mode, we find that, for a given quantum trajectory, the state of the system converges towards a coherent state, i.e., the ground state, displaced in phase space. We show that, provided losses are recorded with a temporal and spatially resolved detector, quantum feedback can be implemented and cooling to the ground state of one or several modes can be realized.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Experiments of the highly non-linear Rayleigh-Taylor instability regime and dependence on Atwood Number

NASA Astrophysics Data System (ADS)

Elgin, L.; Handy, T.; Malamud, G.; Huntington, C. M.; Trantham, M. R.; Klein, S. R.; Kuranz, C. C.; Drake, R. P.; Shvarts, D.

2017-10-01

Potential flow models predict that a Rayleigh-Taylor unstable system will reach a terminal velocity (and constant Froude number) at low Atwood numbers. Numerical simulations predict a re-acceleration phase of Rayleigh-Taylor Instability (RTI) and higher Froude number at late times. To observe this effect, we are conducting a series of experiments at OMEGA 60 to measure single-mode RTI growth at low and high Atwood numbers and late times. X-ray radiographs spanning 40 + ns capture the evolution of these systems. Experimental design challenges and initial results are discussed here. This work is funded by the Lawrence Livermore National Laboratory under subcontract B614207, and was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

Satellite land remote sensing advancements for the eighties; Proceedings of the Eighth Pecora Symposium, Sioux Falls, SD, October 4-7, 1983

NASA Technical Reports Server (NTRS)

1984-01-01

Among the topics discussed are NASA's land remote sensing plans for the 1980s, the evolution of Landsat 4 and the performance of its sensors, the Landsat 4 thematic mapper image processing system radiometric and geometric characteristics, data quality, image data radiometric analysis and spectral/stratigraphic analysis, and thematic mapper agricultural, forest resource and geological applications. Also covered are geologic applications of side-looking airborne radar, digital image processing, the large format camera, the RADARSAT program, the SPOT 1 system's program status, distribution plans, and simulation program, Space Shuttle multispectral linear array studies of the optical and biological properties of terrestrial land cover, orbital surveys of solar-stimulated luminescence, the Space Shuttle imaging radar research facility, and Space Shuttle-based polar ice sounding altimetry.

Nonautonomous characteristics of the breathers and rogue waves for a amplifier nonlinear Schrödinger Maxwell-Bloch system

NASA Astrophysics Data System (ADS)

Wang, Lei; Li, Xiao; Zhang, Lu Lu; Li, Min; Qi, Feng-Hua

2015-09-01

Under investigation in this paper is a amplifier nonlinear Schrödinger Maxwell-Bloch (NLS-MB) system which describes the propagation of optical pulses in an inhomogeneous erbium doped fiber. Nonautonomous breather and rogue wave (RW) solutions of the amplifier NLS-MB system are constructed via the modified Darboux transformation with the inhomogeneous parameters. By suitably choosing the dispersion coefficient function, several types of inhomogeneous nonlinear waves are obtained in: (1) periodically fluctuating dispersion profile; (2) exponentially increasing (or decreasing) dispersion profile; and (3) linearly decreasing (increasing) dispersion profile. The nonautonomous characteristics of the breathers and RWs are graphically investigated, including the breather accelerating and decelerating motions, boomerang breather, breather compression, breather evolution, periodic RW, boomerang RW and stationary RW. Such novel patterns as the periodic breathers and rogue-wave fission of the amplifier NLS-MB system are exhibited by properly adjusting the group velocity dispersion function and interaction parameter between silica and doped atoms.

Linear modal stability analysis of bowed-strings.

PubMed

Debut, V; Antunes, J; Inácio, O

2017-03-01

Linearised models are often invoked as a starting point to study complex dynamical systems. Besides their attractive mathematical simplicity, they have a central role for determining the stability properties of static or dynamical states, and can often shed light on the influence of the control parameters on the system dynamical behaviour. While the bowed string dynamics has been thoroughly studied from a number of points of view, mainly by time-domain computer simulations, this paper proposes to explore its dynamical behaviour adopting a linear framework, linearising the friction force near an equilibrium state in steady sliding conditions, and using a modal representation of the string dynamics. Starting from the simplest idealisation of the friction force given by Coulomb's law with a velocity-dependent friction coefficient, the linearised modal equations of the bowed string are presented, and the dynamical changes of the system as a function of the bowing parameters are studied using linear stability analysis. From the computed complex eigenvalues and eigenvectors, several plots of the evolution of the modal frequencies, damping values, and modeshapes with the bowing parameters are produced, as well as stability charts for each system mode. By systematically exploring the influence of the parameters, this approach appears as a preliminary numerical characterisation of the bifurcations of the bowed string dynamics, with the advantage of being very simple compared to sophisticated numerical approaches which demand the regularisation of the nonlinear interaction force. To fix the idea about the potential of the proposed approach, the classic one-degree-of-freedom friction-excited oscillator is first considered, and then the case of the bowed string. Even if the actual stick-slip behaviour is rather far from the linear description adopted here, the results show that essential musical features of bowed string vibrations can be interpreted from this simple approach, at least qualitatively. Notably, the technique provides an instructive and original picture of bowed motions, in terms of groups of well-defined unstable modes, which is physically intuitive to discuss tonal changes observed in real bowed string.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

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

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R.

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes aremore » limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.« less

Investigation of electrodes under flow of a submicrosecond current pulse with linear density up to 3 MA/cm

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

Branitskii, A. V.; Grabovskii, E. V.; Dzhangobegov, V. V.

The states of current-carrying elements at the transmission of megaampere current into load are studied. It is determined that the expansion velocity of plasma generated at the outer surface of cylindrical tubes produced of stainless steel, at flowing through them of submicrosecond current pulses with linear density of 3 MA/cm is 5.5 km/s. The evolution of various modes of instability is analyzed.

Corrigendum

NASA Astrophysics Data System (ADS)

Lemons, Don S.; Gary, S. Peter; Winske, D.

1980-02-01

It has been called to our attention that our paper on the nonlinear evolution of a temperature anisotropic plasma (T > T¶) in the absence of an external magnetic field (Lemons, Winske & Gary 1979) did not make reference to several relevant and previously published works. Specifically, the linear theory of this unstable plasma has been explored by Kalman, Montes & Quemada (1968), the quasi-linear theory by Smith (1969) and Montes, Coste & Diener (1970) while additional thermodynamic considerations were given by Montes & Peyraud (1972). We regret this oversight.

Monotonic entropy growth for a nonlinear model of random exchanges.

PubMed

Apenko, S M

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Relativistic magnetised perturbations: magnetic pressure versus magnetic tension

NASA Astrophysics Data System (ADS)

Tseneklidou, Dimitra; Tsagas, Christos G.; Barrow, John D.

2018-06-01

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field’s pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field’s tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field’s pressure and tension, on the linear evolution of cosmological density perturbations.

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

Dumitru, Adrian; Skokov, Vladimir

The conventional and linearly polarized Weizsäcker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity Y ~ 1/αs. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function g2trmore » A+(q)A+(-q). For transverse momenta on the order of the saturation scale we observe large variations across configurations (evolution trajectories) of the linearly polarized distribution up to several times its average, and even to negative values.« less

Importance of Resolving the Spectral Support of Beam-plasma Instabilities in Simulations

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

Shalaby, Mohamad; Broderick, Avery E.; Chang, Philip

2017-10-20

Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the spectral support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable to the maximum growth rate occupy a narrow range of wavenumbers. This places stringent requirements on the box-sizes when simulating the evolution of the instabilities. We identify the implied lower limits on the box size imposed by the longitudinal beam plasma instability, i.e., typically the most stringent condition required to correctly capture the linear evolution of the instabilities in multidimensional simulations. We find that sizes many orders ofmore » magnitude larger than the resonant wavelength are typically required. Using one-dimensional particle-in-cell simulations, we show that the failure to sufficiently resolve the spectral support of the longitudinal instability yields slower growth and lower levels of saturation, potentially leading to erroneous physical conclusion.« less

Monotonic entropy growth for a nonlinear model of random exchanges

NASA Astrophysics Data System (ADS)

Apenko, S. M.

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific “coarse graining” of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

A Kalman filter for a two-dimensional shallow-water model

NASA Technical Reports Server (NTRS)

Parrish, D. F.; Cohn, S. E.

1985-01-01

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Operation of a high impedance applied-B extraction ion diode on the SABRE positive polarity linear induction accelerator

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

Hanson, D.L.; Cuneo, M.E.; McKay, P.F.

We present results from initial experiments with a high impedance applied-B extraction diode on the SABRE ten stage linear induction accelerator (6.7 MV, 300 kA). We have demonstrated efficient coupling of power from the accelerator through an extended MITL (Magnetically Insulated Transmission Line) into a high intensity ion beam. Both MITL electron flow in the diode region and ion diode behavior, including ion source turn-on, virtual cathode formation and evolution, enhancement delay, and ion coupling efficiency, are strongly influenced by the geometry of the diode insulating magnetic field. For our present diode electrode geometry, electrons from the diode feed stronglymore » influence the evolution of the virtual cathode. Both experimental data and particle-in-cell numerical simulations show that uniform insulation of these feed electrons is required for uniform ion emission and efficient diode operation.« less

Growth Evolution and Characterization of PLD Zn(Mg)O Nanowire Arrays

NASA Astrophysics Data System (ADS)

Rahm, Andreas; Nobis, Thomas; Lorenz, Michael; Zimmermann, Gregor; Boukos, Nikos; Travlos, Anastasios; Grundmann, Marius

ZnO and Zn0.98Mg0.02O nanowires have been grown by high-pressure pulsed laser deposition on sapphire substrates covered with gold colloidal particles as nucleation sites. We present a detailed study of the nanowire size and length distribution and of the growth evolution. We find that the aspect ratio varies linearly with deposition time. The linearity coefficient is independent of the catalytic gold particle size and lateral nanowire density. The superior structural quality of the whiskers is proven by X-ray diffraction and transmission electron microscopy. The defect-free ZnO nanowires exhibit a FWHM(2θ-ω) of the ZnO(0002) reflection of 22 arcsec. We show (0-11) step habit planes on the side faces of the nanowires that are a few atomic steps in height. The microscopic homogeneity of the optical properties is confirmed by temperature-dependent cathodoluminescence.

Darboux theorems and Wronskian formulas for integrable systems I. Constrained KP flows

NASA Astrophysics Data System (ADS)

Oevel, W.

1993-05-01

Generalizations of the classical Darboux theorem are established for pseudo-differential scattering operators of the form L = limit∑i=0N u i∂ i + limitΣi=1m Φ i∂ -1limitΨi†i. Iteration of the Darboux transformations leads to a gauge transformed operator with coefficients given by Wronskian formulas involving a set of eigenfunctions of L. Nonlinear integrable partial differential equations are associated with the scattering operator L which arise as a symmetry reduction of the multicomponent KP hierarchy. With a suitable linear time evolution for the eigenfunctions the Darboux transformation is used to obtain solutions of the integrable equations in terms of Wronskian determinants.

Dynamics of bright-bright solitons in Bose-Einstein condensate with Raman-induced one-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun

2018-03-01

We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.

Exact solution of a ratchet with switching sawtooth potential

NASA Astrophysics Data System (ADS)

Saakian, David B.; Klümper, Andreas

2018-01-01

We consider the flashing potential ratchet model with general asymmetric potential. Using Bloch functions, we derive equations which allow for the calculation of both the ratchet's flux and higher moments of distribution for rather general potentials. We indicate how to derive the optimal transition rates for maximal velocity of the ratchet. We calculate explicitly the exact velocity of a ratchet with simple sawtooth potential from the solution of a system of 8 linear algebraic equations. Using Bloch functions, we derive the equations for the ratchet with potentials changing periodically with time. We also consider the case of the ratchet with evolution with two different potentials acting for some random periods of time.

The Sensitivity of Earth's Climate History To Changes In The Rates of Biological And Geological Evolution

NASA Astrophysics Data System (ADS)

Waltham, D.

2014-12-01

The faint young Sun paradox (early Earth had surface liquid water despite solar luminosity 70% of the modern value) implies that our planet's albedo has increased through time and/or greenhouse warming has fallen. The obvious explanation is that negative feedback processes stabilized temperatures. However, the limited temperature data available does not exhibit the expected residual temperature rise and, at least for the Phanerozoic, estimates of climate sensitivity exceed the Planck sensitivity (the zero net-feedback value). The alternate explanation is that biological and geological evolution have tended to cool Earth through time hence countering solar-driven warming. The coincidence that Earth-evolution has roughly cancelled Solar-evolution can then be explained as an emergent property of a complex system (the Gaia hypothesis) or the result of the unavoidable observational bias that Earth's climate history must be compatible with our existence (the anthropic principle). Here, I use a simple climate model to investigate the sensitivity of Earth's climate to changes in the rate of Earth-evolution. Earth-evolution is represented by an effective emissivity which has an intrinsic variation through time (due to continental growth, the evolution of cyanobacteria, orbital fluctuations etc) plus a linear feedback term which enhances emissivity variations. An important feature of this model is a predicted maximum in the radiated-flux versus temperature function. If the increasing solar flux through time had exceeded this value then runaway warming would have occurred. For the best-guess temperature history and climate sensitivity, the Earth has always been within a few percent of this maximum. There is no obvious Gaian explanation for this flux-coincidence but the anthropic principle naturally explains it: If the rate of biological/geological evolution is naturally slow then Earth is a fortunate outlier which evolved just fast enough to avoid solar-induced over-heating. However, there are large uncertainties concerning the temperature history of our planet and concerning climate sensitivity in the Archean and Proterozoic. When these are included, the solar-flux through time might have been as little as 70-90 % of the maximum thus reducing the significance of the flux-coincidence.

Discovery of a complex linearly polarized spectrum of Betelgeuse dominated by depolarization of the continuum

NASA Astrophysics Data System (ADS)

Aurière, M.; López Ariste, A.; Mathias, P.; Lèbre, A.; Josselin, E.; Montargès, M.; Petit, P.; Chiavassa, A.; Paletou, F.; Fabas, N.; Konstantinova-Antova, R.; Donati, J.-F.; Grunhut, J. H.; Wade, G. A.; Herpin, F.; Kervella, P.; Perrin, G.; Tessore, B.

2016-06-01

Context. Betelgeuse is an M supergiant that harbors spots and giant granules at its surface and presents linear polarization of its continuum. Aims: We have previously discovered linear polarization signatures associated with individual lines in the spectra of cool and evolved stars. Here, we investigate whether a similar linearly polarized spectrum exists for Betelgeuse. Methods: We used the spectropolarimeter Narval, combining multiple polarimetric sequences to obtain high signal-to-noise ratio spectra of individual lines, as well as the least-squares deconvolution (LSD) approach, to investigate the presence of an averaged linearly polarized profile for the photospheric lines. Results: We have discovered the existence of a linearly polarized spectrum for Betelgeuse, detecting a rather strong signal (at a few times 10-4 of the continuum intensity level), both in individual lines and in the LSD profiles. Studying its properties and the signal observed for the resonant Na I D lines, we conclude that we are mainly observing depolarization of the continuum by the absorption lines. The linear polarization of the Betelgeuse continuum is due to the anisotropy of the radiation field induced by brightness spots at the surface and Rayleigh scattering in the atmosphere. We have developed a geometrical model to interpret the observed polarization, from which we infer the presence of two brightness spots and their positions on the surface of Betelgeuse. We show that applying the model to each velocity bin along the Stokes Q and U profiles allows the derivation of a map of the bright spots. We use the Narval linear polarization observations of Betelgeuse obtained over a period of 1.4 yr to study the evolution of the spots and of the atmosphere. Conclusions: Our study of the linearly polarized spectrum of Betelgeuse provides a novel method for studying the evolution of brightness spots at its surface and complements quasi-simultaneous observations obtained with PIONIER at the VLTI. Based on observations obtained at the Télescope Bernard Lyot (TBL) at Observatoire du Pic du Midi, CNRS/INSU and Université de Toulouse, France.

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

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

Yang, Chao-Chin; Johansen, Anders, E-mail: ccyang@astro.lu.se, E-mail: anders@astro.lu.se

2016-06-01

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct,more » we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.« less

Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach

NASA Astrophysics Data System (ADS)

Rubín de Celis, Emilio; Tomasini, Cecilia; Simeone, Claudio

Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

Aging-related changes in respiratory system mechanics and morphometry in mice.

PubMed

Elliott, Jonathan E; Mantilla, Carlos B; Pabelick, Christina M; Roden, Anja C; Sieck, Gary C

2016-07-01

Previous work investigating respiratory system mechanics in mice has reported an aging-related increase in compliance and mean linear intercept (Lm). However, these changes were assessed using only a young (2-mo-old) and old (20- and 26-mo-old) group yet were interpreted to reflect a linear evolution across the life span. Therefore, to investigate respiratory system mechanics and lung morphometry across a more complete spectrum of ages, we utilized 2 (100% survival, n = 6)-, 6 (100% survival, n = 12)-, 18 (90% survival, n = 12)-, 24 (75% survival, n = 12)-, and 30 (25% survival, n = 12)-mo-old C57BL/6 mice. We found a nonlinear aging-related decrease in respiratory system resistance and increase in dynamic compliance and hysteresis between 2- and 24-mo-old mice. However, in 30-mo-old mice, respiratory system resistance increased, and dynamic compliance and hysteresis decreased relative to 24-mo-old mice. Respiratory system impedance spectra were measured between 1-20.5 Hz at positive end-expiratory pressures (PEEP) of 1, 3, 5, and 7 cmH2O. Respiratory system resistance and reactance at each level of PEEP were increased and decreased, respectively, only in 2-mo-old animals. No differences in the respiratory system impedance spectra were observed in 6-, 18-, 24-, and 30-mo-old mice. Additionally, lungs were fixed following tracheal instillation of 4% paraformaldehyde at 25 cmH2O and processed for Lm and airway collagen deposition. There was an aging-related increase in Lm consistent with emphysematous-like changes and no evidence of increased airway collagen deposition. Accordingly, we demonstrate nonlinear aging-related changes in lung mechanics and morphometry in C57BL/6 mice. Copyright © 2016 the American Physiological Society.

Initial conditions for accurate N-body simulations of massive neutrino cosmologies

NASA Astrophysics Data System (ADS)

Zennaro, M.; Bel, J.; Villaescusa-Navarro, F.; Carbone, C.; Sefusatti, E.; Guzzo, L.

2017-04-01

The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the simulation. The implementation of this practical solution requires more care in the context of massive neutrino cosmologies, mainly because of the non-trivial scale-dependence of the linear growth that characterizes these models. In this work, we consider a simple two-fluid, Newtonian approximation for cold dark matter and massive neutrinos perturbations that can reproduce the cold matter linear evolution predicted by Boltzmann codes such as CAMB or CLASS with a 0.1 per cent accuracy or below for all redshift relevant to non-linear structure formation. We use this description, in the first place, to quantify the systematic errors induced by several approximations often assumed in numerical simulations, including the typical set-up of the initial conditions for massive neutrino cosmologies adopted in previous works. We then take advantage of the flexibility of this approach to rescale the late-time linear power spectra to the simulation initial redshift, in order to be as consistent as possible with the dynamics of the N-body code and the approximations it assumes. We implement our method in a public code (REPS rescaled power spectra for initial conditions with massive neutrinos https://github.com/matteozennaro/reps) providing the initial displacements and velocities for cold dark matter and neutrino particles that will allow accurate, I.e. 1 per cent level, numerical simulations for this cosmological scenario.

Appraisal of jump distributions in ensemble-based sampling algorithms

NASA Astrophysics Data System (ADS)

Dejanic, Sanda; Scheidegger, Andreas; Rieckermann, Jörg; Albert, Carlo

2017-04-01

Sampling Bayesian posteriors of model parameters is often required for making model-based probabilistic predictions. For complex environmental models, standard Monte Carlo Markov Chain (MCMC) methods are often infeasible because they require too many sequential model runs. Therefore, we focused on ensemble methods that use many Markov chains in parallel, since they can be run on modern cluster architectures. Little is known about how to choose the best performing sampler, for a given application. A poor choice can lead to an inappropriate representation of posterior knowledge. We assessed two different jump moves, the stretch and the differential evolution move, underlying, respectively, the software packages EMCEE and DREAM, which are popular in different scientific communities. For the assessment, we used analytical posteriors with features as they often occur in real posteriors, namely high dimensionality, strong non-linear correlations or multimodality. For posteriors with non-linear features, standard convergence diagnostics based on sample means can be insufficient. Therefore, we resorted to an entropy-based convergence measure. We assessed the samplers by means of their convergence speed, robustness and effective sample sizes. For posteriors with strongly non-linear features, we found that the stretch move outperforms the differential evolution move, w.r.t. all three aspects.

Self-induced temporal instability from a neutrino antenna

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

Capozzi, Francesco; INFN - Sezione di Padova,Via Marzolo 8, 35131 Padova; Dasgupta, Basudeb

2016-04-21

It has been recently shown that the flavor composition of a self-interacting neutrino gas can spontaneously acquire a time-dependent pulsating component during its flavor evolution. In this work, we perform a more detailed study of this effect in a model where neutrinos are assumed to be emitted in a two-dimensional plane from an infinite line that acts as a neutrino antenna. We consider several examples with varying matter and neutrino densities and find that temporal instabilities with various frequencies are excited in a cascade. We compare the numerical calculations of the flavor evolution with the predictions of linearized stability analysismore » of the equations of motion. The results obtained with these two approaches are in good agreement in the linear regime, while a dramatic speed-up of the flavor conversions occurs in the non-linear regime due to the interactions among the different pulsating modes. We show that large flavor conversions can take place if some of the temporal modes are unstable for long enough, and that this can happen even if the matter and neutrino densities are changing, as long as they vary slowly.« less

Quantifying Melt Ponds in the Beaufort MIZ using Linear Support Vector Machines from High Resolution Panchromatic Images

NASA Astrophysics Data System (ADS)

Ortiz, M.; Graber, H. C.; Wilkinson, J.; Nyman, L. M.; Lund, B.

2017-12-01

Much work has been done on determining changes in summer ice albedo and morphological properties of melt ponds such as depth, shape and distribution using in-situ measurements and satellite-based sensors. Although these studies have dedicated much pioneering work in this area, there still lacks sufficient spatial and temporal scales. We present a prototype algorithm using Linear Support Vector Machines (LSVMs) designed to quantify the evolution of melt pond fraction from a recently government-declassified high-resolution panchromatic optical dataset. The study area of interest lies within the Beaufort marginal ice zone (MIZ), where several in-situ instruments were deployed by the British Antarctic Survey in joint with the MIZ Program, from April-September, 2014. The LSVM uses four dimensional feature data from the intensity image itself, and from various textures calculated from a modified first-order histogram technique using probability density of occurrences. We explore both the temporal evolution of melt ponds and spatial statistics such as pond fraction, pond area, and number pond density, to name a few. We also introduce a linear regression model that can potentially be used to estimate average pond area by ingesting several melt pond statistics and shape parameters.

Measurement and potential barrier evolution analysis of cold field emission in fracture fabricated Si nanogap

NASA Astrophysics Data System (ADS)

Banerjee, Amit; Hirai, Yoshikazu; Tsuchiya, Toshiyuki; Tabata, Osamu

2017-06-01

Cold field emission characteristics of a fracture fabricated Si nanogap (˜100 nm) were investigated with an ascending electric field (voltage) sweep. The nanogap was formed by controlled fracture of a free-standing silicon micro-beam along <111> direction by a microelectromechanical device, which results in flat, smooth, and conformal electrode pairs. This facilitates simultaneous large area emission, which gives rise to a significant current at low bias voltage, which usually remains indiscernible in nanogaps of this size. The measured emission current-voltage (I-V) characteristics clearly depict two distinct regimes: a linear (I ∝ V) regime at low bias voltage and a nonlinear [ln(I/V 2) ∝ V -1] regime at high bias voltage, separated by a transition point. We propose that the linear regime is owed to direct tunneling of electrons, whereas the nonlinear regime is due to Fowler-Nordheim type emission. This proposition essentially implies that the tunneling potential barrier gradually evolved from a rectangular shape to a triangular shape with increasing field (V). This type of evolution is usually observed in molecular size gaps. We have attempted to correlate the I-V curves acquired through the experiments with the electric field induced barrier shape evolution by numerical calculations involving standard quantum mechanics. The observed linear regime at low bias voltage (<5 V) in a relatively large size gap (˜100 nm) is attributed to the fabrication method adopted in this study. The reported study and the fabricated device are significant for developing a futuristic thermotunneling refrigerator that will find a wide range of application in nanoelectronic devices.

Dynamical emergence of Markovianity in local time scheme.

PubMed

Jeknić-Dugić, J; Arsenijević, M; Dugić, M

2016-06-01

Recently we pointed out the so-called local time scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper, we introduce and analyse in depth a rather non-standard dynamical map that is imposed by the scheme. On the one hand, the map does not allow for introducing a properly defined generator of the evolution nor does it represent a quantum channel. On the other hand, the map is linear, positive, trace preserving and unital as well as completely positive, but is not divisible and therefore non-Markovian. Nevertheless, we provide quantitative criteria for dynamical emergence of time-coarse-grained Markovianity, for exact dynamics of an open system, as well as for operationally defined approximation of a closed or open many-particle system. A closed system never reaches a steady state, whereas an open system may reach a unique steady state given by the Lüders-von Neumann formula; where the smaller the open system, the faster a steady state is attained. These generic findings extend the standard open quantum systems theory and substantially tackle certain cosmological issues.

Squiggles in Hellas Planitia

NASA Image and Video Library

2017-10-25

At around 2,200 kilometers in diameter, Hellas Planitia is the largest visible impact basin in the Solar System, and hosts the lowest elevations on Mars' surface as well as a variety of landscapes. This image from NASA's Mars Reconnaisance Orbiter (MRO) covers a small central portion of the basin and shows a dune field with lots of dust devil trails. In the middle, we see what appears to be long and straight "scratch marks" running down the southeast (bottom-right) facing dune slopes. If we look closer, we can see these scratch marks actually squiggle back and forth on their way down the dune. These scratch marks are linear gullies. Just like on Earth, high-latitude regions on Mars are covered with frost in the winter. However, the winter frost on Mars is made of carbon dioxide ice (dry ice) instead of water ice. We believe linear gullies are the result of this dry ice breaking apart into blocks, which then slide or roll down warmer sandy slopes, sublimating and carving as they go. The linear gullies exhibit exceptional sinuosity (the squiggle pattern) and we believe this to be the result of repeated movement of dry ice blocks in the same path, possibly in combination with different hardness or flow resistance of the sand within the dune slopes. Determining the specific process that causes the formation and evolution of sinuosity in linear gullies is a question scientists are still trying to answer. What do you think causes the squiggles? https://photojournal.jpl.nasa.gov/catalog/PIA22052

Mineralization of Surfactants by the Microbiota of Submerged Plant Detritus

PubMed Central

Federle, Thomas W.; Ventullo, Roy M.

1990-01-01

In wetlands and canopied bodies of water, plant detritus is an important source of carbon and energy. Detrital materials possess a large surface area for sorption of dissolved organics and are colonized by a large and diverse microbiota. To examine the biodegradation of surfactants by these microorganisms, submerged oak leaves were obtained from a laundromat wastewater pond, its overflow, and a pristine control pond. Leaves were cut into disks and incubated in sterile water amended with 50 μg of 14C-labeled linear alkylbenzene sulfonate (LAS), linear alcohol ethoxylate, stearyltrimethyl ammonium chloride, distearyldimethyl ammonium chloride, benzoic acid, or mixed amino acids per liter. Sorption of the test compounds to the detritus and evolution of 14CO2 were followed with time. All of the compounds sorbed to the detritus to various degrees, with LAS and stearyltrimethyl ammonium chloride the most sorptive and benzoic acid the least. All compounds were mineralized without a lag. With leaves from the laundromat wastewater pond, half-lives were 12.6 days for LAS, 8.4 days for linear alcohol ethoxylate, 14.2 days for stearyltrimethyl ammonium chloride, 1.0 days for benzoic acid, and 2.7 days for mixed amino acids. Mineralization of LAS and linear alcohol ethoxylate by control pond leaves was slower and exhibited an S-shaped rather than a typical first-order pattern. This study shows that detritus represents a significant site of surfactant removal in detritus-rich systems. Images PMID:16348111

Ultrafast Non-thermal Response of Plasmonic Resonance in Gold Nanoantennas

NASA Astrophysics Data System (ADS)

Soavi, Giancarlo; Valle, Giuseppe Della; Biagioni, Paolo; Cattoni, Andrea; Longhi, Stefano; Cerullo, Giulio; Brida, Daniele

Ultrafast thermalization of electrons in metal nanostructures is studied by means of pump-probe spectroscopy. We track in real-time the plasmon resonance evolution, providing a tool for understanding and controlling gold nanoantennas non-linear optical response.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Microstructure and Solidification Crack Susceptibility of Al 6014 Molten Alloy Subjected to a Spatially Oscillated Laser Beam.

PubMed

Kang, Minjung; Han, Heung Nam; Kim, Cheolhee

2018-04-23

Oscillating laser beam welding for Al 6014 alloy was performed using a single mode fiber laser and two-axis scanner system. Its effect on the microstructural evolution of the fusion zone was investigated. To evaluate the influence of oscillation parameters, self-restraint test specimens were fabricated with different beam patterns, widths, and frequencies. The behavior of hot cracking propagation was analyzed by high-speed camera and electron backscatter diffraction. The behavior of crack propagation was observed to be highly correlated with the microstructural evolution of the fusion zone. For most oscillation conditions, the microstructure resembled that of linear welds. A columnar structure was formed near the fusion line and an equiaxed structure was generated at its center. The wide equiaxed zone of oscillation welding increased solidification crack susceptibility. For an oscillation with an infinite-shaped scanning pattern at 100 Hz and 3.5 m/min welding speed, the bead width, solidification microstructure, and the width of the equiaxed zone at the center of fusion fluctuated. Furthermore, the equiaxed and columnar regions alternated periodically, which could reduce solidification cracking susceptibility.

Electrical Stressing Induced Monolayer Vacancy Island Growth on TiSe2

NASA Astrophysics Data System (ADS)

Zheng, Husong; Valtierra, Salvador; Ofori-Opoku, Nana; Chen, Chuanhui; Sun, Lifei; Yuan, Shuaishuai; Jiao, Liying; Bevan, Kirk H.; Tao, Chenggang

2018-03-01

To ensure the practical application of atomically thin transition metal dichalcogenides, it is essential to characterize their structural stability under external stimuli such as electric fields and currents. Using vacancy monolayer islands on TiSe2 surfaces as a model system, for the first time we have observed a shape evolution and growth from triangular to hexagonal driven by scanning tunneling microscopy (STM) electrical stressing. The size of islands shows linear growth with a rate of (3.00 +- 0.05) x 10-3 nm/s, when the STM scanning parameters are held fixed at Vs = 1.0 V and I = 1.8 nA. We further quantified how the growth rate is related to the tunneling current magnitude. Our simulations of monolayer island evolution using phase-field modeling are in good agreement with our experimental observations, and point towards preferential edge atom dissociation under STM scanning driving the observed growth. The results could be potentially important for device applications of ultrathin transition metal dichalcogenides and related 2D materials subject to electrical stressing under device operating conditions.

Microstructure and Solidification Crack Susceptibility of Al 6014 Molten Alloy Subjected to a Spatially Oscillated Laser Beam

PubMed Central

Kang, Minjung; Han, Heung Nam

2018-01-01

Oscillating laser beam welding for Al 6014 alloy was performed using a single mode fiber laser and two-axis scanner system. Its effect on the microstructural evolution of the fusion zone was investigated. To evaluate the influence of oscillation parameters, self-restraint test specimens were fabricated with different beam patterns, widths, and frequencies. The behavior of hot cracking propagation was analyzed by high-speed camera and electron backscatter diffraction. The behavior of crack propagation was observed to be highly correlated with the microstructural evolution of the fusion zone. For most oscillation conditions, the microstructure resembled that of linear welds. A columnar structure was formed near the fusion line and an equiaxed structure was generated at its center. The wide equiaxed zone of oscillation welding increased solidification crack susceptibility. For an oscillation with an infinite-shaped scanning pattern at 100 Hz and 3.5 m/min welding speed, the bead width, solidification microstructure, and the width of the equiaxed zone at the center of fusion fluctuated. Furthermore, the equiaxed and columnar regions alternated periodically, which could reduce solidification cracking susceptibility. PMID:29690630

Evolution of Associative Learning in Chemical Networks

PubMed Central

McGregor, Simon; Vasas, Vera; Husbands, Phil; Fernando, Chrisantha

2012-01-01

Organisms that can learn about their environment and modify their behaviour appropriately during their lifetime are more likely to survive and reproduce than organisms that do not. While associative learning – the ability to detect correlated features of the environment – has been studied extensively in nervous systems, where the underlying mechanisms are reasonably well understood, mechanisms within single cells that could allow associative learning have received little attention. Here, using in silico evolution of chemical networks, we show that there exists a diversity of remarkably simple and plausible chemical solutions to the associative learning problem, the simplest of which uses only one core chemical reaction. We then asked to what extent a linear combination of chemical concentrations in the network could approximate the ideal Bayesian posterior of an environment given the stimulus history so far? This Bayesian analysis revealed the ‘memory traces’ of the chemical network. The implication of this paper is that there is little reason to believe that a lack of suitable phenotypic variation would prevent associative learning from evolving in cell signalling, metabolic, gene regulatory, or a mixture of these networks in cells. PMID:23133353

Modeling of yield surface evolution in uniaxial and biaxial loading conditions using a prestrained large scale specimen

NASA Astrophysics Data System (ADS)

Zaman, Shakil Bin; Barlat, Frédéric; Kim, Jin Hwan

2018-05-01

Large-scale advanced high strength steel (AHSS) sheet specimens were deformed in uniaxial tension, using a novel grip system mounted on a MTS universal tension machine. After pre-strain, they were used as a pre-strained material to examine the anisotropic response in the biaxial tension tests with various load ratios, and orthogonal tension tests at 45° and 90° from the pre-strain axis. The flow curve and the instantaneous r-value of the pre-strained steel in each of the aforementioned uniaxial testing conditions were also measured and compared with those of the undeformed steel. Furthermore, an exhaustive analysis of the yield surface was also conducted and the results, prior and post-prestrain were represented and compared. The homogeneous anisotropic hardening (HAH) model [1] was employed to predict the behavior of the pre-strained material. It was found that the HAH-predicted flow curves after non-linear strain path change and the yield loci after uniaxial pre-strain were in good agreement with the experiments, while the r-value evolution after strain path change was qualitatively well predicted.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Numerical calculations of spectral turnover and synchrotron self-absorption in CSS and GPS radio sources

NASA Astrophysics Data System (ADS)

Jeyakumar, S.

2016-06-01

The dependence of the turnover frequency on the linear size is presented for a sample of Giga-hertz Peaked Spectrum and Compact Steep Spectrum radio sources derived from complete samples. The dependence of the luminosity of the emission at the peak frequency with the linear size and the peak frequency is also presented for the galaxies in the sample. The luminosity of the smaller sources evolve strongly with the linear size. Optical depth effects have been included to the 3D model for the radio source of Kaiser to study the spectral turnover. Using this model, the observed trend can be explained by synchrotron self-absorption. The observed trend in the peak-frequency-linear-size plane is not affected by the luminosity evolution of the sources.

The Impact of Frictional Healing on Stick-Slip Recurrence Interval and Stress Drop: Implications for Earthquake Scaling

NASA Astrophysics Data System (ADS)

Im, Kyungjae; Elsworth, Derek; Marone, Chris; Leeman, John

2017-12-01

Interseismic frictional healing is an essential process in the seismic cycle. Observations of both natural and laboratory earthquakes demonstrate that the magnitude of stress drop scales with the logarithm of recurrence time, which is a cornerstone of the rate and state friction (RSF) laws. However, the origin of this log linear behavior and short time "cutoff" for small recurrence intervals remains poorly understood. Here we use RSF laws to demonstrate that the back-projected time of null-healing intrinsically scales with the initial frictional state θi. We explore this behavior and its implications for (1) the short-term cutoff time of frictional healing and (2) the connection between healing rates derived from stick-slip sliding versus slide-hold-slide tests. We use a novel, continuous solution of RSF for a one-dimensional spring-slider system with inertia. The numerical solution continuously traces frictional state evolution (and healing) and shows that stick-slip cutoff time also scales with frictional state at the conclusion of the dynamic slip process θi (=Dc/Vpeak). This numerical investigation on the origins of stick-slip response is verified by comparing laboratory data for a range of peak slip velocities. Slower slip motions yield lesser magnitude of friction drop at a given time due to higher frictional state at the end of each slip event. Our results provide insight on the origin of log linear stick-slip evolution and suggest an approach to estimating the critical slip distance on faults that exhibit gradual accelerations, such as for slow earthquakes.

Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy

DOE PAGES

Dumitru, Adrian; Lappi, Tuomas; Skokov, Vladimir

2015-12-17

In this study, we determine the distribution of linearly polarized gluons of a dense target at small x by solving the Balitsky–Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner rapidity evolution equations. From these solutions, we estimate the amplitude of cos2Φ azimuthal asymmetries in deep inelastic scattering dijet production at high energies. We find sizable long-range in rapidity azimuthal asymmetries with a magnitude in the range of v 2=~10%.

The High Temperature Resistivity of Ba2YCu3O7-x

NASA Astrophysics Data System (ADS)

Xingkui, Zhang; Shining, Zhu; Hao, Wang; Shiyuan, Zhang; Su, Ye; Ningshen, Zhou; Ziran, Xu

The high temperature resistivity (ρ), thermogravimetry (TG) and derivative thermogravimetry (DTG) have been used to characterize superconductor Ba2YCu3O7-x (BYCO) in O2, air and N2. The resistivity is linear from room temperature to 350°C and then deviate from linearity with oxygen evolution, the derivative of resistivity dρ/dT increases abruptly near orthorhombic to tetragonal phase transition. These phenomena can give good explanations for a two-band Drude model.

Natural approach to quantum dissipation

NASA Astrophysics Data System (ADS)

Taj, David; Öttinger, Hans Christian

2015-12-01

The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.

Fundamental Principles of Classical Mechanics: a Geometrical Perspectives

NASA Astrophysics Data System (ADS)

Lam, Kai S.

2014-07-01

Classical mechanics is the quantitative study of the laws of motion for oscopic physical systems with mass. The fundamental laws of this subject, known as Newton's Laws of Motion, are expressed in terms of second-order differential equations governing the time evolution of vectors in a so-called configuration space of a system (see Chapter 12). In an elementary setting, these are usually vectors in 3-dimensional Euclidean space, such as position vectors of point particles; but typically they can be vectors in higher dimensional and more abstract spaces. A general knowledge of the mathematical properties of vectors, not only in their most intuitive incarnations as directed arrows in physical space but as elements of abstract linear vector spaces, and those of linear operators (transformations) on vector spaces as well, is then indispensable in laying the groundwork for both the physical and the more advanced mathematical - more precisely topological and geometrical - concepts that will prove to be vital in our subject. In this beginning chapter we will review these properties, and introduce the all-important related notions of dual spaces and tensor products of vector spaces. The notational convention for vectorial and tensorial indices used for the rest of this book (except when otherwise specified) will also be established...

Developmental Pathways of Psammotermes hybostoma (Isoptera: Rhinotermitidae): Old Pseudergates Make up a New Sterile Caste

PubMed Central

Bourguignon, Thomas; Šobotník, Jan; Sillam-Dussès, David; Jiroš, Pavel; Hanus, Robert; Roisin, Yves; Miura, Toru

2012-01-01

Background Ergonomic efficiency is in termites maximized by task partitioning among specialized castes. The isopteran caste systems can be classified as either (i) linear, when tasks are performed by pluripotent immatures (pseudergates), retaining the ability to develop into winged imagoes or (ii) bifurcated, with the presence of a true worker caste, which diverges early and permanently from the sexual (nymph/alate) line. Principal Findings Here, we report on the ontogenetic potentialities of the highly polymorphic sand termite Psammotermes hybostoma. Beside numerous pluripotent pseudergates, constituting the main work force, some larger non-feeding apterous immatures, also occur. These individuals are unable to proceed to the winged imago stage, but store large amounts of fat and also give rise to large soldiers. Soldiers therefore originate from a wide range of apterous instars, consequently being highly polymorphic. Conclusions The caste system of P. hybostoma is essentially linear, as in other basal Rhinotermitidae, but is distinguished by the late bifurcation leading to large apterous immatures. Because these large worker-like individuals deviate late and do not perform worker tasks, they cannot be considered homologous to the true workers of Termitidae and advanced Rhinotermitidae, but they provide a novel example of the evolution of sterile immatures in termites. PMID:23028554

Quantitative analysis of lead in aqueous solutions by ultrasonic nebulizer assisted laser induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Zhong, Shi-Lei; Lu, Yuan; Kong, Wei-Jin; Cheng, Kai; Zheng, Ronger

2016-08-01

In this study, an ultrasonic nebulizer unit was established to improve the quantitative analysis ability of laser-induced breakdown spectroscopy (LIBS) for liquid samples detection, using solutions of the heavy metal element Pb as an example. An analytical procedure was designed to guarantee the stability and repeatability of the LIBS signal. A series of experiments were carried out strictly according to the procedure. The experimental parameters were optimized based on studies of the pulse energy influence and temporal evolution of the emission features. The plasma temperature and electron density were calculated to confirm the LTE state of the plasma. Normalizing the intensities by background was demonstrated to be an appropriate method in this work. The linear range of this system for Pb analysis was confirmed over a concentration range of 0-4,150ppm by measuring 12 samples with different concentrations. The correlation coefficient of the fitted calibration curve was as high as 99.94% in the linear range, and the LOD of Pb was confirmed as 2.93ppm. Concentration prediction experiments were performed on a further six samples. The excellent quantitative ability of the system was demonstrated by comparison of the real and predicted concentrations of the samples. The lowest relative error was 0.043% and the highest was no more than 7.1%.

SKYWARD: the next generation airborne infrared search and track

NASA Astrophysics Data System (ADS)

Fortunato, L.; Colombi, G.; Ondini, A.; Quaranta, C.; Giunti, C.; Sozzi, B.; Balzarotti, G.

2016-05-01

Infrared Search and Track systems are an essential element of the modern and future combat aircrafts. Passive automatic search, detection and tracking functions, are key points for silent operations or jammed tactical scenarios. SKYWARD represents the latest evolution of IRST technology in which high quality electro-optical components, advanced algorithms, efficient hardware and software solutions are harmonically integrated to provide high-end affordable performances. Additionally, the reduction of critical opto-mechanical elements optimises weight and volume and increases the overall reliability. Multiple operative modes dedicated to different situations are available; many options can be selected among multiple or single target tracking, for surveillance or engagement, and imaging, for landing or navigation aid, assuring the maximum system flexibility. The high quality 2D-IR sensor is exploited by multiple parallel processing chains, based on linear and non-linear techniques, to extract the possible targets from background, in different conditions, with false alarm rate control. A widely tested track processor manages a large amount of candidate targets simultaneously and allows discriminating real targets from noise whilst operating with low target to background contrasts. The capability of providing reliable passive range estimation is an additional qualifying element of the system. Particular care has been dedicated to the detector non-uniformities, a possible limiting factor for distant targets detection, as well as to the design of the electro-optics for a harsh airborne environment. The system can be configured for LWIR or MWIR waveband according to the customer operational requirements. An embedded data recorder saves all the necessary images and data for mission debriefing, particularly useful during inflight system integration and tuning.

A Thermodynamic Approach to Soil-Plant-Atmosphere Modeling: From Metabolic Biochemical Processes to Water-Carbon-Nitrogen Balance

NASA Astrophysics Data System (ADS)

Clavijo, H. W.

2016-12-01

Modeling the soil-plant-atmosphere continuum has been central part of understanding interrelationships among biogeochemical and hydrological processes. Theory behind of couplings Land Surface Models (LSM) and Dynamical Global Vegetation Models (DGVM) are based on physical and physiological processes connected by input-output interactions mainly. This modeling framework could be improved by the application of non-equilibrium thermodynamic basis that could encompass the majority of biophysical processes in a standard fashion. This study presents an alternative model for plant-water-atmosphere based on energy-mass thermodynamics. The system of dynamic equations derived is based on the total entropy, the total energy balance for the plant, the biomass dynamics at metabolic level and the water-carbon-nitrogen fluxes and balances. One advantage of this formulation is the capability to describe adaptation and evolution of dynamics of plant as a bio-system coupled to the environment. Second, it opens a window for applications on specific conditions from individual plant scale, to watershed scale, to global scale. Third, it enhances the possibility of analyzing anthropogenic impacts on the system, benefiting from the mathematical formulation and its non-linearity. This non-linear model formulation is analyzed under the concepts of qualitative system dynamics theory, for different state-space phase portraits. The attractors and sources are pointed out with its stability analysis. Possibility of bifurcations are explored and reported. Simulations for the system dynamics under different conditions are presented. These results show strong consistency and applicability that validates the use of the non-equilibrium thermodynamic theory.

Observation of CO2 in Comet C/2012 K5 LINEAR

NASA Astrophysics Data System (ADS)

McKay, Adam; Kelley, Michael; DiSanti, Michael; Chanover, Nancy

2012-12-01

The study of cometary composition is important to understanding the formation and evolution of our solar system. Comets have undergone very little thermal evolution in their lifetimes, which results in their near pristine composition. The nucleus of a comet is very rarely detected directly. Instead, we observe the coma that surrounds the nucleus. Physical and chemical processes in the coma affect its composition, and therefore coma composition is not a direct representation of nuclear composition. An important trend is the observed variation of coma composition with heliocentric distance, most likely influenced by the volatility of the main surface ices, H2O, CO2, and CO. Infrared studies of these molecules are complicated by telluric features, so often daughter molecules of these species such as OH are observed instead. A potentially effective tracer for these primary ices is atomic oxygen in the coma. However, the relationship between these ices and atomic oxygen is only understood at a qualitative level. We propose to use Spitzer observations in IRAC's 4.5 micron band pass to observe the CO2 v3 band at 4.26 microns in comet C/2012 K5 LINEAR. These observations will be coordinated with observations of atomic oxygen obtained at Apache Point Observatory and observations of H2O at Keck. These near simultaneous observations of H2O, CO2, and atomic oxygen in a cometary coma will increase our understanding of the link between these primary ices and atomic oxygen. With a complete understanding of the relationship between atomic oxygen and the primary ices on the nucleus, observations of atomic oxygen can serve as a powerful proxy for the production of these primary volatiles and aid our understanding of the variation in coma composition as a function of heliocentric distance, and therefore the composition of the nucleus and how our solar system was formed.

Non-uniform Erosion and Surface Evolution of Plasma-Facing Materials for Electric Propulsion

NASA Astrophysics Data System (ADS)

Matthes, Christopher Stanley Rutter

A study regarding the surface evolution of plasma-facing materials is presented. Experimental efforts were performed in the UCLA Pi Facility, designed to explore the physics of plasma-surface interactions. The influence of micro-architectured surfaces on the effects of plasma sputtering is compared with the response of planar samples. Ballistic deposition of sputtered atoms as a result of geometric re-trapping is observed. This provides a self-healing mechanism of micro-architectured surfaces during plasma exposure. This result is quantified using a QCM to demonstrate the evolution of surface features and the corresponding influence on the instantaneous sputtering yield. The sputtering yield of textured molybdenum samples exposed to 300 eV Ar plasma is found to be roughly 1 of the 2 corresponding value of flat samples, and increases with ion fluence. Mo samples exhibited a sputtering yield initially as low as 0.22+/-8%, converging to 0.4+/-8% at high fluence. Although the yield is dependent on the initial surface structure, it is shown to be transient, reaching a steady-state value that is independent of initial surface conditions. A continuum model of surface evolution resulting from sputtering, deposition and surface diffusion is also derived to resemble the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear stability analysis of the evolution equation provides an estimate of the selected wavelength, and its dependence on the ion energy and angle of incidence. The analytical results are confirmed by numerical simulations of the equation with a Fast Fourier Transform method. It is shown that for an initially flat surface, small perturbations lead to the evolution of a selected surface pattern that has nano- scale wavelength. When the surface is initially patterned by other means, the final resulting pattern is a competition between the "templated" pattern and the "self-organized" structure. Potential future routes of research are also discussed, corresponding to a design analysis of the current experimental study.

Steep Decay Phase Shaped by the Curvature Effect. II. Spectral Evolution

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

Lin, Da-Bin; Mu, Hui-Jun; Lu, Rui-Jing

We derive a simple analytical formula to describe the evolution of spectral index β in the steep decay phase shaped by the curvature effect with the assumption that the spectral parameters and Lorentz factor of the jet shell are the same for different latitudes. Here, the value of β is estimated in the 0.3−10 keV energy band. For a spherical thin shell with a cutoff power-law (CPL) intrinsic radiation spectrum, the spectral evolution can be read as a linear function of observer time. For the situation with the Band function intrinsic radiation spectrum, the spectral evolution may be complex. Ifmore » the observed break energy of the radiation spectrum is larger than 10 keV, the spectral evolution is the same as that shaped by jet shells with a CPL spectrum. If the observed break energy is less than 0.3 keV, the value of β would be a constant. For others, the spectral evolution can be approximated as a logarithmal function of the observer time in general.« less

Optimized growth and reorientation of anisotropic material based on evolution equations

NASA Astrophysics Data System (ADS)

Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

2018-07-01

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

Ice Roughness and Thickness Evolution on a Swept NACA 0012 Airfoil

NASA Technical Reports Server (NTRS)

McClain, Stephen T.; Vargas, Mario; Tsao, Jen-Ching

2017-01-01

Several recent studies have been performed in the Icing Research Tunnel (IRT) at NASA Glenn Research Center focusing on the evolution, spatial variations, and proper scaling of ice roughness on airfoils without sweep exposed to icing conditions employed in classical roughness studies. For this study, experiments were performed in the IRT to investigate the ice roughness and thickness evolution on a 91.44-cm (36-in.) chord NACA 0012 airfoil, swept at 30-deg with 0deg angle of attack, and exposed to both Appendix C and Appendix O (SLD) icing conditions. The ice accretion event times used in the study were less than the time required to form substantially three-dimensional structures, such as scallops, on the airfoil surface. Following each ice accretion event, the iced airfoils were scanned using a ROMER Absolute Arm laser-scanning system. The resulting point clouds were then analyzed using the self-organizing map approach of McClain and Kreeger to determine the spatial roughness variations along the surfaces of the iced airfoils. The resulting measurements demonstrate linearly increasing roughness and thickness parameters with ice accretion time. Further, when compared to dimensionless or scaled results from unswept airfoil investigations, the results of this investigation indicate that the mechanisms for early stage roughness and thickness formation on swept wings are similar to those for unswept wings.

Coherent spin-exchange via a quantum mediator.

PubMed

Baart, Timothy Alexander; Fujita, Takafumi; Reichl, Christian; Wegscheider, Werner; Vandersypen, Lieven Mark Koenraad

2017-01-01

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling 'on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO (ref. 27), high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.

Instability of supersonic cold streams feeding galaxies - I. Linear Kelvin-Helmholtz instability with body modes

NASA Astrophysics Data System (ADS)

Mandelker, Nir; Padnos, Dan; Dekel, Avishai; Birnboim, Yuval; Burkert, Andreas; Krumholz, Mark R.; Steinberg, Elad

2016-12-01

Massive galaxies at high redshift are predicted to be fed from the cosmic web by narrow, dense streams of cold gas that penetrate through the hot medium encompassed by a stable shock near the virial radius of the dark-matter halo. Our long-term goal is to explore the heating and dissipation rate of the streams and their fragmentation and possible breakup, in order to understand how galaxies are fed, and how this affects their star formation rate and morphology. We present here the first step, where we analyse the linear Kelvin-Helmholtz instability (KHI) of a cold, dense slab or cylinder in 3D flowing supersonically through a hot, dilute medium. The current analysis is limited to the adiabatic case with no gravity. By analytically solving the linear dispersion relation, we find a transition from a dominance of the familiar rapidly growing surface modes in the subsonic regime to more slowly growing body modes in the supersonic regime. The system is parametrized by three parameters: the density contrast between stream and medium, the Mach number of stream velocity with respect to the medium and the stream width with respect to the halo virial radius. A realistic choice for these parameters places the streams near the mode transition, with the KHI exponential-growth time in the range 0.01-10 virial crossing times for a perturbation wavelength comparable to the stream width. We confirm our analytic predictions with idealized hydrodynamical simulations. Our linear estimates thus indicate that KHI may be effective in the evolution of streams before they reach the galaxy. More definite conclusions await the extension of the analysis to the non-linear regime and the inclusion of cooling, thermal conduction, the halo potential well, self-gravity and magnetic fields.

Computational investigation of large-scale vortex interaction with flexible bodies

NASA Astrophysics Data System (ADS)

Connell, Benjamin; Yue, Dick K. P.

2003-11-01

The interaction of large-scale vortices with flexible bodies is examined with particular interest paid to the energy and momentum budgets of the system. Finite difference direct numerical simulation of the Navier-Stokes equations on a moving curvilinear grid is coupled with a finite difference structural solver of both a linear membrane under tension and linear Euler-Bernoulli beam. The hydrodynamics and structural dynamics are solved simultaneously using an iterative procedure with the external structural forcing calculated from the hydrodynamics at the surface and the flow-field velocity boundary condition given by the structural motion. We focus on an investigation into the canonical problem of a vortex-dipole impinging on a flexible membrane. It is discovered that the structural properties of the membrane direct the interaction in terms of the flow evolution and the energy budget. Pressure gradients associated with resonant membrane response are shown to sustain the oscillatory motion of the vortex pair. Understanding how the key mechanisms in vortex-body interactions are guided by the structural properties of the body is a prerequisite to exploiting these mechanisms.

Theoretical Model for Cellular Shapes Driven by Protrusive and Adhesive Forces

PubMed Central

Kabaso, Doron; Shlomovitz, Roie; Schloen, Kathrin; Stradal, Theresia; Gov, Nir S.

2011-01-01

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix. PMID:21573201

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

PubMed

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Acceleration of incremental-pressure-correction incompressible flow computations using a coarse-grid projection method

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne

2016-11-01

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping functions transfer data between the two grids. Here we propose a version of CGP for incompressible flow computations using incremental pressure correction methods, called IFEi-CGP (implicit-time-integration, finite-element, incremental coarse grid projection). Incremental pressure correction schemes solve Poisson's equation for an intermediate variable and not the pressure itself. This fact contributes to IFEi-CGP's efficiency in two ways. First, IFEi-CGP preserves the velocity field accuracy even for a high level of pressure field grid coarsening and thus significant speedup is achieved. Second, because incremental schemes reduce the errors that arise from boundaries with artificial homogenous Neumann conditions, CGP generates undamped flows for simulations with velocity Dirichlet boundary conditions. Comparisons of the data accuracy and CPU times for the incremental-CGP versus non-incremental-CGP computations are presented.