On the Rayleigh-Taylor Instability in Presence of a Background Shear

NASA Astrophysics Data System (ADS)

Shvydkoy, Roman

2018-01-01

In this note we revisit the classical subject of the Rayleigh-Taylor instability in presence of an incompressible background shear flow. We derive a formula for the essential spectral radius of the evolution group generated by the linearization near the steady state and reveal that the velocity variations neutralize shortwave instabilities. The formula is a direct generalization of the result of Hwang and Guo (Arch Ration Mech Anal 167(3):235-253, (2003). Furthermore, we construct a class of steady states which posses unstable discrete spectrum with neutral essential spectrum. The technique involves the WKB analysis of the evolution equation and contains novel compactness criterion for pseudo-differential operators on unbounded domains.

Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

Multilevel ensemble Kalman filtering

DOE PAGES

Hoel, Hakon; Law, Kody J. H.; Tempone, Raul

2016-06-14

This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

NASA Astrophysics Data System (ADS)

Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.

2006-05-01

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

Traveling waves in discretized Balitsky Kovchegov evolution

NASA Astrophysics Data System (ADS)

Marquet, C.; Peschanski, R.; Soyez, G.; Bialas, A.

2006-02-01

We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete steps in rapidity. We derive a closed iterative equation in momentum space. We show that it possesses traveling-wave solutions and extract their properties. We find no evidence for chaotic behaviour due to discretization.

Differentiated cell behavior: a multiscale approach using measure theory.

PubMed

Colombi, Annachiara; Scianna, Marco; Tosin, Andrea

2015-11-01

This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving measures, rather than at individual cell paths, we obtain an ensemble representation stemming from the phenomenological behavior of the single component cells. In particular, as a key advantage of our approach, the scale of representation of the system, i.e., microscopic/discrete vs. macroscopic/continuous, can be chosen a posteriori according only to the spatial structure given to the aforesaid measures. The paper focuses in particular on the use of different scales based on the specific functions performed by cells. A two-population hybrid system is considered, where cells with a specialized/differentiated phenotype are treated as a discrete population of point masses while unspecialized/undifferentiated cell aggregates are represented by a continuous approximation. Numerical simulations and analytical investigations emphasize the role of some biologically relevant parameters in determining the specific evolution of such a hybrid cell system.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Genomic differentiation among wild cyanophages despite widespread horizontal gene transfer

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

Gregory, Ann C.; Solonenko, Sergei A.; Ignacio-Espinoza, J. Cesar

Genetic recombination is a driving force in genome evolution. Among viruses it has a dual role. For genomes with higher fitness, it maintains genome integrity in the face of high mutation rates. Conversely, for genomes with lower fitness, it provides immediate access to sequence space that cannot be reached by mutation alone. Understanding how recombination impacts the cohesion and dissolution of individual whole genomes within viral sequence space is poorly understood across double-stranded DNA bacteriophages (a.k.a phages) due to the challenges of obtaining appropriately scaled genomic datasets. Here in this study we explore the role of recombination in both maintainingmore » and differentiating whole genomes of 142 wild double-stranded DNA marine cyanophages. Phylogenomic analysis across the 51 core genes revealed ten lineages, six of which were well represented. These phylogenomic lineages represent discrete genotypic populations based on comparisons of intra- and inter- lineage shared gene content, genome-wide average nucleotide identity, as well as detected gaps in the distribution of pairwise differences between genomes. McDonald-Kreitman selection tests identified putative niche-differentiating genes under positive selection that differed across the six well-represented genotypic populations and that may have driven initial divergence. Concurrent with patterns of recombination of discrete populations, recombination analyses of both genic and intergenic regions largely revealed decreased genetic exchange across individual genomes between relative to within populations. Lastly, these findings suggest that discrete double-stranded DNA marine cyanophage populations occur in nature and are maintained by patterns of recombination akin to those observed in bacteria, archaea and in sexual eukaryotes.« less

Genomic differentiation among wild cyanophages despite widespread horizontal gene transfer

DOE PAGES

Gregory, Ann C.; Solonenko, Sergei A.; Ignacio-Espinoza, J. Cesar; ...

2016-11-16

Genetic recombination is a driving force in genome evolution. Among viruses it has a dual role. For genomes with higher fitness, it maintains genome integrity in the face of high mutation rates. Conversely, for genomes with lower fitness, it provides immediate access to sequence space that cannot be reached by mutation alone. Understanding how recombination impacts the cohesion and dissolution of individual whole genomes within viral sequence space is poorly understood across double-stranded DNA bacteriophages (a.k.a phages) due to the challenges of obtaining appropriately scaled genomic datasets. Here in this study we explore the role of recombination in both maintainingmore » and differentiating whole genomes of 142 wild double-stranded DNA marine cyanophages. Phylogenomic analysis across the 51 core genes revealed ten lineages, six of which were well represented. These phylogenomic lineages represent discrete genotypic populations based on comparisons of intra- and inter- lineage shared gene content, genome-wide average nucleotide identity, as well as detected gaps in the distribution of pairwise differences between genomes. McDonald-Kreitman selection tests identified putative niche-differentiating genes under positive selection that differed across the six well-represented genotypic populations and that may have driven initial divergence. Concurrent with patterns of recombination of discrete populations, recombination analyses of both genic and intergenic regions largely revealed decreased genetic exchange across individual genomes between relative to within populations. Lastly, these findings suggest that discrete double-stranded DNA marine cyanophage populations occur in nature and are maintained by patterns of recombination akin to those observed in bacteria, archaea and in sexual eukaryotes.« less

Ensemble-type numerical uncertainty information from single model integrations

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

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

Discrete Biogeography Based Optimization for Feature Selection in Molecular Signatures.

PubMed

Liu, Bo; Tian, Meihong; Zhang, Chunhua; Li, Xiangtao

2015-04-01

Biomarker discovery from high-dimensional data is a complex task in the development of efficient cancer diagnoses and classification. However, these data are usually redundant and noisy, and only a subset of them present distinct profiles for different classes of samples. Thus, selecting high discriminative genes from gene expression data has become increasingly interesting in the field of bioinformatics. In this paper, a discrete biogeography based optimization is proposed to select the good subset of informative gene relevant to the classification. In the proposed algorithm, firstly, the fisher-markov selector is used to choose fixed number of gene data. Secondly, to make biogeography based optimization suitable for the feature selection problem; discrete migration model and discrete mutation model are proposed to balance the exploration and exploitation ability. Then, discrete biogeography based optimization, as we called DBBO, is proposed by integrating discrete migration model and discrete mutation model. Finally, the DBBO method is used for feature selection, and three classifiers are used as the classifier with the 10 fold cross-validation method. In order to show the effective and efficiency of the algorithm, the proposed algorithm is tested on four breast cancer dataset benchmarks. Comparison with genetic algorithm, particle swarm optimization, differential evolution algorithm and hybrid biogeography based optimization, experimental results demonstrate that the proposed method is better or at least comparable with previous method from literature when considering the quality of the solutions obtained. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

The nature of plant species.

PubMed

Rieseberg, Loren H; Wood, Troy E; Baack, Eric J

2006-03-23

Many botanists doubt the existence of plant species, viewing them as arbitrary constructs of the human mind, as opposed to discrete, objective entities that represent reproductively independent lineages or 'units of evolution'. However, the discreteness of plant species and their correspondence with reproductive communities have not been tested quantitatively, allowing zoologists to argue that botanists have been overly influenced by a few 'botanical horror stories', such as dandelions, blackberries and oaks. Here we analyse phenetic and/or crossing relationships in over 400 genera of plants and animals. We show that although discrete phenotypic clusters exist in most genera (> 80%), the correspondence of taxonomic species to these clusters is poor (< 60%) and no different between plants and animals. Lack of congruence is caused by polyploidy, asexual reproduction and over-differentiation by taxonomists, but not by contemporary hybridization. Nonetheless, crossability data indicate that 70% of taxonomic species and 75% of phenotypic clusters in plants correspond to reproductively independent lineages (as measured by postmating isolation), and thus represent biologically real entities. Contrary to conventional wisdom, plant species are more likely than animal species to represent reproductively independent lineages.

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

On the adaptivity and complexity embedded into differential evolution

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

Senkerik, Roman; Pluhacek, Michal; Jasek, Roman

2016-06-08

This research deals with the comparison of the two modern approaches for evolutionary algorithms, which are the adaptivity and complex chaotic dynamics. This paper aims on the investigations on the chaos-driven Differential Evolution (DE) concept. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of chaotic pseudo random number generators for the DE and comparing the influence to the performance with the state of the art adaptive representative jDE. This research is focused mainly on the possible disadvantages and advantages of both compared approaches. Repeated simulations for Lozi map driving chaotic systems were performedmore » on the simple benchmark functions set, which are more close to the real optimization problems. Obtained results are compared with the canonical not-chaotic and not adaptive DE. Results show that with used simple test functions, the performance of ChaosDE is better in the most cases than jDE and Canonical DE, furthermore due to the unique sequencing in CPRNG given by the hidden chaotic dynamics, thus better and faster selection of unique individuals from population, ChaosDE is faster.« less

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

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.

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

NASA Astrophysics Data System (ADS)

Charles, Alexandre; Ballard, Patrick

2016-08-01

The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this formulation.

Sexual species are separated by larger genetic gaps than asexual species in rotifers.

PubMed

Tang, Cuong Q; Obertegger, Ulrike; Fontaneto, Diego; Barraclough, Timothy G

2014-10-01

Why organisms diversify into discrete species instead of showing a continuum of genotypic and phenotypic forms is an important yet rarely studied question in speciation biology. Does species discreteness come from adaptation to fill discrete niches or from interspecific gaps generated by reproductive isolation? We investigate the importance of reproductive isolation by comparing genetic discreteness, in terms of intra- and interspecific variation, between facultatively sexual monogonont rotifers and obligately asexual bdelloid rotifers. We calculated the age (phylogenetic distance) and average pairwise genetic distance (raw distance) within and among evolutionarily significant units of diversity in six bdelloid clades and seven monogonont clades sampled for 4211 individuals in total. We find that monogonont species are more discrete than bdelloid species with respect to divergence between species but exhibit similar levels of intraspecific variation (species cohesiveness). This pattern arises because bdelloids have diversified into discrete genetic clusters at a faster net rate than monogononts. Although sampling biases or differences in ecology that are independent of sexuality might also affect these patterns, the results are consistent with the hypothesis that bdelloids diversified at a faster rate into less discrete species because their diversification does not depend on the evolution of reproductive isolation. © 2014 The Authors. Evolution published by Wiley Periodicals, Inc. on behalf of The Society for the Study of Evolution.

Discrete differential geometry: The nonplanar quadrilateral mesh

NASA Astrophysics Data System (ADS)

Twining, Carole J.; Marsland, Stephen

2012-06-01

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

Non-autonomous equations with unpredictable solutions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2018-06-01

To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and uniqueness of the unpredictable solution for a delay differential equation are proved as well as for quasilinear discrete systems. As a corollary of the theorem, a similar assertion for a quasilinear ordinary differential equation is formulated. The results are demonstrated numerically, and an application to Hopfield neural networks is provided. In particular, Poincaré chaos near periodic orbits is observed. The completed research contributes to the theory of chaos as well as to the theory of differential and discrete equations, considering unpredictable solutions.

Neutral dynamics and cell renewal of colonic crypts in homeostatic regime

NASA Astrophysics Data System (ADS)

Fendrik, A. J.; Romanelli, L.; Rotondo, E.

2018-05-01

The self renewal process in colonic crypts is the object of several studies. We present here a new compartment model with the following characteristics: (a) we distinguish different classes of cells: stem cells, six generations of transit amplifying cells and the differentiated cells; (b) in order to take into account the monoclonal character of crypts in homeostatic regimes we include symmetric divisions of the stem cells. We first consider the dynamic differential equations that describe the evolution of the mean values of the populations, but the small observed value of the total number of cells involved plus the huge dispersion of experimental data found in the literature leads us to study the stochastic discrete process. This analysis allows us to study fluctuations, the neutral drift that leads to monoclonality, and the effects of the fixation of mutant clones.

Discrete stochastic simulation methods for chemically reacting systems.

PubMed

Cao, Yang; Samuels, David C

2009-01-01

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

Inaccurate Color Discrimination by Pollinators Promotes Evolution of Discrete Color Polymorphism in Food-Deceptive Flowers.

PubMed

Kagawa, Kotaro; Takimoto, Gaku

2016-02-01

Many plant species employing a food-deceptive pollination strategy show discrete or continuous floral polymorphism within their populations. Previous studies have suggested that negative frequency-dependent selection (NFDS) caused by the learning behavior of pollinators was responsible for the maintenance of floral polymorphism. However, NFDS alone does not explain why and when discrete or continuous polymorphism evolves. In this study, we use an evolutionary simulation model to propose that inaccurate discrimination of flower colors by pollinators results in evolution of discrete flower color polymorphism. Simulations showed that associative learning based on inaccurate discrimination in pollinators caused disruptive selection of flower colors. The degree of inaccuracy determined the number of discrete flower colors that evolved. Our results suggest that animal behavior based on inaccurate discrimination may be a general cause of disruptive selection that promotes discrete trait polymorphism.

The discrete adjoint method for parameter identification in multibody system dynamics.

PubMed

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

Compatible Spatial Discretizations for Partial Differential Equations

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

Arnold, Douglas, N, ed.

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide varietymore » of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.« less

Integrated model of multiple kernel learning and differential evolution for EUR/USD trading.

PubMed

Deng, Shangkun; Sakurai, Akito

2014-01-01

Currency trading is an important area for individual investors, government policy decisions, and organization investments. In this study, we propose a hybrid approach referred to as MKL-DE, which combines multiple kernel learning (MKL) with differential evolution (DE) for trading a currency pair. MKL is used to learn a model that predicts changes in the target currency pair, whereas DE is used to generate the buy and sell signals for the target currency pair based on the relative strength index (RSI), while it is also combined with MKL as a trading signal. The new hybrid implementation is applied to EUR/USD trading, which is the most traded foreign exchange (FX) currency pair. MKL is essential for utilizing information from multiple information sources and DE is essential for formulating a trading rule based on a mixture of discrete structures and continuous parameters. Initially, the prediction model optimized by MKL predicts the returns based on a technical indicator called the moving average convergence and divergence. Next, a combined trading signal is optimized by DE using the inputs from the prediction model and technical indicator RSI obtained from multiple timeframes. The experimental results showed that trading using the prediction learned by MKL yielded consistent profits.

On a free-surface problem with moving contact line: From variational principles to stable numerical approximations

NASA Astrophysics Data System (ADS)

Fumagalli, Ivan; Parolini, Nicola; Verani, Marco

2018-02-01

We analyze a free-surface problem described by time-dependent Navier-Stokes equations. Surface tension, capillary effects and wall friction are taken into account in the evolution of the system, influencing the motion of the contact line - where the free surface hits the wall - and of the dynamics of the contact angle. The differential equations governing the phenomenon are first derived from the variational principle of minimum reduced dissipation, and then discretized by means of the ALE approach. The numerical properties of the resulting scheme are investigated, drawing a parallel with the physical properties holding at the continuous level. Some instability issues are addressed in detail, in the case of an explicit treatment of the geometry, and novel additional terms are introduced in the discrete formulation in order to damp the instabilities. Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.

On the Importance of the Dynamics of Discretizations

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)

1995-01-01

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

Thermal evolution of magma reservoirs in the shallow crust and incidence on magma differentiation: the St-Jean-du-Doigt layered intrusion (Brittany, France)

NASA Astrophysics Data System (ADS)

Barboni, M.; Bussy, F.; Ovtcharova, M.; Schoene, B.

2009-12-01

Understanding the emplacement and growth of intrusive bodies in terms of mechanism, duration, thermal evolution and rates are fundamental aspects of crustal evolution. Recent studies show that many plutons grow in several Ma by in situ accretion of discrete magma pulses, which constitute small-scale magmatic reservoirs. The residence time of magmas, and hence their capacities to interact and differentiate, are controlled by the local thermal environment. The latter is highly dependant on 1) the emplacement depth, 2) the magmas and country rock composition, 3) the country rock thermal conductivity, 4) the rate of magma injection and 5) the geometry of the intrusion. In shallow level plutons, where magmas solidify quickly, evidence for magma mixing and/or differentiation processes is considered by many authors to be inherited from deeper levels. We show however that in-situ differentiation and magma interactions occurred within basaltic and felsic sills at shallow depth (0.3 GPa) in the St-Jean-du-Doigt bimodal intrusion, France. Field evidence coupled to high precision zircon U-Pb dating document progressive thermal maturation within the incrementally built laccolith. Early m-thick mafic sills are homogeneous and fine-grained with planar contacts with neighbouring felsic sills; within a minimal 0.5 Ma time span, the system gets warmer, adjacent sills interact and mingle, and mafic sills are differentiating in the top 40 cm of the layer. Rheological and thermal modelling show that observed in-situ differentiation-accumulation processes may be achieved in less than 10 years at shallow depth, provided that (1) the differentiating sills are injected beneath consolidated, yet still warm basalt sills, which act as low conductive insulating screens, (2) the early mafic sills accreted under the roof of the laccolith as a 100m thick top layer within 0.5 My, and (3) subsequent and sustained magmatic activity occurred on a short time scale (years) at an injection rate of ca. 0.5m/y. Extraction of differentiated residual liquids might eventually take place and mix with newly injected magma as documented in active syn-emplacement shear-zones. These low-pressure differentiated liquids can potentially contribute to subaerial volcanic activity along the major shear-zones.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Blood Based Biomarkers of Early Onset Breast Cancer

DTIC Science & Technology

2016-12-01

discretizes the data, and also using logistic elastic net – a form of linear regression - we were unable to build a classifier that could accurately...classifier for differentiating cases from controls off discretized data. The first pass analysis demonstrated a 35 gene signature that differentiated...to the discretized data for mRNA gene signature, the samples used to “train” were also included in the final samples used to “test” the algorithm

The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

NASA Astrophysics Data System (ADS)

Ma, Xiaoping; Li, Dianzhong

2018-07-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

NASA Astrophysics Data System (ADS)

Ma, Xiaoping; Li, Dianzhong

2018-03-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

[A correction method of baseline drift of discrete spectrum of NIR].

PubMed

Hu, Ai-Qin; Yuan, Hong-Fu; Song, Chun-Feng; Li, Xiao-Yu

2014-10-01

In the present paper, a new correction method of baseline drift of discrete spectrum is proposed by combination of cubic spline interpolation and first order derivative. A fitting spectrum is constructed by cubic spline interpolation, using the datum in discrete spectrum as interpolation nodes. The fitting spectrum is differentiable. First order derivative is applied to the fitting spectrum to calculate derivative spectrum. The spectral wavelengths which are the same as the original discrete spectrum were taken out from the derivative spectrum to constitute the first derivative spectra of the discrete spectra, thereby to correct the baseline drift of the discrete spectra. The effects of the new method were demonstrated by comparison of the performances of multivariate models built using original spectra, direct differential spectra and the spectra pretreated by the new method. The results show that negative effects on the performance of multivariate model caused by baseline drift of discrete spectra can be effectively eliminated by the new method.

Patterns of Post-Glacial Genetic Differentiation in Marginal Populations of a Marine Microalga

PubMed Central

Tahvanainen, Pia; Alpermann, Tilman J.; Figueroa, Rosa Isabel; John, Uwe; Hakanen, Päivi; Nagai, Satoshi; Blomster, Jaanika; Kremp, Anke

2012-01-01

This study investigates the genetic structure of an eukaryotic microorganism, the toxic dinoflagellate Alexandrium ostenfeldii, from the Baltic Sea, a geologically young and ecologically marginal brackish water estuary which is predicted to support evolution of distinct, genetically impoverished lineages of marine macroorganisms. Analyses of the internal transcribed spacer (ITS) sequences and Amplified Fragment Length Polymorphism (AFLP) of 84 A. ostenfeldii isolates from five different Baltic locations and multiple external sites revealed that Baltic A. ostenfeldii is phylogenetically differentiated from other lineages of the species and micro-geographically fragmented within the Baltic Sea. Significant genetic differentiation (F ST) between northern and southern locations was correlated to geographical distance. However, instead of discrete genetic units or continuous genetic differentiation, the analysis of population structure suggests a complex and partially hierarchic pattern of genetic differentiation. The observed pattern suggests that initial colonization was followed by local differentiation and varying degrees of dispersal, most likely depending on local habitat conditions and prevailing current systems separating the Baltic Sea populations. Local subpopulations generally exhibited low levels of overall gene diversity. Association analysis suggests predominately asexual reproduction most likely accompanied by frequency shifts of clonal lineages during planktonic growth. Our results indicate that the general pattern of genetic differentiation and reduced genetic diversity of Baltic populations found in large organisms also applies to microscopic eukaryotic organisms. PMID:23300940

Patterns of post-glacial genetic differentiation in marginal populations of a marine microalga.

PubMed

Tahvanainen, Pia; Alpermann, Tilman J; Figueroa, Rosa Isabel; John, Uwe; Hakanen, Päivi; Nagai, Satoshi; Blomster, Jaanika; Kremp, Anke

2012-01-01

This study investigates the genetic structure of an eukaryotic microorganism, the toxic dinoflagellate Alexandrium ostenfeldii, from the Baltic Sea, a geologically young and ecologically marginal brackish water estuary which is predicted to support evolution of distinct, genetically impoverished lineages of marine macroorganisms. Analyses of the internal transcribed spacer (ITS) sequences and Amplified Fragment Length Polymorphism (AFLP) of 84 A. ostenfeldii isolates from five different Baltic locations and multiple external sites revealed that Baltic A. ostenfeldii is phylogenetically differentiated from other lineages of the species and micro-geographically fragmented within the Baltic Sea. Significant genetic differentiation (F(ST)) between northern and southern locations was correlated to geographical distance. However, instead of discrete genetic units or continuous genetic differentiation, the analysis of population structure suggests a complex and partially hierarchic pattern of genetic differentiation. The observed pattern suggests that initial colonization was followed by local differentiation and varying degrees of dispersal, most likely depending on local habitat conditions and prevailing current systems separating the Baltic Sea populations. Local subpopulations generally exhibited low levels of overall gene diversity. Association analysis suggests predominately asexual reproduction most likely accompanied by frequency shifts of clonal lineages during planktonic growth. Our results indicate that the general pattern of genetic differentiation and reduced genetic diversity of Baltic populations found in large organisms also applies to microscopic eukaryotic organisms.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Dynamics of embryonic stem cell differentiation inferred from single-cell transcriptomics show a series of transitions through discrete cell states

PubMed Central

Jang, Sumin; Choubey, Sandeep; Furchtgott, Leon; Zou, Ling-Nan; Doyle, Adele; Menon, Vilas; Loew, Ethan B; Krostag, Anne-Rachel; Martinez, Refugio A; Madisen, Linda; Levi, Boaz P; Ramanathan, Sharad

2017-01-01

The complexity of gene regulatory networks that lead multipotent cells to acquire different cell fates makes a quantitative understanding of differentiation challenging. Using a statistical framework to analyze single-cell transcriptomics data, we infer the gene expression dynamics of early mouse embryonic stem (mES) cell differentiation, uncovering discrete transitions across nine cell states. We validate the predicted transitions across discrete states using flow cytometry. Moreover, using live-cell microscopy, we show that individual cells undergo abrupt transitions from a naïve to primed pluripotent state. Using the inferred discrete cell states to build a probabilistic model for the underlying gene regulatory network, we further predict and experimentally verify that these states have unique response to perturbations, thus defining them functionally. Our study provides a framework to infer the dynamics of differentiation from single cell transcriptomics data and to build predictive models of the gene regulatory networks that drive the sequence of cell fate decisions during development. DOI: http://dx.doi.org/10.7554/eLife.20487.001 PMID:28296635

Discrete fractional solutions of a Legendre equation

NASA Astrophysics Data System (ADS)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

Bound states of moving potential wells in discrete wave mechanics

NASA Astrophysics Data System (ADS)

Longhi, S.

2017-10-01

Discrete wave mechanics describes the evolution of classical or matter waves on a lattice, which is governed by a discretized version of the Schrödinger equation. While for a vanishing lattice spacing wave evolution of the continuous Schrödinger equation is retrieved, spatial discretization and lattice effects can deeply modify wave dynamics. Here we discuss implications of breakdown of exact Galilean invariance of the discrete Schrödinger equation on the bound states sustained by a smooth potential well which is uniformly moving on the lattice with a drift velocity v. While in the continuous limit the number of bound states does not depend on the drift velocity v, as one expects from the covariance of ordinary Schrödinger equation for a Galilean boost, lattice effects can lead to a larger number of bound states for the moving potential well as compared to the potential well at rest. Moreover, for a moving potential bound states on a lattice become rather generally quasi-bound (resonance) states.

Integrated Model of Multiple Kernel Learning and Differential Evolution for EUR/USD Trading

PubMed Central

Deng, Shangkun; Sakurai, Akito

2014-01-01

Currency trading is an important area for individual investors, government policy decisions, and organization investments. In this study, we propose a hybrid approach referred to as MKL-DE, which combines multiple kernel learning (MKL) with differential evolution (DE) for trading a currency pair. MKL is used to learn a model that predicts changes in the target currency pair, whereas DE is used to generate the buy and sell signals for the target currency pair based on the relative strength index (RSI), while it is also combined with MKL as a trading signal. The new hybrid implementation is applied to EUR/USD trading, which is the most traded foreign exchange (FX) currency pair. MKL is essential for utilizing information from multiple information sources and DE is essential for formulating a trading rule based on a mixture of discrete structures and continuous parameters. Initially, the prediction model optimized by MKL predicts the returns based on a technical indicator called the moving average convergence and divergence. Next, a combined trading signal is optimized by DE using the inputs from the prediction model and technical indicator RSI obtained from multiple timeframes. The experimental results showed that trading using the prediction learned by MKL yielded consistent profits. PMID:25097891

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

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

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

META 2f: Probabilistic, Compositional, Multi-dimension Model-Based Verification (PROMISE)

DTIC Science & Technology

2011-10-01

Equational Logic, Rewriting Logic, and Maude ................................................ 52  5.3  Results and Discussion...and its discrete transitions are left unchanged. However, the differential equations describing the continuous dynamics (in each mode) are replaced by...by replacing hard-to-analyze differential equations by discrete transitions. In principle, predicate and qualitative abstraction can be used on a

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

PubMed

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

Thermal plasticity of growth and development varies adaptively among alternative developmental pathways.

PubMed

Kivelä, Sami M; Svensson, Beatrice; Tiwe, Alma; Gotthard, Karl

2015-09-01

Polyphenism, the expression of discrete alternative phenotypes, is often a consequence of a developmental switch. Physiological changes induced by a developmental switch potentially affect reaction norms, but the evolution and existence of alternative reaction norms remains poorly understood. Here, we demonstrate that, in the butterfly Pieris napi (Lepidoptera: Pieridae), thermal reaction norms of several life history traits vary adaptively among switch-induced alternative developmental pathways of diapause and direct development. The switch was affected both by photoperiod and temperature, ambient temperature during late development having the potential to override earlier photoperiodic cues. Directly developing larvae had higher development and growth rates than diapausing ones across the studied thermal gradient. Reaction norm shapes also differed between the alternative developmental pathways, indicating pathway-specific selection on thermal sensitivity. Relative mass increments decreased linearly with increasing temperature and were higher under direct development than diapause. Contrary to predictions, population phenology did not explain trait variation or thermal sensitivity, but our experimental design probably lacks power for finding subtle phenology effects. We demonstrate adaptive differentiation in thermal reaction norms among alternative phenotypes, and suggest that the consequences of an environmentally dependent developmental switch primarily drive the evolution of alternative thermal reaction norms in P. napi. © 2015 The Author(s). Evolution © 2015 The Society for the Study of Evolution.

a Non-Overlapping Discretization Method for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Rosas-Medina, A.; Herrera, I.

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Engineering and Science, lead to a great variety of partial differential equations whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by engineering and scientific applications. The emergence of parallel computing prompted on the part of the computational-modeling community a continued and systematic effort with the purpose of harnessing it for the endeavor of solving boundary-value problems (BVPs) of partial differential equations. Very early after such an effort began, it was recognized that domain decomposition methods (DDM) were the most effective technique for applying parallel computing to the solution of partial differential equations, since such an approach drastically simplifies the coordination of the many processors that carry out the different tasks and also reduces very much the requirements of information-transmission between them. Ideally, DDMs intend producing algorithms that fulfill the DDM-paradigm; i.e., such that "the global solution is obtained by solving local problems defined separately in each subdomain of the coarse-mesh -or domain-decomposition-". Stated in a simplistic manner, the basic idea is that, when the DDM-paradigm is satisfied, full parallelization can be achieved by assigning each subdomain to a different processor. When intensive DDM research began much attention was given to overlapping DDMs, but soon after attention shifted to non-overlapping DDMs. This evolution seems natural when the DDM-paradigm is taken into account: it is easier to uncouple the local problems when the subdomains are separated. However, an important limitation of non-overlapping domain decompositions, as that concept is usually understood today, is that interface nodes are shared by two or more subdomains of the coarse-mesh and, therefore, even non-overlapping DDMs are actually overlapping when seen from the perspective of the nodes used in the discretization. In this talk we present and discuss a discretization method in which the nodes used are non-overlapping, in the sense that each one of them belongs to one and only one subdomain of the coarse-mesh.

Cross Coursing in Mathematics: Physical Modelling in Differential Equations Crossing to Discrete Dynamical Systems

ERIC Educational Resources Information Center

Winkel, Brian

2012-01-01

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Five Misunderstandings About Cultural Evolution.

PubMed

Henrich, Joseph; Boyd, Robert; Richerson, Peter J

2008-06-01

Recent debates about memetics have revealed some widespread misunderstandings about Darwinian approaches to cultural evolution. Drawing from these debates, this paper disputes five common claims: (1) mental representations are rarely discrete, and therefore models that assume discrete, gene-like particles (i.e., replicators) are useless; (2) replicators are necessary for cumulative, adaptive evolution; (3) content-dependent psychological biases are the only important processes that affect the spread of cultural representations; (4) the "cultural fitness" of a mental representation can be inferred from its successful transmission; and (5) selective forces only matter if the sources of variation are random. We close by sketching the outlines of a unified evolutionary science of culture.

Hybrid discrete-time neural networks.

PubMed

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

Nonlinear Control and Discrete Event Systems

NASA Technical Reports Server (NTRS)

Meyer, George; Null, Cynthia H. (Technical Monitor)

1995-01-01

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Genetic-evolution-based optimization methods for engineering design

NASA Technical Reports Server (NTRS)

Rao, S. S.; Pan, T. S.; Dhingra, A. K.; Venkayya, V. B.; Kumar, V.

1990-01-01

This paper presents the applicability of a biological model, based on genetic evolution, for engineering design optimization. Algorithms embodying the ideas of reproduction, crossover, and mutation are developed and applied to solve different types of structural optimization problems. Both continuous and discrete variable optimization problems are solved. A two-bay truss for maximum fundamental frequency is considered to demonstrate the continuous variable case. The selection of locations of actuators in an actively controlled structure, for minimum energy dissipation, is considered to illustrate the discrete variable case.

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.

Competitive Binding of Natural Amphiphiles with Graphene Derivatives

NASA Astrophysics Data System (ADS)

Radic, Slaven; Geitner, Nicholas K.; Podila, Ramakrishna; Käkinen, Aleksandr; Chen, Pengyu; Ke, Pu Chun; Ding, Feng

2013-07-01

Understanding the transformation of graphene derivatives by natural amphiphiles is essential for elucidating the biological and environmental implications of this emerging class of engineered nanomaterials. Using rapid discrete-molecular-dynamics simulations, we examined the binding of graphene and graphene oxide with peptides, fatty acids, and cellulose, and complemented our simulations by experimental studies of Raman spectroscopy, FTIR, and UV-Vis spectrophotometry. Specifically, we established a connection between the differential binding and the conformational flexibility, molecular geometry, and hydrocarbon content of the amphiphiles. Importantly, our dynamics simulations revealed a Vroman-like competitive binding of the amphiphiles for the graphene oxide substrate. This study provides a mechanistic basis for addressing the transformation, evolution, transport, biocompatibility, and toxicity of graphene derivatives in living systems and the natural environment.

Competitive Binding of Natural Amphiphiles with Graphene Derivatives

PubMed Central

Radic, Slaven; Geitner, Nicholas K.; Podila, Ramakrishna; Käkinen, Aleksandr; Chen, Pengyu; Ke, Pu Chun; Ding, Feng

2013-01-01

Understanding the transformation of graphene derivatives by natural amphiphiles is essential for elucidating the biological and environmental implications of this emerging class of engineered nanomaterials. Using rapid discrete-molecular-dynamics simulations, we examined the binding of graphene and graphene oxide with peptides, fatty acids, and cellulose, and complemented our simulations by experimental studies of Raman spectroscopy, FTIR, and UV-Vis spectrophotometry. Specifically, we established a connection between the differential binding and the conformational flexibility, molecular geometry, and hydrocarbon content of the amphiphiles. Importantly, our dynamics simulations revealed a Vroman-like competitive binding of the amphiphiles for the graphene oxide substrate. This study provides a mechanistic basis for addressing the transformation, evolution, transport, biocompatibility, and toxicity of graphene derivatives in living systems and the natural environment. PMID:23881402

Direct Discrete Method for Neutronic Calculations

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

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for amore » cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)« less

Epigenetic differentiation and relationship to adaptive genetic divergence in discrete populations of the violet Viola cazorlensis.

PubMed

Herrera, Carlos M; Bazaga, Pilar

2010-08-01

*In plants, epigenetic variations based on DNA methylation are often heritable and could influence the course of evolution. Before this hypothesis can be assessed, fundamental questions about epigenetic variation remain to be addressed in a real-world context, including its magnitude, structuring within and among natural populations, and autonomy in relation to the genetic context. *Extent and patterns of cytosine methylation, and the relationship to adaptive genetic divergence between populations, were investigated for wild populations of the southern Spanish violet Viola cazorlensis (Violaceae) using the methylation-sensitive amplified polymorphism (MSAP) technique, a modification of the amplified fragment length polymorphism method (AFLP) based on the differential sensitivity of isoschizomeric restriction enzymes to site-specific cytosine methylation. *The genome of V. cazorlensis plants exhibited extensive levels of methylation, and methylation-based epigenetic variation was structured into distinct between- and within- population components. Epigenetic differentiation of populations was correlated with adaptive genetic divergence revealed by a Bayesian population-genomic analysis of AFLP data. Significant associations existed at the individual genome level between adaptive AFLP loci and the methylation state of methylation-susceptible MSAP loci. *Population-specific, divergent patterns of correlated selection on epigenetic and genetic individual variation could account for the coordinated epigenetic-genetic adaptive population differentiation revealed by this study.

Discrete and morphometric traits reveal contrasting patterns and processes in the macroevolutionary history of a clade of scorpions.

PubMed

Mongiardino Koch, N; Ceccarelli, F S; Ojanguren-Affilastro, A A; Ramírez, M J

2017-04-01

Many palaeontological studies have investigated the evolution of entire body plans, generally relying on discrete character-taxon matrices. In contrast, macroevolutionary studies performed by neontologists have mostly focused on morphometric traits. Although these data types are very different, some studies have suggested that they capture common patterns. Nonetheless, the tests employed to support this claim have not explicitly incorporated a phylogenetic framework and may therefore be susceptible to confounding effects due to the presence of common phylogenetic structure. We address this question using the scorpion genus Brachistosternus Pocock 1893 as case study. We make use of a time-calibrated multilocus molecular phylogeny, and compile discrete and traditional morphometric data sets, both capturing the overall morphology of the organisms. We find that morphospaces derived from these matrices are significantly different, and that the degree of discordance cannot be replicated by simulations of random character evolution. Moreover, we find strong support for contrasting modes of evolution, with discrete characters being congruent with an 'early burst' scenario whereas morphometric traits suggest species-specific adaptations to have driven morphological evolution. The inferred macroevolutionary dynamics are therefore contingent on the choice of character type. Finally, we confirm that metrics of correlation fail to detect these profound differences given common phylogenetic structure in both data sets, and that methods incorporating a phylogenetic framework and accounting for expected covariance should be favoured. © 2017 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2017 European Society For Evolutionary Biology.

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.

The yan gene is highly conserved in Drosophila and its expression suggests a complex role throughout development.

PubMed

Price, M D; Lai, Z

1999-04-01

Competence for cell fate determination and cellular differentiation is under tight control of regulatory genes. Yan, a nuclear target of receptor tyrosine kinase (RTK) signaling, is an E twenty six (ETS) DNA-binding protein that functions as a negative regulator of cell differentiation and proliferation in Drosophila. Most members of RTK signaling pathways are highly conserved through evolution, yet no yan orthologues have been identified to date in vertebrates. To investigate the degree of yan conservation during evolution, we have characterized a yan homologue from a sibling species of D. melanogaster, D. virilis. Our results show that the organization, primary structure and expression pattern of yan are highly conserved. Both genes span over 20 kb and contain four exons with introns at identical positions. The areas with highest amino acid similarity include the Pointed and ETS domain but there are other discrete regions with a high degree of similarity. Phylogenetic analysis reveals that yan's closest relative is the human tel gene, a negative regulator of differentiation in hematopoetic precursors. In both species, Yan is dynamically expressed beginning as early as stage 4/5 and persisting throughout embryogenesis. In third instar larvae, Yan is expressed in and behind the morphogenetic furrow of the eye imaginal disc as well as in the laminar precursor cells of the brain. Ovarian follicle cells also contain Yan protein. Conservation of the structure and expression patterns of yan genes strongly suggests that regulatory mechanisms for their expression are also conserved in these two species.

Evaluating sample allocation and effort in detecting population differentiation for discrete and continuously distributed individuals

Treesearch

Erin L. Landguth; Michael K. Schwartz

2014-01-01

One of the most pressing issues in spatial genetics concerns sampling. Traditionally, substructure and gene flow are estimated for individuals sampled within discrete populations. Because many species may be continuously distributed across a landscape without discrete boundaries, understanding sampling issues becomes paramount. Given large-scale, geographically broad...

Discretization-dependent model for weakly connected excitable media

NASA Astrophysics Data System (ADS)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Distinct timing mechanisms produce discrete and continuous movements.

PubMed

Huys, Raoul; Studenka, Breanna E; Rheaume, Nicole L; Zelaznik, Howard N; Jirsa, Viktor K

2008-04-25

The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems) to accomplish varying behavioral functions such as speed constraints.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

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

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

Differential results integrated with continuous and discrete gravity measurements between nearby stations

NASA Astrophysics Data System (ADS)

Xu, Weimin; Chen, Shi; Lu, Hongyan

2016-04-01

Integrated gravity is an efficient way in studying spatial and temporal characteristics of the dynamics and tectonics. Differential measurements based on the continuous and discrete gravity observations shows highly competitive in terms of both efficiency and precision with single result. The differential continuous gravity variation between the nearby stations, which is based on the observation of Scintrex g-Phone relative gravimeters in every single station. It is combined with the repeated mobile relative measurements or absolute results to study the regional integrated gravity changes. Firstly we preprocess the continuous records by Tsoft software, and calculate the theoretical earth tides and ocean tides by "MT80TW" program through high precision tidal parameters from "WPARICET". The atmospheric loading effects and complex drift are strictly considered in the procedure. Through above steps we get the continuous gravity in every station and we can calculate the continuous gravity variation between nearby stations, which is called the differential continuous gravity changes. Then the differential results between related stations is calculated based on the repeated gravity measurements, which are carried out once or twice every year surrounding the gravity stations. Hence we get the discrete gravity results between the nearby stations. Finally, the continuous and discrete gravity results are combined in the same related stations, including the absolute gravity results if necessary, to get the regional integrated gravity changes. This differential gravity results is more accurate and effective in dynamical monitoring, regional hydrologic effects studying, tectonic activity and other geodynamical researches. The time-frequency characteristics of continuous gravity results are discussed to insure the accuracy and efficiency in the procedure.

Identifying heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi).

PubMed

Lloyd, Graeme T; Wang, Steve C; Brusatte, Stephen L

2012-02-01

Quantifying rates of morphological evolution is important in many macroevolutionary studies, and critical when assessing possible adaptive radiations and episodes of punctuated equilibrium in the fossil record. However, studies of morphological rates of change have lagged behind those on taxonomic diversification, and most authors have focused on continuous characters and quantifying patterns of morphological rates over time. Here, we provide a phylogenetic approach, using discrete characters and three statistical tests to determine points on a cladogram (branches or entire clades) that are characterized by significantly high or low rates of change. These methods include a randomization approach that identifies branches with significantly high rates and likelihood ratio tests that pinpoint either branches or clades that have significantly higher or lower rates than the pooled rate of the remainder of the tree. As a test case for these methods, we analyze a discrete character dataset of lungfish, which have long been regarded as "living fossils" due to an apparent slowdown in rates since the Devonian. We find that morphological rates are highly heterogeneous across the phylogeny and recover a general pattern of decreasing rates along the phylogenetic backbone toward living taxa, from the Devonian until the present. Compared with previous work, we are able to report a more nuanced picture of lungfish evolution using these new methods. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Fast Principal-Component Analysis Reveals Convergent Evolution of ADH1B in Europe and East Asia

PubMed Central

Galinsky, Kevin J.; Bhatia, Gaurav; Loh, Po-Ru; Georgiev, Stoyan; Mukherjee, Sayan; Patterson, Nick J.; Price, Alkes L.

2016-01-01

Searching for genetic variants with unusual differentiation between subpopulations is an established approach for identifying signals of natural selection. However, existing methods generally require discrete subpopulations. We introduce a method that infers selection using principal components (PCs) by identifying variants whose differentiation along top PCs is significantly greater than the null distribution of genetic drift. To enable the application of this method to large datasets, we developed the FastPCA software, which employs recent advances in random matrix theory to accurately approximate top PCs while reducing time and memory cost from quadratic to linear in the number of individuals, a computational improvement of many orders of magnitude. We apply FastPCA to a cohort of 54,734 European Americans, identifying 5 distinct subpopulations spanning the top 4 PCs. Using the PC-based test for natural selection, we replicate previously known selected loci and identify three new genome-wide significant signals of selection, including selection in Europeans at ADH1B. The coding variant rs1229984∗T has previously been associated to a decreased risk of alcoholism and shown to be under selection in East Asians; we show that it is a rare example of independent evolution on two continents. We also detect selection signals at IGFBP3 and IGH, which have also previously been associated to human disease. PMID:26924531

Evolution of Particle Size Distributions in Fragmentation Over Time

NASA Astrophysics Data System (ADS)

Charalambous, C. A.; Pike, W. T.

2013-12-01

We present a new model of fragmentation based on a probabilistic calculation of the repeated fracture of a particle population. The resulting continuous solution, which is in closed form, gives the evolution of fragmentation products from an initial block, through a scale-invariant power-law relationship to a final comminuted powder. Models for the fragmentation of particles have been developed separately in mainly two different disciplines: the continuous integro-differential equations of batch mineral grinding (Reid, 1965) and the fractal analysis of geophysics (Turcotte, 1986) based on a discrete model with a single probability of fracture. The first gives a time-dependent development of the particle-size distribution, but has resisted a closed-form solution, while the latter leads to the scale-invariant power laws, but with no time dependence. Bird (2009) recently introduced a bridge between these two approaches with a step-wise iterative calculation of the fragmentation products. The development of the particle-size distribution occurs with discrete steps: during each fragmentation event, the particles will repeatedly fracture probabilistically, cascading down the length scales to a final size distribution reached after all particles have failed to further fragment. We have identified this process as the equivalent to a sequence of trials for each particle with a fixed probability of fragmentation. Although the resulting distribution is discrete, it can be reformulated as a continuous distribution in maturity over time and particle size. In our model, Turcotte's power-law distribution emerges at a unique maturation index that defines a regime boundary. Up to this index, the fragmentation is in an erosional regime with the initial particle size setting the scaling. Fragmentation beyond this index is in a regime of comminution with rebreakage of the particles down to the size limit of fracture. The maturation index can increment continuously, for example under grinding conditions, or as discrete steps, such as with impact events. In both cases our model gives the energy associated with the fragmentation in terms of the developing surface area of the population. We show the agreement of our model to the evolution of particle size distributions associated with episodic and continuous fragmentation and how the evolution of some popular fractals may be represented using this approach. C. A. Charalambous and W. T. Pike (2013). Multi-Scale Particle Size Distributions of Mars, Moon and Itokawa based on a time-maturation dependent fragmentation model. Abstract Submitted to the AGU 46th Fall Meeting. Bird, N. R. A., Watts, C. W., Tarquis, A. M., & Whitmore, A. P. (2009). Modeling dynamic fragmentation of soil. Vadose Zone Journal, 8(1), 197-201. Reid, K. J. (1965). A solution to the batch grinding equation. Chemical Engineering Science, 20(11), 953-963. Turcotte, D. L. (1986). Fractals and fragmentation. Journal of Geophysical Research: Solid Earth 91(B2), 1921-1926.

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

Phylogeographic separation and formation of sexually discrete lineages in a global population of Yersinia pseudotuberculosis

PubMed Central

Seecharran, Tristan; Kalin-Manttari, Laura; Koskela, Katja; Nikkari, Simo; Dickins, Benjamin; Corander, Jukka; Skurnik, Mikael

2017-01-01

Yersinia pseudotuberculosis is a Gram-negative intestinal pathogen of humans and has been responsible for several nationwide gastrointestinal outbreaks. Large-scale population genomic studies have been performed on the other human pathogenic species of the genus Yersinia, Yersinia pestis and Yersinia enterocolitica allowing a high-resolution understanding of the ecology, evolution and dissemination of these pathogens. However, to date no purpose-designed large-scale global population genomic analysis of Y. pseudotuberculosis has been performed. Here we present analyses of the genomes of 134 strains of Y. pseudotuberculosis isolated from around the world, from multiple ecosystems since the 1960s. Our data display a phylogeographic split within the population, with an Asian ancestry and subsequent dispersal of successful clonal lineages into Europe and the rest of the world. These lineages can be differentiated by CRISPR cluster arrays, and we show that the lineages are limited with respect to inter-lineage genetic exchange. This restriction of genetic exchange maintains the discrete lineage structure in the population despite co-existence of lineages for thousands of years in multiple countries. Our data highlights how CRISPR can be informative of the evolutionary trajectory of bacterial lineages, and merits further study across bacteria. PMID:29177091

Open shop scheduling problem to minimize total weighted completion time

NASA Astrophysics Data System (ADS)

Bai, Danyu; Zhang, Zhihai; Zhang, Qiang; Tang, Mengqian

2017-01-01

A given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Tamascelli, D.; Smirne, A.; Huelga, S. F.; Plenio, M. B.

2018-01-01

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments—one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Differential porosimetry and permeametry for random porous media.

PubMed

Hilfer, R; Lemmer, A

2015-07-01

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography (μ-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly 850μm, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

NASA Astrophysics Data System (ADS)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first meeting with the name `Symmetries and Integrability of Discrete Equations (SIDE)' was held in Estérel, Québec, Canada. This was organized by D Levi, P Winternitz and L Vinet. After the success of the first meeting the scientific community decided to hold bi-annual SIDE meetings. They were held in 1996 at the University of Kent (UK), 1998 in Sabaudia (Italy), 2000 at the University of Tokyo (Japan), 2002 in Giens (France), 2004 in Helsinki (Finland) and in 2006 at the University of Melbourne (Australia). In 2008 the SIDE 8 meeting was again organized near Montreal, in Ste-Adèle, Québec, Canada. The SIDE 8 International Advisory Committee (also the SIDE steering committee) consisted of Frank Nijhoff, Alexander Bobenko, Basil Grammaticos, Jarmo Hietarinta, Nalini Joshi, Decio Levi, Vassilis Papageorgiou, Junkichi Satsuma, Yuri Suris, Claude Vialet and Pavel Winternitz. The local organizing committee consisted of Pavel Winternitz, John Harnad, Véronique Hussin, Decio Levi, Peter Olver and Luc Vinet. Financial support came from the Centre de Recherches Mathématiques in Montreal and the National Science Foundation (through the University of Minnesota). Proceedings of the first three SIDE meetings were published in the LMS Lecture Note series. Since 2000 the emphasis has been on publishing selected refereed articles in response to a general call for papers issued after the conference. This allows for a wider author base, since the call for papers is not restricted to conference participants. The SIDE topics thus are represented in special issues of Journal of Physics A: Mathematical and General 34 (48) and Journal of Physics A: Mathematical and Theoretical, 40 (42) (SIDE 4 and SIDE 7, respectively), Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2) (SIDE 5 and SIDE 6 respectively). The SIDE 8 meeting was organized around several topics and the contributions to this special issue reflect the diversity presented during the meeting. The papers presented at the SIDE 8 meeting were organized into the following special sessions: geometry of discrete and continuous Painlevé equations; continuous symmetries of discrete equations—theory and computational applications; algebraic aspects of discrete equations; singularity confinement, algebraic entropy and Nevanlinna theory; discrete differential geometry; discrete integrable systems and isomonodromy transformations; special functions as solutions of difference and q-difference equations. This special issue of the journal is organized along similar lines. The first three articles are topical review articles appearing in alphabetical order (by first author). The article by Doliwa and Nieszporski describes the Darboux transformations in a discrete setting, namely for the discrete second order linear problem. The article by Grammaticos, Halburd, Ramani and Viallet concentrates on the integrability of the discrete systems, in particular they describe integrability tests for difference equations such as singularity confinement, algebraic entropy (growth and complexity), and analytic and arithmetic approaches. The topical review by Konopelchenko explores the relationship between the discrete integrable systems and deformations of associative algebras. All other articles are presented in alphabetical order (by first author). The contributions were solicited from all participants as well as from the general scientific community. The contributions published in this special issue can be loosely grouped into several overlapping topics, namely: •Geometry of discrete and continuous Painlevé equations (articles by Spicer and Nijhoff and by Lobb and Nijhoff). •Continuous symmetries of discrete equations—theory and applications (articles by Dorodnitsyn and Kozlov; Levi, Petrera and Scimiterna; Scimiterna; Ste-Marie and Tremblay; Levi and Yamilov; Rebelo and Winternitz). •Yang--Baxter maps (article by Xenitidis and Papageorgiou). •Algebraic aspects of discrete equations (articles by Doliwa and Nieszporski; Konopelchenko; Tsarev and Wolf). •Singularity confinement, algebraic entropy and Nevanlinna theory (articles by Grammaticos, Halburd, Ramani and Viallet; Grammaticos, Ramani and Tamizhmani). •Discrete integrable systems and isomonodromy transformations (article by Dzhamay). •Special functions as solutions of difference and q-difference equations (articles by Atakishiyeva, Atakishiyev and Koornwinder; Bertola, Gekhtman and Szmigielski; Vinet and Zhedanov). •Other topics (articles by Atkinson; Grünbaum Nagai, Kametaka and Watanabe; Nagiyev, Guliyeva and Jafarov; Sahadevan and Uma Maheswari; Svinin; Tian and Hu; Yao, Liu and Zeng). This issue is the result of the collaboration of many individuals. We would like to thank the authors who contributed and everyone else involved in the preparation of this special issue.

Use of Microcomputers and Personal Computers in Pacing

PubMed Central

Sasmor, L.; Tarjan, P.; Mumford, V.; Smith, E.

1983-01-01

This paper describes the evolution from the early discrete circuit pacemaker of the past to the sophisticated microprocessor based pacemakers of today. The necessary computerized supporting instrumentation is also described. Technological and economical reasons for this evolution are discussed.

A VHDL Core for Intrinsic Evolution of Discrete Time Filters with Signal Feedback

NASA Technical Reports Server (NTRS)

Gwaltney, David A.; Dutton, Kenneth

2005-01-01

The design of an Evolvable Machine VHDL Core is presented, representing a discrete-time processing structure capable of supporting control system applications. This VHDL Core is implemented in an FPGA and is interfaced with an evolutionary algorithm implemented in firmware on a Digital Signal Processor (DSP) to create an evolvable system platform. The salient features of this architecture are presented. The capability to implement IIR filter structures is presented along with the results of the intrinsic evolution of a filter. The robustness of the evolved filter design is tested and its unique characteristics are described.

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, Charles E.

1990-01-01

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

Comparing the Discrete and Continuous Logistic Models

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

Correlated evolution of migration and sexual dichromatism in the New World orioles (icterus).

PubMed

Friedman, Nicholas R; Hofmann, Christopher M; Kondo, Beatrice; Omland, Kevin E

2009-12-01

The evolution of sexual dimorphism has long been attributed to sexual selection, specifically as it would drive repeated gains of elaborate male traits. In contrast to this pattern, New World oriole species all exhibit elaborate male plumage, and the repeated gains of sexual dichromatism observed in the genus are due to losses of female elaboration. Interestingly, most sexually dichromatic orioles belong to migratory or temperate-breeding clades. Using character scoring and ancestral state reconstructions from two recent studies in Icterus, we tested a hypothesis of correlated evolution between migration and sexual dichromatism. We employed two discrete phylogenetic comparative approaches: the concentrated changes test and Pagel's discrete likelihood test. Our results show that the evolution of these traits is significantly correlated (CCT: uncorrected P < 0.05; ML: LRT = 12.470, P < 0.005). Indeed, our best model of character evolution suggests that gains of sexual dichromatism are 23 times more likely to occur in migratory taxa. This study demonstrates that a life-history trait with no direct relationship with sexual selection has a strong influence on the evolution of sexual dichromatism. We recommend that researchers further investigate the role of selection on elaborate female traits in the evolution of sexual dimorphism.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Microstructural comparison of the kinematics of discrete and continuum dislocations models

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Po, Giacomo

2015-12-01

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

PubMed

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

Generalized Synchronization in AN Array of Nonlinear Dynamic Systems with Applications to Chaotic Cnn

NASA Astrophysics Data System (ADS)

Min, Lequan; Chen, Guanrong

This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Opening up closure. Semiotics across scales

PubMed

Lemke

2000-01-01

The dynamic emergence of new levels of organization in complex systems is related to the semiotic reorganization of discrete/continuous variety at the level below as continuous/discrete meaning for the level above. In this view both the semiotic and the dynamic closure of system levels is reopened to allow the development and evolution of greater complexity.

Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal Evolution of the MIZ

DTIC Science & Technology

2014-09-30

distribution (Hopkins & Thorndike 2006). The DEM treats sea ice as a collection of discrete pieces of ice, thus affording the method certain...Annals of Glaciology, 33(1), 355-360. Hopkins, M. A., & Thorndike , A. S. (2006) Floe formation in Arctic sea ice. Journal of Geophysical Research

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems

NASA Technical Reports Server (NTRS)

Hermann, Robert

1997-01-01

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Emotion differentiation and intensity during acute tobacco abstinence: A comparison of heavy and light smokers.

PubMed

Sheets, Erin S; Bujarski, Spencer; Leventhal, Adam M; Ray, Lara A

2015-08-01

The ability to recognize and label discrete emotions, termed emotion differentiation, is particularly pertinent to overall emotion regulation abilities. Patterns of deficient emotion differentiation have been associated with mood and anxiety disorders but have yet to be examined in relation to nicotine dependence. This study employed ecological momentary assessment to examine smokers' subjective experience of discrete emotions during 24-h of forced tobacco abstinence. Thirty daily smokers rated their emotions up to 23 times over the 24-hour period, and smoking abstinence was biologically verified. From these data, we computed individual difference measures of emotion differentiation, overall emotion intensity, and emotional variability. As hypothesized, heavy smokers reported poorer negative emotion differentiation than light smokers (d=0.55), along with more intense negative emotion (d=0.97) and greater negative emotion variability (d=0.97). No differences were observed in positive emotion differentiation. Across the sample, poorer negative emotion differentiation was associated with greater endorsement of psychological motives to smoke, including negative and positive reinforcement motives, while positive emotion differentiation was not. Copyright © 2015 Elsevier Ltd. All rights reserved.

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Discrete False-Discovery Rate Improves Identification of Differentially Abundant Microbes.

PubMed

Jiang, Lingjing; Amir, Amnon; Morton, James T; Heller, Ruth; Arias-Castro, Ery; Knight, Rob

2017-01-01

Differential abundance testing is a critical task in microbiome studies that is complicated by the sparsity of data matrices. Here we adapt for microbiome studies a solution from the field of gene expression analysis to produce a new method, discrete false-discovery rate (DS-FDR), that greatly improves the power to detect differential taxa by exploiting the discreteness of the data. Additionally, DS-FDR is relatively robust to the number of noninformative features, and thus removes the problem of filtering taxonomy tables by an arbitrary abundance threshold. We show by using a combination of simulations and reanalysis of nine real-world microbiome data sets that this new method outperforms existing methods at the differential abundance testing task, producing a false-discovery rate that is up to threefold more accurate, and halves the number of samples required to find a given difference (thus increasing the efficiency of microbiome experiments considerably). We therefore expect DS-FDR to be widely applied in microbiome studies. IMPORTANCE DS-FDR can achieve higher statistical power to detect significant findings in sparse and noisy microbiome data compared to the commonly used Benjamini-Hochberg procedure and other FDR-controlling procedures.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

NASA Technical Reports Server (NTRS)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Decoherence and discrete symmetries in deformed relativistic kinematics

NASA Astrophysics Data System (ADS)

Arzano, Michele

2018-01-01

Models of deformed Poincaré symmetries based on group valued momenta have long been studied as effective modifications of relativistic kinematics possibly capturing quantum gravity effects. In this contribution we show how they naturally lead to a generalized quantum time evolution of the type proposed to model fundamental decoherence for quantum systems in the presence of an evaporating black hole. The same structures which determine such generalized evolution also lead to a modification of the action of discrete symmetries and of the CPT operator. These features can in principle be used to put phenomenological constraints on models of deformed relativistic symmetries using precision measurements of neutral kaons.

Approaches to quantitating the results of differentially dyed cottons

USDA-ARS?s Scientific Manuscript database

The differential dyeing (DD) method has served as a subjective method for visually determining immature cotton fibers. In an attempt to quantitate the results of the differential dyeing method, and thus offer an efficient means of elucidating cotton maturity without visual discretion, image analysi...

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Evolution of specialization under non-equilibrium population dynamics.

PubMed

Nurmi, Tuomas; Parvinen, Kalle

2013-03-21

We analyze the evolution of specialization in resource utilization in a mechanistically underpinned discrete-time model using the adaptive dynamics approach. We assume two nutritionally equivalent resources that in the absence of consumers grow sigmoidally towards a resource-specific carrying capacity. The consumers use resources according to the law of mass-action with rates involving trade-off. The resulting discrete-time model for the consumer population has over-compensatory dynamics. We illuminate the way non-equilibrium population dynamics affect the evolutionary dynamics of the resource consumption rates, and show that evolution to the trimorphic coexistence of a generalist and two specialists is possible due to asynchronous non-equilibrium population dynamics of the specialists. In addition, various forms of cyclic evolutionary dynamics are possible. Furthermore, evolutionary suicide may occur even without Allee effects and demographic stochasticity. Copyright © 2013 Elsevier Ltd. All rights reserved.

Discrete element modeling of shock-induced particle jetting

NASA Astrophysics Data System (ADS)

Xue, Kun; Cui, Haoran

2018-05-01

The dispersal of particle shell or ring by divergent impulsive loads takes the form of coherent particle jets with the dimensions several orders larger than that of constituent grain. Particle-scale simulations based on the discrete element method have been carried out to reveal the evolution of jets in semi-two-dimensional rings before they burst out of the external surface. We identify two key events which substantially change the resulted jetting pattern, specifically, the annihilation of incipient jets and the tip-slipping of jets, which become active in different phases of jet evolution. Parametric investigations have been done to assess the correlations between the jetting pattern and a variety of structural parameters. Overpressure, the internal and outer diameters of ring as well as the packing density are found to have effects on the jet evolution with different relative importance.

An advanced environment for hybrid modeling of biological systems based on modelica.

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

The influence of discrete emotions on judgement and decision-making: a meta-analytic review.

PubMed

Angie, Amanda D; Connelly, Shane; Waples, Ethan P; Kligyte, Vykinta

2011-12-01

During the past three decades, researchers interested in emotions and cognition have attempted to understand the relationship that affect and emotions have with cognitive outcomes such as judgement and decision-making. Recent research has revealed the importance of examining more discrete emotions, showing that same-valence emotions (e.g., anger and fear) differentially impact judgement and decision-making outcomes. Narrative reviews of the literature (Lerner & Tiedens, 2006 ; Pham, 2007 ) have identified some under-researched topics, but provide a limited synthesis of findings. The purpose of this study was to review the research examining the influence of discrete emotions on judgement and decision-making outcomes and provide an assessment of the observed effects using a meta-analytic approach. Results, overall, show that discrete emotions have moderate to large effects on judgement and decision-making outcomes. However, moderator analyses revealed differential effects for study-design characteristics and emotion-manipulation characteristics by emotion type. Implications are discussed.

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

The 25 kW power module evolution study. Part 2: Payload supports system evolution

NASA Technical Reports Server (NTRS)

1978-01-01

The addition of system elements for the 25 kW power module and logical evolutionary paths, by discrete growth stages, to provide capability for accommodating the increasing mission requirements through the early 1990's within reasonable resources are conceptualized.

Stencil computations for PDE-based applications with examples from DUNE and hypre

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

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

On the Dynamics of an Incursion Describing the Interactions between Functionally Differentiated Subsystems of a Discrete-time Anticipatory System

NASA Astrophysics Data System (ADS)

Burke, Mark E.

2010-11-01

Dubois coined the term incursion, for an inclusive or implicit recursion, to describe a discrete-time anticipatory system which computes its future states by reference to its future states as well as its current and past states. In this paper, we look at a model which has been proposed in the context of a social system which has functionally differentiated subsystems. The model is derived from a discrete-time compartmental SIS epidemic model. We analyse a low order instance of the model both in its form as a recursion with no anticipatory capacity, and also as an incursion with associated anticipatory capacity. The properties of the incursion are compared and contrasted with those of the underlying recursion.

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

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

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1972-01-01

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

NASA Technical Reports Server (NTRS)

Majda, George

1986-01-01

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

A Behavioral Continuum: A Look at Personality Disorders.

ERIC Educational Resources Information Center

Harris, George; Kirk, Nancy A.

1985-01-01

Suggests that narcissistic, borderline, and antisocial personality disorders are not discrete diagnostic categories, but that they lie along a continuum and have in common the dimensions of degree of self-centeredness and degree of differentiation. Presents evidence supporting existence of continuum of behavior rather than discrete diagnostic…

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Partially incorrect fossil data augment analyses of discrete trait evolution in living species.

PubMed

Puttick, Mark N

2016-08-01

Ancestral state reconstruction of discrete character traits is often vital when attempting to understand the origins and homology of traits in living species. The addition of fossils has been shown to alter our understanding of trait evolution in extant taxa, but researchers may avoid using fossils alongside extant species if only few are known, or if the designation of the trait of interest is uncertain. Here, I investigate the impacts of fossils and incorrectly coded fossils in the ancestral state reconstruction of discrete morphological characters under a likelihood model. Under simulated phylogenies and data, likelihood-based models are generally accurate when estimating ancestral node values. Analyses with combined fossil and extant data always outperform analyses with extant species alone, even when around one quarter of the fossil information is incorrect. These results are especially pronounced when model assumptions are violated, such as when there is a trend away from the root value. Fossil data are of particular importance when attempting to estimate the root node character state. Attempts should be made to include fossils in analysis of discrete traits under likelihood, even if there is uncertainty in the fossil trait data. © 2016 The Authors.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Recent Evolution of the Introductory Curriculum in Computing.

ERIC Educational Resources Information Center

Tucker, Allen B.; Garnick, David K.

1991-01-01

Traces the evolution of introductory computing courses for undergraduates based on the Association for Computing Machinery (ACM) guidelines published in "Curriculum 78." Changes in the curricula are described, including the role of discrete mathematics and theory; and the need for a broader model for designing introductory courses is…

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

A discrete mathematical model of the dynamic evolution of a transportation network

NASA Astrophysics Data System (ADS)

Malinetskii, G. G.; Stepantsov, M. E.

2009-09-01

A dynamic model of the evolution of a transportation network is proposed. The main feature of this model is that the evolution of the transportation network is not a process of centralized transportation optimization. Rather, its dynamic behavior is a result of the system self-organization that occurs in the course of the satisfaction of needs in goods transportation and the evolution of the infrastructure of the network nodes. Nonetheless, the possibility of soft control of the network evolution direction is taken into account.

Developmental Progression in the Coral Acropora digitifera Is Controlled by Differential Expression of Distinct Regulatory Gene Networks

PubMed Central

Reyes-Bermudez, Alejandro; Villar-Briones, Alejandro; Ramirez-Portilla, Catalina; Hidaka, Michio; Mikheyev, Alexander S.

2016-01-01

Corals belong to the most basal class of the Phylum Cnidaria, which is considered the sister group of bilaterian animals, and thus have become an emerging model to study the evolution of developmental mechanisms. Although cell renewal, differentiation, and maintenance of pluripotency are cellular events shared by multicellular animals, the cellular basis of these fundamental biological processes are still poorly understood. To understand how changes in gene expression regulate morphogenetic transitions at the base of the eumetazoa, we performed quantitative RNA-seq analysis during Acropora digitifera’s development. We collected embryonic, larval, and adult samples to characterize stage-specific transcription profiles, as well as broad expression patterns. Transcription profiles reconstructed development revealing two main expression clusters. The first cluster grouped blastula and gastrula and the second grouped subsequent developmental time points. Consistently, we observed clear differences in gene expression between early and late developmental transitions, with higher numbers of differentially expressed genes and fold changes around gastrulation. Furthermore, we identified three coexpression clusters that represented discrete gene expression patterns. During early transitions, transcriptional networks seemed to regulate cellular fate and morphogenesis of the larval body. In late transitions, these networks seemed to play important roles preparing planulae for switch in lifestyle and regulation of adult processes. Although developmental progression in A. digitifera is regulated to some extent by differential coexpression of well-defined gene networks, stage-specific transcription profiles appear to be independent entities. While negative regulation of transcription is predominant in early development, cell differentiation was upregulated in larval and adult stages. PMID:26941230

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Differential-Evolution Control Parameter Optimization for Unmanned Aerial Vehicle Path Planning

PubMed Central

Kok, Kai Yit; Rajendran, Parvathy

2016-01-01

The differential evolution algorithm has been widely applied on unmanned aerial vehicle (UAV) path planning. At present, four random tuning parameters exist for differential evolution algorithm, namely, population size, differential weight, crossover, and generation number. These tuning parameters are required, together with user setting on path and computational cost weightage. However, the optimum settings of these tuning parameters vary according to application. Instead of trial and error, this paper presents an optimization method of differential evolution algorithm for tuning the parameters of UAV path planning. The parameters that this research focuses on are population size, differential weight, crossover, and generation number. The developed algorithm enables the user to simply define the weightage desired between the path and computational cost to converge with the minimum generation required based on user requirement. In conclusion, the proposed optimization of tuning parameters in differential evolution algorithm for UAV path planning expedites and improves the final output path and computational cost. PMID:26943630

The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies.

PubMed

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2013-07-21

Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate how well the discrete Laplace distribution approximates a more complicated distribution that arises by investigating the well-known population genetic Fisher-Wright model of evolution by a single-step mutation process. It was shown how the discrete Laplace distribution can be used to estimate haplotype frequencies for haploid lineage DNA markers (such as Y-chromosomal short tandem repeats), which in turn can be used to assess the evidential weight of a DNA profile found at a crime scene. This was done by making inference in a mixture of multivariate, marginally independent, discrete Laplace distributions using the EM algorithm to estimate the probabilities of membership of a set of unobserved subpopulations. The discrete Laplace distribution can be used to estimate haplotype frequencies with lower prediction error than other existing estimators. Furthermore, the calculations could be performed on a normal computer. This method was implemented in the freely available open source software R that is supported on Linux, MacOS and MS Windows. Copyright © 2013 Elsevier Ltd. All rights reserved.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Maglev Train Signal Processing Architecture Based on Nonlinear Discrete Tracking Differentiator.

PubMed

Wang, Zhiqiang; Li, Xiaolong; Xie, Yunde; Long, Zhiqiang

2018-05-24

In a maglev train levitation system, signal processing plays an important role for the reason that some sensor signals are prone to be corrupted by noise due to the harsh installation and operation environment of sensors and some signals cannot be acquired directly via sensors. Based on these concerns, an architecture based on a new type of nonlinear second-order discrete tracking differentiator is proposed. The function of this signal processing architecture includes filtering signal noise and acquiring needed signals for levitation purposes. The proposed tracking differentiator possesses the advantages of quick convergence, no fluttering, and simple calculation. Tracking differentiator's frequency characteristics at different parameter values are studied in this paper. The performance of this new type of tracking differentiator is tested in a MATLAB simulation and this tracking-differentiator is implemented in Very-High-Speed Integrated Circuit Hardware Description Language (VHDL). In the end, experiments are conducted separately on a test board and a maglev train model. Simulation and experiment results show that the performance of this novel signal processing architecture can fulfill the real system requirement.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

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

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Motion of Discrete Interfaces Through Mushy Layers

NASA Astrophysics Data System (ADS)

Braides, Andrea; Solci, Margherita

2016-08-01

We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

PubMed

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal Evolution of the MIZ

DTIC Science & Technology

2015-09-30

wave-ice interaction (Hopkins & Shen 2001), and the mesoscale evolution of the floe size distribution (Hopkins & Thorndike 2006). This modeling effort...33(1), 355-360. Hopkins, M. A., & Thorndike , A. S. (2006) Floe formation in Arctic sea ice. Journal of Geophysical Research: Oceans (1978–2012), 111

Beverton-Holt discrete pest management models with pulsed chemical control and evolution of pesticide resistance

NASA Astrophysics Data System (ADS)

Liang, Juhua; Tang, Sanyi; Cheke, Robert A.

2016-07-01

Pest resistance to pesticides is usually managed by switching between different types of pesticides. The optimal switching time, which depends on the dynamics of the pest population and on the evolution of the pesticide resistance, is critical. Here we address how the dynamic complexity of the pest population, the development of resistance and the spraying frequency of pulsed chemical control affect optimal switching strategies given different control aims. To do this, we developed novel discrete pest population growth models with both impulsive chemical control and the evolution of pesticide resistance. Strong and weak threshold conditions which guarantee the extinction of the pest population, based on the threshold values of the analytical formula for the optimal switching time, were derived. Further, we addressed switching strategies in the light of chosen economic injury levels. Moreover, the effects of the complex dynamical behaviour of the pest population on the pesticide switching times were also studied. The pesticide application period, the evolution of pesticide resistance and the dynamic complexity of the pest population may result in complex outbreak patterns, with consequent effects on the pesticide switching strategies.

Three-Dimensional mRNA Measurements Reveal Minimal Regional Heterogeneity in Esophageal Squamous Cell Carcinoma

PubMed Central

Yan, Wusheng; Shih, Joanna; Rodriguez-Canales, Jaime; Tangrea, Michael A.; Player, Audrey; Diao, Lixia; Hu, Nan; Goldstein, Alisa M.; Wang, Jing; Taylor, Philip R.; Lippman, Scott M.; Wistuba, Ignacio I.; Emmert-Buck, Michael R.; Erickson, Heidi S.

2014-01-01

The classic tumor clonal evolution theory postulates that cancers change over time to produce unique molecular subclones within a parent neoplasm, presumably including regional differences in gene expression. More recently, however, this notion has been challenged by studies showing that tumors maintain a relatively stable transcript profile. To examine these competing hypotheses, we microdissected discrete subregions containing approximately 3000 to 8000 cells (500 to 1500 μm in diameter) from ex vivo esophageal squamous cell carcinoma (ESCC) specimens and analyzed transcriptomes throughout three-dimensional tumor space. Overall mRNA profiles were highly similar in all 59 intratumor comparisons, in distinct contrast to the markedly different global expression patterns observed in other dissected cell populations. For example, normal esophageal basal cells contained 1918 and 624 differentially expressed genes at a greater than twofold level (95% confidence level of <5% false positives), compared with normal differentiated esophageal cells and ESCC, respectively. In contrast, intratumor regions had only zero to four gene changes at a greater than twofold level, with most tumor comparisons showing none. The present data indicate that, when analyzed using a standard array-based method at this level of histological resolution, ESCC contains little regional mRNA heterogeneity. PMID:23219752

The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

NASA Astrophysics Data System (ADS)

Gegenhasi

2017-07-01

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential-difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

NASA Astrophysics Data System (ADS)

Kreeft, Jasper; Gerritsma, Marc

2013-05-01

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

Modeling Seismic Anisotropy From the Top to the Bottom of the Mantle

NASA Astrophysics Data System (ADS)

Ribe, N. M.; Castelnau, O.

2011-12-01

Understanding the origin of seismic anisotropy in the mantle requires quantifying the link between the strain history experienced by a rock and the evolving orientation distribution of its constituent crystals (`crystal preferred orientation' or CPO). The fundamental quantity of interest in any model of CPO is the vector spin ω(g, d) of the crystallographic axes of each crystal, which depends on the crystal's orientation g and on the velocity gradient tensor d of the aggregate-scale deformation. Existing methods for determining ω(g, d) rely on unwieldy discrete representations of the crystal orientation distribution in terms of 103-104 individual grains. We propose a new method based on (1) an analytical expression for ω(g, d) and (2) a representation of CPO in terms of a small number (N≤4) of continuous functions of g (`structured basis functions' or SBFs) each of which satisfies the hyperbolic partial differential equation governing the evolution of CPO when only a single slip system is active. The SBFs are then combined via an appropriate weighting scheme to represent a realistic CPO produced by the simultaneous activity of several slip systems.The approach yields a set of N coupled ordinary differential equations for the temporal evolution of the coefficients of the SBFs, which can be solved numerically for an arbitrary strain history at a computational cost ≈10-6 that of homogenization methods such as VPSC. Example calculations will be shown for model mineralogies and strain histories appropriate for the uppermost and lowermost mantles.

Evolution and origin of sympatric shallow-water morphotypes of Lake Trout, Salvelinus namaycush, in Canada's Great Bear Lake

PubMed Central

Harris, L N; Chavarie, L; Bajno, R; Howland, K L; Wiley, S H; Tonn, W M; Taylor, E B

2015-01-01

Range expansion in north-temperate fishes subsequent to the retreat of the Wisconsinan glaciers has resulted in the rapid colonization of previously unexploited, heterogeneous habitats and, in many situations, secondary contact among conspecific lineages that were once previously isolated. Such ecological opportunity coupled with reduced competition likely promoted morphological and genetic differentiation within and among post-glacial fish populations. Discrete morphological forms existing in sympatry, for example, have now been described in many species, yet few studies have directly assessed the association between morphological and genetic variation. Morphotypes of Lake Trout, Salvelinus namaycush, are found in several large-lake systems including Great Bear Lake (GBL), Northwest Territories, Canada, where several shallow-water forms are known. Here, we assess microsatellite and mitochondrial DNA variation among four morphotypes of Lake Trout from the five distinct arms of GBL, and also from locations outside of this system to evaluate several hypotheses concerning the evolution of morphological variation in this species. Our data indicate that morphotypes of Lake Trout from GBL are genetically differentiated from one another, yet the morphotypes are still genetically more similar to one another compared with populations from outside of this system. Furthermore, our data suggest that Lake Trout colonized GBL following dispersal from a single glacial refugium (the Mississippian) and support an intra-lake model of divergence. Overall, our study provides insights into the origins of morphological and genetic variation in post-glacial populations of fishes and provides benchmarks important for monitoring Lake Trout biodiversity in a region thought to be disproportionately susceptible to impacts from climate change. PMID:25204304

Evolution and origin of sympatric shallow-water morphotypes of Lake Trout, Salvelinus namaycush, in Canada's Great Bear Lake.

PubMed

Harris, L N; Chavarie, L; Bajno, R; Howland, K L; Wiley, S H; Tonn, W M; Taylor, E B

2015-01-01

Range expansion in north-temperate fishes subsequent to the retreat of the Wisconsinan glaciers has resulted in the rapid colonization of previously unexploited, heterogeneous habitats and, in many situations, secondary contact among conspecific lineages that were once previously isolated. Such ecological opportunity coupled with reduced competition likely promoted morphological and genetic differentiation within and among post-glacial fish populations. Discrete morphological forms existing in sympatry, for example, have now been described in many species, yet few studies have directly assessed the association between morphological and genetic variation. Morphotypes of Lake Trout, Salvelinus namaycush, are found in several large-lake systems including Great Bear Lake (GBL), Northwest Territories, Canada, where several shallow-water forms are known. Here, we assess microsatellite and mitochondrial DNA variation among four morphotypes of Lake Trout from the five distinct arms of GBL, and also from locations outside of this system to evaluate several hypotheses concerning the evolution of morphological variation in this species. Our data indicate that morphotypes of Lake Trout from GBL are genetically differentiated from one another, yet the morphotypes are still genetically more similar to one another compared with populations from outside of this system. Furthermore, our data suggest that Lake Trout colonized GBL following dispersal from a single glacial refugium (the Mississippian) and support an intra-lake model of divergence. Overall, our study provides insights into the origins of morphological and genetic variation in post-glacial populations of fishes and provides benchmarks important for monitoring Lake Trout biodiversity in a region thought to be disproportionately susceptible to impacts from climate change.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Design of Flight Vehicle Management Systems

NASA Technical Reports Server (NTRS)

Meyer, George; Aiken, Edwin W. (Technical Monitor)

1994-01-01

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possess much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability.

PubMed

Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A

2016-12-01

An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

Josephson junction in the quantum mesoscopic electric circuits with charge discreteness

NASA Astrophysics Data System (ADS)

Pahlavani, H.

2018-04-01

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Multiobjective Optimization Using a Pareto Differential Evolution Approach

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

PubMed

Jin, Bangti; Li, Buyang; Zhou, Zhi

2018-01-01

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Infant differential behavioral responding to discrete emotions.

PubMed

Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J

2017-10-01

Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Revisiting "The evolution of reciprocity in sizable groups": continuous reciprocity in the repeated n-person prisoner's dilemma.

PubMed

Takezawa, Masanori; Price, Michael E

2010-05-21

For many years in evolutionary science, the consensus view has been that while reciprocal altruism can evolve in dyadic interactions, it is unlikely to evolve in sizable groups. This view had been based on studies which have assumed cooperation to be discrete rather than continuous (i.e., individuals can either fully cooperate or else fully defect, but they cannot continuously vary their level of cooperation). In real world cooperation, however, cooperation is often continuous. In this paper, we re-examine the evolution of reciprocity in sizable groups by presenting a model of the n-person prisoner's dilemma that assumes continuous rather than discrete cooperation. This model shows that continuous reciprocity has a dramatically wider basin of attraction than discrete reciprocity, and that this basin's size increases with efficiency of cooperation (marginal per capita return). Further, we find that assortative interaction interacts synergistically with continuous reciprocity to a much greater extent than it does with discrete reciprocity. These results suggest that previous models may have underestimated reciprocity's adaptiveness in groups. However, we also find that the invasion of continuous reciprocators into a population of unconditional defectors becomes realistic only within a narrow parameter space in which the efficiency of cooperation is close to its maximum bound. Therefore our model suggests that continuous reciprocity can evolve in large groups more easily than discrete reciprocity only under unusual circumstances. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

A Continuous Square Root in Formation Filter-Swoother with Discrete Data Update

NASA Technical Reports Server (NTRS)

Miller, J. K.

1994-01-01

A differential equation for the square root information matrix is derived and adapted to the problems of filtering and smoothing. The resulting continuous square root information filter (SRIF) performs the mapping of state and process noise by numerical integration of the SRIF matrix and admits data via a discrete least square update.

Differential Recognition of Pitch Patterns in Discrete and Gliding Stimuli in Congenital Amusia: Evidence from Mandarin Speakers

ERIC Educational Resources Information Center

Liu, Fang; Xu, Yi; Patel, Aniruddh D.; Francart, Tom; Jiang, Cunmei

2012-01-01

This study examined whether "melodic contour deafness" (insensitivity to the direction of pitch movement) in congenital amusia is associated with specific types of pitch patterns (discrete versus gliding pitches) or stimulus types (speech syllables versus complex tones). Thresholds for identification of pitch direction were obtained using discrete…

Thermal history and differential exhumation across the Eastern Musgrave Province, South Australia: Insights from low-temperature thermochronology

NASA Astrophysics Data System (ADS)

Glorie, Stijn; Agostino, Kate; Dutch, Rian; Pawley, Mark; Hall, James; Danišík, Martin; Evans, Noreen J.; Collins, Alan S.

2017-04-01

Multi-method geo- and thermochronological data obtained for Palaeo- and Mesoproterozoic granitoids traversing the main structural architecture of the eastern Musgrave Province within South Australia reveal multiphase cooling histories. Apatite U-Pb dating on six samples yield consistent ages of 1075-1025 Ma, suggesting a thermal reset coinciding with mantle-derived magmatism of the greater Warakurna Large Igneous Province ( 1080-1040 Ma). Apatite fission track (AFT) analysis indicate that four discrete thermal events affected the study area, inducing cooling through the AFT partial annealing zone ( 60-120 °C), supported by apatite and zircon (U-Th-Sm)/He data. Late Neoproterozoic cooling from deep crustal levels to temperatures < 200 °C was discerned, which is thought to be related to exhumation and denudation during the Petermann Orogeny. Subsequent cooling events at 450-400 Ma (Silurian-Devonian) and 310-290 Ma (Late Carboniferous) are interpreted to represent exhumation associated with the Alice Springs Orogeny. The latter event exhumed the sampled plutons to shallow crustal depths. An additional Triassic - early Jurassic thermal event, likely recording elevated geothermal gradients at that time, was observed throughout the study area, however, more data is needed to further support this interpretation. The high sample density across the structural architecture of the study area furthermore reveals patterns of fault reactivation and resulting differential exhumation, indicating shallower exhumation levels in the centre and deeper exhumation towards the margins of the sampled transect. The observed differential exhumation patterns match with existing seismic data and fit a model of an inverted graben system for the Phanerozoic evolution of the eastern Musgraves. The results highlight a complex Phanerozoic thermal history for the eastern Musgraves and help to elucidate the poorly appreciated tectonic evolution of inland Australia. This study further demonstrates how high-density sample transects across structural architecture can assess the relative crustal level and associated preservation of the thermal history record within fault-reactivated terranes.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

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

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

NASA Astrophysics Data System (ADS)

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

2013-12-01

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

The evolution of plant virus transmission pathways.

PubMed

Hamelin, Frédéric M; Allen, Linda J S; Prendeville, Holly R; Hajimorad, M Reza; Jeger, Michael J

2016-05-07

The evolution of plant virus transmission pathways is studied through transmission via seed, pollen, or a vector. We address the questions: under what circumstances does vector transmission make pollen transmission redundant? Can evolution lead to the coexistence of multiple virus transmission pathways? We restrict the analysis to an annual plant population in which reproduction through seed is obligatory. A semi-discrete model with pollen, seed, and vector transmission is formulated to investigate these questions. We assume vector and pollen transmission rates are frequency-dependent and density-dependent, respectively. An ecological stability analysis is performed for the semi-discrete model and used to inform an evolutionary study of trade-offs between pollen and seed versus vector transmission. Evolutionary dynamics critically depend on the shape of the trade-off functions. Assuming a trade-off between pollen and vector transmission, evolution either leads to an evolutionarily stable mix of pollen and vector transmission (concave trade-off) or there is evolutionary bi-stability (convex trade-off); the presence of pollen transmission may prevent evolution of vector transmission. Considering a trade-off between seed and vector transmission, evolutionary branching and the subsequent coexistence of pollen-borne and vector-borne strains is possible. This study contributes to the theory behind the diversity of plant-virus transmission patterns observed in nature. Copyright © 2016 Elsevier Ltd. All rights reserved.

Applications of algebraic topology to compatible spatial discretizations.

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

Bochev, Pavel Blagoveston; Hyman, James M.

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstructionmore » operator and when they are equivalent.« less

An extension of the OpenModelica compiler for using Modelica models in a discrete event simulation

DOE PAGES

Nutaro, James

2014-11-03

In this article, a new back-end and run-time system is described for the OpenModelica compiler. This new back-end transforms a Modelica model into a module for the adevs discrete event simulation package, thereby extending adevs to encompass complex, hybrid dynamical systems. The new run-time system that has been built within the adevs simulation package supports models with state-events and time-events and that comprise differential-algebraic systems with high index. Finally, although the procedure for effecting this transformation is based on adevs and the Discrete Event System Specification, it can be adapted to any discrete event simulation package.

Partition-based discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo

2018-04-01

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

Beyond happiness: Building a science of discrete positive emotions.

PubMed

Shiota, Michelle N; Campos, Belinda; Oveis, Christopher; Hertenstein, Matthew J; Simon-Thomas, Emiliana; Keltner, Dacher

2017-10-01

While trait positive emotionality and state positive-valence affect have long been the subject of intense study, the importance of differentiating among several "discrete" positive emotions has only recently begun to receive serious attention. In this article, we synthesize existing literature on positive emotion differentiation, proposing that the positive emotions are best described as branches of a "family tree" emerging from a common ancestor mediating adaptive management of fitness-critical resources (e.g., food). Examples are presented of research indicating the importance of differentiating several positive emotion constructs. We then offer a new theoretical framework, built upon a foundation of phylogenetic, neuroscience, and behavioral evidence, that accounts for core features as well as mechanisms for differentiation. We propose several directions for future research suggested by this framework and develop implications for the application of positive emotion research to translational issues in clinical psychology and the science of behavior change. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

A toolbox for discrete modelling of cell signalling dynamics.

PubMed

Paterson, Yasmin Z; Shorthouse, David; Pleijzier, Markus W; Piterman, Nir; Bendtsen, Claus; Hall, Benjamin A; Fisher, Jasmin

2018-06-18

In an age where the volume of data regarding biological systems exceeds our ability to analyse it, many researchers are looking towards systems biology and computational modelling to help unravel the complexities of gene and protein regulatory networks. In particular, the use of discrete modelling allows generation of signalling networks in the absence of full quantitative descriptions of systems, which are necessary for ordinary differential equation (ODE) models. In order to make such techniques more accessible to mainstream researchers, tools such as the BioModelAnalyzer (BMA) have been developed to provide a user-friendly graphical interface for discrete modelling of biological systems. Here we use the BMA to build a library of discrete target functions of known canonical molecular interactions, translated from ordinary differential equations (ODEs). We then show that these BMA target functions can be used to reconstruct complex networks, which can correctly predict many known genetic perturbations. This new library supports the accessibility ethos behind the creation of BMA, providing a toolbox for the construction of complex cell signalling models without the need for extensive experience in computer programming or mathematical modelling, and allows for construction and simulation of complex biological systems with only small amounts of quantitative data.

Differences in Cell Division Rates Drive the Evolution of Terminal Differentiation in Microbes

PubMed Central

Matias Rodrigues, João F.; Rankin, Daniel J.; Rossetti, Valentina; Wagner, Andreas; Bagheri, Homayoun C.

2012-01-01

Multicellular differentiated organisms are composed of cells that begin by developing from a single pluripotent germ cell. In many organisms, a proportion of cells differentiate into specialized somatic cells. Whether these cells lose their pluripotency or are able to reverse their differentiated state has important consequences. Reversibly differentiated cells can potentially regenerate parts of an organism and allow reproduction through fragmentation. In many organisms, however, somatic differentiation is terminal, thereby restricting the developmental paths to reproduction. The reason why terminal differentiation is a common developmental strategy remains unexplored. To understand the conditions that affect the evolution of terminal versus reversible differentiation, we developed a computational model inspired by differentiating cyanobacteria. We simulated the evolution of a population of two cell types –nitrogen fixing or photosynthetic– that exchange resources. The traits that control differentiation rates between cell types are allowed to evolve in the model. Although the topology of cell interactions and differentiation costs play a role in the evolution of terminal and reversible differentiation, the most important factor is the difference in division rates between cell types. Faster dividing cells always evolve to become the germ line. Our results explain why most multicellular differentiated cyanobacteria have terminally differentiated cells, while some have reversibly differentiated cells. We further observed that symbioses involving two cooperating lineages can evolve under conditions where aggregate size, connectivity, and differentiation costs are high. This may explain why plants engage in symbiotic interactions with diazotrophic bacteria. PMID:22511858

Evidence of correlated evolution and adaptive differentiation of stem and leaf functional traits in the herbaceous genus, Helianthus.

PubMed

Pilote, Alex J; Donovan, Lisa A

2016-12-01

Patterns of plant stem traits are expected to align with a "fast-slow" plant economic spectrum across taxa. Although broad patterns support such tradeoffs in field studies, tests of hypothesized correlated trait evolution and adaptive differentiation are more robust when taxa relatedness and environment are taken into consideration. Here we test for correlated evolution of stem and leaf traits and their adaptive differentiation across environments in the herbaceous genus, Helianthus. Stem and leaf traits of 14 species of Helianthus (28 populations) were assessed in a common garden greenhouse study. Phylogenetically independent contrasts were used to test for evidence of correlated evolution of stem hydraulic and biomechanical properties, correlated evolution of stem and leaf traits, and adaptive differentiation associated with source habitat environments. Among stem traits, there was evidence for correlated evolution of some hydraulic and biomechanical properties, supporting an expected tradeoff between stem theoretical hydraulic efficiency and resistance to bending stress. Population differentiation for suites of stem and leaf traits was found to be consistent with a "fast-slow" resource-use axis for traits related to water transport and use. Associations of population traits with source habitat characteristics supported repeated evolution of a resource-acquisitive "drought-escape" strategy in arid environments. This study provides evidence of correlated evolution of stem and leaf traits consistent with the fast-slow spectrum of trait combinations related to water transport and use along the stem-to-leaf pathway. Correlations of traits with source habitat characteristics further indicate that the correlated evolution is associated, at least in part, with adaptive differentiation of Helianthus populations among native habitats differing in climate. © 2016 Botanical Society of America.

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO 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.

An allelic series at pax7a is associated with colour polymorphism diversity in Lake Malawi cichlid fish.

PubMed

Roberts, Reade B; Moore, Emily C; Kocher, Thomas D

2017-05-01

Despite long-standing interest in the evolution and maintenance of discrete phenotypic polymorphisms, the molecular genetic basis of such polymorphism in the wild is largely unknown. Female sex-associated blotched colour polymorphisms found in cichlids of Lake Malawi, East Africa, represent a highly successful polymorphic phenotype, found and maintained in four genera across the geographic expanse of the lake. Previously, we identified an association with an allelic variant of the paired-box transcription factor gene pax7a and blotched colour morphs in Lake Malawi cichlid fishes. Although a diverse range of blotched phenotypes are present in Lake Malawi cichlid species, they all appeared to result from an allele of pax7a that produces increased levels of transcript. Here, we examine the developmental and genetic basis of variation among blotched morphs. First, we confirm that pax7a-associated blotch morphs result primarily from modulation of melanophore development and survival. From laboratory crosses and natural population studies, we identify at least three alleles of pax7a associated with discrete subtypes of blotched morphs, in addition to the ancestral pax7a allele. Genotypes at pax7a support initial evolution of a novel pax7a allele to produce the blotched class of morphs, followed by subsequent evolution of that pax7a blotched allele to produce additional alleles associated with discrete colour morphs. Variant alleles of pax7a produce different levels of pax7a transcript, correlating with pigmentation phenotype at the cellular level. This naturally selected allelic series should serve as a case study for understanding the molecular genetic control of pax7a expression and the evolution of sex-associated alleles. © 2016 John Wiley & Sons Ltd.

SEXUAL SPECIES ARE SEPARATED BY LARGER GENETIC GAPS THAN ASEXUAL SPECIES IN ROTIFERS

PubMed Central

Tang, Cuong Q; Obertegger, Ulrike; Fontaneto, Diego; Barraclough, Timothy G

2014-01-01

Why organisms diversify into discrete species instead of showing a continuum of genotypic and phenotypic forms is an important yet rarely studied question in speciation biology. Does species discreteness come from adaptation to fill discrete niches or from interspecific gaps generated by reproductive isolation? We investigate the importance of reproductive isolation by comparing genetic discreteness, in terms of intra- and interspecific variation, between facultatively sexual monogonont rotifers and obligately asexual bdelloid rotifers. We calculated the age (phylogenetic distance) and average pairwise genetic distance (raw distance) within and among evolutionarily significant units of diversity in six bdelloid clades and seven monogonont clades sampled for 4211 individuals in total. We find that monogonont species are more discrete than bdelloid species with respect to divergence between species but exhibit similar levels of intraspecific variation (species cohesiveness). This pattern arises because bdelloids have diversified into discrete genetic clusters at a faster net rate than monogononts. Although sampling biases or differences in ecology that are independent of sexuality might also affect these patterns, the results are consistent with the hypothesis that bdelloids diversified at a faster rate into less discrete species because their diversification does not depend on the evolution of reproductive isolation. PMID:24975991

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

Differential Weight Procedure of the Conditional P.D.F. Approach for Estimating the Operating Characteristics of Discrete Item Responses.

ERIC Educational Resources Information Center

Samejima, Fumiko

A method is proposed that increases the accuracies of estimation of the operating characteristics of discrete item responses, especially when the true operating characteristic is represented by a steep curve, and also at the lower and upper ends of the ability distribution where the estimation tends to be inaccurate because of the smaller number…

Discretization and Numerical Solution of a Plane Problem in the Mechanics of Interfacial Cracks

NASA Astrophysics Data System (ADS)

Khoroshun, L. P.

2017-01-01

The Fourier transform is used to reduce the linear plane problem of the tension of a body with an interfacial crack to a system of dual equations for the transformed stresses and, then, to a system of integro-differential equations for the difference of displacements of the crack faces. After discretization, this latter system transforms into a system of algebraic equations for displacements of the crack faces. The effect of the bielastic constant and the number of discretization points on the half-length of the crack faces and the distribution of stresses at the interface is studied

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

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

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

A discrete geometric approach for simulating the dynamics of thin viscous threads

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

Audoly, B., E-mail: audoly@lmm.jussieu.fr; Clauvelin, N.; Brun, P.-T.

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistencymore » of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.« less

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Marinelli, Dimitri; Marzuoli, Annalisa

2013-05-01

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second-order difference equation which, by a complex phase change, we turn into a discrete Schrödinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantum mechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary ‘quantum of space’, and a transparent asymptotic picture of the semiclassical and classical regimes emerges. The definition of coordinates adapted to the Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Differential associations of job control components with both waist circumference and body mass index.

PubMed

Bean, Christopher G; Winefield, Helen R; Sargent, Charli; Hutchinson, Amanda D

2015-10-01

The Job Demand-Control-Support (JDCS) model is commonly used to investigate associations between psychosocial work factors and employee health, yet research considering obesity using the JDCS model remains inconclusive. This study investigates which parts of the JDCS model are associated with measures of obesity and provides a comparison between waist circumference (higher values imply central obesity) and body mass index (BMI, higher values imply overall obesity). Contrary to common practice, in this study the JDCS components are not reduced into composite or global scores. In light of emerging evidence that the two components of job control (skill discretion and decision authority) could have differential associations with related health outcomes, components of the JDCS model were analysed at the subscale level. A cross-sectional design with a South Australian cohort (N = 450) combined computer-assisted telephone interview data and clinic-measured height, weight and waist circumference. After controlling for sex, age, household income, work hours and job nature (blue vs. white-collar), the two components of job control were the only parts of the JDCS model to hold significant associations with measures of obesity. Notably, the associations between skill discretion and waist circumference (b = -.502, p = .001), and skill discretion and BMI (b = -.163, p = .005) were negative. Conversely, the association between decision authority and waist circumference (b = .282, p = .022) was positive. These findings are significant since skill discretion and decision authority are typically combined into a composite measure of job control or decision latitude. Our findings suggest skill discretion and decision authority should be treated separately since combining these theoretically distinct components may conceal their differential associations with measures of obesity, masking their individual importance. Psychosocial work factors displayed stronger associations and explained greater variance in waist circumference compared with BMI, and possible reasons for this are discussed. Copyright © 2015 Elsevier Ltd. All rights reserved.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

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

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

Basal friction evolution and crevasse distribution during the surge of Basin 3, Austfonna ice-cap - offline coupling between a continuum ice dynamic model and a discrete element model

NASA Astrophysics Data System (ADS)

Gong, Yongmei; Zwinger, Thomas; Åström, Jan; Gladstone, Rupert; Schellenberger, Thomas; Altena, Bas; Moore, John

2017-04-01

The outlet glacier at Basin 3, Austfonna ice-cap entered its active surge phase in autumn 2012. We assess the evolution of the basal friction during the surge through inverse modelling of basal friction coefficients using recent velocity observation from 2012 to 2014 in a continuum ice dynamic model Elmer/ice. The obtained basal friction coefficient distributions at different time instances are further used as a boundary condition in a discrete element model (HiDEM) that is capable of computing fracturing of ice. The inverted basal friction coefficient evolution shows a gradual 'unplugging' of the stagnant frontal area and northwards and inland expansion of the fast flowing region in the southern basin. The validation between the modeled crevasses distribution and the satellite observation in August 2013 shows a good agreement in shear zones inland and at the frontal area. Crevasse distributions of the summer before and after the glacier reached its maximum velocity in January 2013 (August 2012 and August 2014, respectively) are also evaluated. Previous studies suggest the triggering and development of the surge are linked to surface melt water penetrating through ice to form an efficient basal hydrology system thereby triggering a hydro- thermodynamic feedback. This preliminary offline coupling between a continuum ice dynamic model and a discrete element model will give a hint on future model development of linking supra-glacial to sub-glacial hydrology system.

Technology Development Risk Assessment for Space Transportation Systems

NASA Technical Reports Server (NTRS)

Mathias, Donovan L.; Godsell, Aga M.; Go, Susie

2006-01-01

A new approach for assessing development risk associated with technology development projects is presented. The method represents technology evolution in terms of sector-specific discrete development stages. A Monte Carlo simulation is used to generate development probability distributions based on statistical models of the discrete transitions. Development risk is derived from the resulting probability distributions and specific program requirements. Two sample cases are discussed to illustrate the approach, a single rocket engine development and a three-technology space transportation portfolio.

A Discrete Events Delay Differential System Model for Transmission of Vancomycin-Resistant Enterococcus (VRE) in Hospitals

DTIC Science & Technology

2010-09-19

estimated directly form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after...hospital infections , is used to motivate possibilities of modeling nosocomial infec- tion dynamics. This is done in the context of hospital monitoring and...model development. Key Words: Delay equations, discrete events, nosocomial infection dynamics, surveil- lance data, inverse problems, parameter

Do factors in the psychosocial work environment mediate the effect of socioeconomic position on the risk of myocardial infarction? Study from the Copenhagen Centre for Prospective Population Studies

PubMed Central

Andersen, I; Burr, H; Kristensen, T; Gamborg, M; Osler, M; Prescott, E; Diderichsen, F

2004-01-01

Aim: To investigate whether the effect of socioeconomic position on risk of myocardial infarction (MI) is mediated by differential exposure or differential susceptibility to psychosocial work environment. Methods: Data were used from three prospective population studies conducted in Copenhagen. A total of 16 214 employees, 44% women, aged 20–75 years, with initial examination between 1974 and 1992 were followed until 1996 for incident (hospital admission or death) MI. Register based information on job categories was used. Psychosocial job exposures were measured indirectly by means of a job exposure matrix based on the Danish Work Environment Cohort Study 1990. Results: During follow up, 731 subjects were diagnosed with an MI: 610 men and 121 women (35% fatal). The hazards by socioeconomic position showed a graded effect with a hazard ratio (HR) of 1.57 (95% CI 1.23 to 2.03) for unskilled workers compared to executive managers. Despite a strong and graded association in risk of MI related to decision authority and skill discretion, only skill discretion mediated the effect of socioeconomic position. The HR for unskilled workers was reduced to 1.47 (0.93 to 2.31) after adjustment for decision authority and other cardiovascular risk factors, and to 1.07 (0.72 to 1.60) after adjustment for skill discretion and cardiovascular risk factors. No sign of synergy was found. Conclusions: Decision authority and skill discretion were strongly related to socioeconomic position; and the effect on risk of MI was partially mediated by skill discretion. Improvements in psychosocial work environment, especially possibilities for skill discretion, might contribute to reducing the incidence of MI and social inequality in MI. PMID:15477281

Quasipolynomial generalization of Lotka-Volterra mappings

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Brenig, Léon

2002-07-01

In recent years, it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as physics, population dynamics, chemistry and economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications.

Introduction to the Difference Calculus through the Fibonacci Numbers

ERIC Educational Resources Information Center

Shannon, A. G.; Atanassov, K. T.

2002-01-01

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

A Simple Derivation of Kepler's Laws without Solving Differential Equations

ERIC Educational Resources Information Center

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Multi-channel temperature measurement amplification system. [solar heating systems

NASA Technical Reports Server (NTRS)

Currie, J. R. (Inventor)

1981-01-01

A number of differential outputs of thermocouples are sequentially amplified by a common amplifier. The amplified outputs are compared with a reference temperature signal in an offset correction amplifier, and a particularly poled output signal is provided when a differential output is of a discrete level compared with a reference temperature signal.

Congestion Pricing for Aircraft Pushback Slot Allocation.

PubMed

Liu, Lihua; Zhang, Yaping; Liu, Lan; Xing, Zhiwei

2017-01-01

In order to optimize aircraft pushback management during rush hour, aircraft pushback slot allocation based on congestion pricing is explored while considering monetary compensation based on the quality of the surface operations. First, the concept of the "external cost of surface congestion" is proposed, and a quantitative study on the external cost is performed. Then, an aircraft pushback slot allocation model for minimizing the total surface cost is established. An improved discrete differential evolution algorithm is also designed. Finally, a simulation is performed on Xinzheng International Airport using the proposed model. By comparing the pushback slot control strategy based on congestion pricing with other strategies, the advantages of the proposed model and algorithm are highlighted. In addition to reducing delays and optimizing the delay distribution, the model and algorithm are better suited for use for actual aircraft pushback management during rush hour. Further, it is also observed they do not result in significant increases in the surface cost. These results confirm the effectiveness and suitability of the proposed model and algorithm.

Delay chemical master equation: direct and closed-form solutions

PubMed Central

Leier, Andre; Marquez-Lago, Tatiana T.

2015-01-01

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616

Delay chemical master equation: direct and closed-form solutions.

PubMed

Leier, Andre; Marquez-Lago, Tatiana T

2015-07-08

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

Maximal aggregation of polynomial dynamical systems

PubMed Central

Cardelli, Luca; Tschaikowski, Max

2017-01-01

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory. PMID:28878023

Congestion Pricing for Aircraft Pushback Slot Allocation

PubMed Central

Zhang, Yaping

2017-01-01

In order to optimize aircraft pushback management during rush hour, aircraft pushback slot allocation based on congestion pricing is explored while considering monetary compensation based on the quality of the surface operations. First, the concept of the “external cost of surface congestion” is proposed, and a quantitative study on the external cost is performed. Then, an aircraft pushback slot allocation model for minimizing the total surface cost is established. An improved discrete differential evolution algorithm is also designed. Finally, a simulation is performed on Xinzheng International Airport using the proposed model. By comparing the pushback slot control strategy based on congestion pricing with other strategies, the advantages of the proposed model and algorithm are highlighted. In addition to reducing delays and optimizing the delay distribution, the model and algorithm are better suited for use for actual aircraft pushback management during rush hour. Further, it is also observed they do not result in significant increases in the surface cost. These results confirm the effectiveness and suitability of the proposed model and algorithm. PMID:28114429

Non-integumentary melanosomes can bias reconstructions of the colours of fossil vertebrate skin

NASA Astrophysics Data System (ADS)

McNamara, Maria; Kaye, Jonathan; Benton, Mike; Orr, Patrick

2017-04-01

The soft tissues of many fossil vertebrates preserve melanosomes - micron-scale organelles used to inform on original integumentary coloration and the evolution of visual signalling strategies through time. In extant vertebrates, however, melanosomes also occur in internal tissues, and hence melanosomes preserved in fossils may not derive solely from the integument. Here, by analyzing the internal tissues of extant and fossil frogs, we show that non-integumentary melanosomes are extremely abundant; they are usually localised to the torso in fossils but can also occur in the limbs, presumably due to dispersal during decay. Melanosomes from the body outlines of fossils cannot, therefore, reliably inform on integumentary coloration. Crucially, non-integumentary and integumentary melanosomes differ in geometry in both fossil and modern frogs and, in fossils, occur as discrete layers. Analysis of melanosome geometry, distribution and size-specific layering is required to differentiate integumentary from non-integumentary melanosomes and is essential to any attempt to reconstruct the original colours of vertebrate skin.

Numerical simulation of inductive method for determining spatial distribution of critical current density

NASA Astrophysics Data System (ADS)

Kamitani, A.; Takayama, T.; Tanaka, A.; Ikuno, S.

2010-11-01

The inductive method for measuring the critical current density jC in a high-temperature superconducting (HTS) thin film has been investigated numerically. In order to simulate the method, a non-axisymmetric numerical code has been developed for analyzing the time evolution of the shielding current density. In the code, the governing equation of the shielding current density is spatially discretized with the finite element method and the resulting first-order ordinary differential system is solved by using the 5th-order Runge-Kutta method with an adaptive step-size control algorithm. By using the code, the threshold current IT is evaluated for various positions of a coil. The results of computations show that, near a film edge, the accuracy of the estimating formula for jC is remarkably degraded. Moreover, even the proportional relationship between jC and IT will be lost there. Hence, the critical current density near a film edge cannot be estimated by using the inductive method.

apterous A specifies dorsal wing patterns and sexual traits in butterflies

PubMed Central

2018-01-01

Butterflies have evolved different colour patterns on their dorsal and ventral wing surfaces to serve different signalling functions, yet the developmental mechanisms controlling surface-specific patterning are still unknown. Here, we mutate both copies of the transcription factor apterous in Bicyclus anynana butterflies using CRISPR/Cas9 and show that apterous A, expressed dorsally, functions both as a repressor and modifier of ventral wing colour patterns, as well as a promoter of dorsal sexual ornaments in males. We propose that the surface-specific diversification of wing patterns in butterflies proceeded via the co-option of apterous A or its downstream effectors into various gene regulatory networks involved in the differentiation of discrete wing traits. Further, interactions between apterous and sex-specific factors such as doublesex may have contributed to the origin of sexually dimorphic surface-specific patterns. Finally, we discuss the evolution of eyespot number diversity in the family Nymphalidae within the context of developmental constraints due to apterous regulation. PMID:29467265

Mean-Potential Law in Evolutionary Games

NASA Astrophysics Data System (ADS)

Nałecz-Jawecki, Paweł; Miekisz, Jacek

2018-01-01

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1 /3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

NASA Astrophysics Data System (ADS)

Liu, Nan; Wen, Xiao-Yong

2018-03-01

Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

The Semigeostrophic Equations Discretized in Reference and Dual Variables

NASA Astrophysics Data System (ADS)

Cullen, Mike; Gangbo, Wilfrid; Pisante, Giovanni

2007-08-01

We study the evolution of a system of n particles {\\{(x_i, v_i)\\}_{i=1}n} in {mathbb{R}^{2d}} . That system is a conservative system with a Hamiltonian of the form {H[μ]=W22(μ, νn)} , where W 2 is the Wasserstein distance and μ is a discrete measure concentrated on the set {\\{(x_i, v_i)\\}_{i=1}n} . Typically, μ(0) is a discrete measure approximating an initial L ∞ density and can be chosen randomly. When d = 1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that the limiting densities are absolutely continuous with respect to the Lebesgue measure. When {\\{ν^n\\}_{n=1}^infty} converges to a measure concentrated on a special d-dimensional set, we obtain the Vlasov-Monge-Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov-Poisson system.

A space-time discretization procedure for wave propagation problems

NASA Technical Reports Server (NTRS)

Davis, Sanford

1989-01-01

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Accelerated Evolution of Developmentally Biased Genes in the Tetraphenic Ant Cardiocondyla obscurior.

PubMed

Schrader, Lukas; Helanterä, Heikki; Oettler, Jan

2017-03-01

Plastic gene expression underlies phenotypic plasticity and plastically expressed genes evolve under different selection regimes compared with ubiquitously expressed genes. Social insects are well-suited models to elucidate the evolutionary dynamics of plastic genes for their genetically and environmentally induced discrete polymorphisms. Here, we study the evolution of plastically expressed genes in the ant Cardiocondyla obscurior-a species that produces two discrete male morphs in addition to the typical female polymorphism of workers and queens. Based on individual-level gene expression data from 28 early third instar larvae, we test whether the same evolutionary dynamics that pertain to plastically expressed genes in adults also pertain to genes with plastic expression during development. In order to quantify plasticity of gene expression over multiple contrasts, we develop a novel geometric measure. For genes expressed during development, we show that plasticity of expression is positively correlated with evolutionary rates. We furthermore find a strong correlation between expression plasticity and expression variation within morphs, suggesting a close link between active and passive plasticity of gene expression. Our results support the notion of relaxed selection and neutral processes as important drivers in the evolution of adaptive plasticity. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity

NASA Astrophysics Data System (ADS)

Höhn, P. A.

2012-05-01

In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this thesis, the conundrum of (quantum) gravitational dynamics is approached from two different directions by means of new canonical tools. This thesis is accordingly divided into two parts: In the first part, a general canonical formalism for discrete systems featuring a variational action principle is developed which is equivalent to the covariant formulation following directly from the action. This formalism can handle evolving phase spaces and is thus appropriate for describing evolving lattices. Attention will be devoted to a characterization of the constraints, symmetries and degrees of freedom appearing in such discrete systems which, in the case of evolving phase spaces, is time step dependent. The advantage of this formalism is that it does not depend on the particular discretization and, hence, is suitable for coarse graining procedures. This formalism is applicable to discrete mechanics, lattice field theories and discrete gravity models---underlying some approaches to quantum gravity---and, furthermore, may prove useful for numerical imple mentations. For concreteness, these new tools are employed to formulate Regge Calculus canonically as a theory of the dynamics of discrete hypersurfaces in discrete spacetimes, thereby removing a longstanding obstacle to connecting covariant simplicial gravity models with canonical frameworks. This result is interesting in view of several background independent approaches to quantum gravity. In addition, perturbative expansions around symmetric background solutions of Regge Calculus are studied up to second order. Background gauge modes generically become propagating at second order as a consequence of a symmetry breaking. In the second part of this thesis, the paradigm of relational dynamics is considered. Dynamical observables in gravity are relational. Unfortunately, their construction and evaluation is notoriously difficult, especially in the quantum theory. An effective canonical framework is devised which permits to evaluate the semiclassical relational dynamics of constrained quantum systems by sidestepping technical problems associated with explicit constructions of physical Hilbert spaces. This effective approach is well-geared for addressing the concept of relational evolution in general quantum cosmological models since it (i) allows to depart from idealized relational `clock references’ and, instead, to employ generic degrees of freedom as imperfect relational `clocks’, (ii) enables one to systematically switch between different such `clocks’ and (iii) yields a consistent (temporally) local time evolution with transient observables so long as semiclassicality holds. These techniques are illustrated by toy models and, finally, are applied to a non-integrable cosmological model. It is argued that relational evolution is generically only a transient and semiclassical phenomenon

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

A homogenization-based quasi-discrete method for the fracture of heterogeneous materials

NASA Astrophysics Data System (ADS)

Berke, P. Z.; Peerlings, R. H. J.; Massart, T. J.; Geers, M. G. D.

2014-05-01

The understanding and the prediction of the failure behaviour of materials with pronounced microstructural effects is of crucial importance. This paper presents a novel computational methodology for the handling of fracture on the basis of the microscale behaviour. The basic principles presented here allow the incorporation of an adaptive discretization scheme of the structure as a function of the evolution of strain localization in the underlying microstructure. The proposed quasi-discrete methodology bridges two scales: the scale of the material microstructure, modelled with a continuum type description; and the structural scale, where a discrete description of the material is adopted. The damaging material at the structural scale is divided into unit volumes, called cells, which are represented as a discrete network of points. The scale transition is inspired by computational homogenization techniques; however it does not rely on classical averaging theorems. The structural discrete equilibrium problem is formulated in terms of the underlying fine scale computations. Particular boundary conditions are developed on the scale of the material microstructure to address damage localization problems. The performance of this quasi-discrete method with the enhanced boundary conditions is assessed using different computational test cases. The predictions of the quasi-discrete scheme agree well with reference solutions obtained through direct numerical simulations, both in terms of crack patterns and load versus displacement responses.

Does Geophysics Need "A new kind of Science"?

NASA Astrophysics Data System (ADS)

Turcotte, D. L.; Rundle, J. B.

2002-12-01

Stephen Wolfram's book "A New Kind of Science" has received a great deal of attention in the last six months, both positive and negative. The theme of the book is that "cellular automata", which arise from spatial and temporal coarse-graining of equations of motion, provide the foundations for a new nonlinear science of "complexity". The old science is the science of partial differential equations. Some of the major contributions of this old science have been in geophysics, i.e. gravity, magnetics, seismic waves, heat flow. The basis of the new science is the use of massive computing and numerical simulations. The new science is motivated by the observations that many physical systems display a vast multiplicity of space and time scales, and have hidden dynamics that in many cases are impossible to directly observe. An example would be molecular dynamics. Statistical physics derives continuum equations from the discrete interactions between atoms and molecules, in the modern world the continuum equations are then discretized using finite differences, finite elements, etc. in order to obtain numerical solutions. Examples of widely used cellular automata models include diffusion limited aggregation and site percolation. Also the class of models that are said to exhibit self-organized criticality, the sand-pile model, the slider-block model, the forest-fire model. Applications of these models include drainage networks, seismicity, distributions of minerals,and the evolution of landforms and coastlines. Simple cellular automata models generate deterministic chaos, i.e. the logistic map.

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

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

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

A Wave Diagnostics in Geophysics: Algorithmic Extraction of Atmosphere Disturbance Modes

NASA Astrophysics Data System (ADS)

Leble, S.; Vereshchagin, S.

2018-04-01

The problem of diagnostics in geophysics is discussed and a proposal based on dynamic projecting operators technique is formulated. The general exposition is demonstrated by an example of symbolic algorithm for the wave and entropy modes in the exponentially stratified atmosphere. The novel technique is developed as a discrete version for the evolution operator and the corresponding projectors via discrete Fourier transformation. Its explicit realization for directed modes in exponential one-dimensional atmosphere is presented via the correspondent projection operators in its discrete version in terms of matrices with a prescribed action on arrays formed from observation tables. A simulation based on opposite directed (upward and downward) wave train solution is performed and the modes' extraction from a mixture is illustrated.

An Unsplit Monte-Carlo solver for the resolution of the linear Boltzmann equation coupled to (stiff) Bateman equations

NASA Astrophysics Data System (ADS)

Bernede, Adrien; Poëtte, Gaël

2018-02-01

In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a medium whose composition evolves with time due to interactions. As a constraint, we want to use of Monte-Carlo (MC) scheme for the transport phase. A common resolution strategy consists in a splitting between the MC/transport phase and the time discretization scheme/medium evolution phase. After going over and illustrating the main drawbacks of split solvers in a simplified configuration (monokinetic, scalar Bateman problem), we build a new Unsplit MC (UMC) solver improving the accuracy of the solutions, avoiding numerical instabilities, and less sensitive to time discretization. The new solver is essentially based on a Monte Carlo scheme with time dependent cross sections implying the on-the-fly resolution of a reduced model for each MC particle describing the time evolution of the matter along their flight path.

On the vacuum Einstein equations along curves with a discrete local rotation and reflection symmetry

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

Korzyński, Mikołaj; Hinder, Ian; Bentivegna, Eloisa, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: eloisa.bentivegna@ct.infn.it

We discuss the possibility of a dimensional reduction of the Einstein equations in S{sup 3} black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotation and reflection symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accountsmore » for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation.« less

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph

2015-09-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces.

On the Definition of Surface Potentials for Finite-Difference Operators

NASA Technical Reports Server (NTRS)

Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

Solving SAT Problem Based on Hybrid Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan

Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.

Shape Optimization of Rubber Bushing Using Differential Evolution Algorithm

PubMed Central

2014-01-01

The objective of this study is to design rubber bushing at desired level of stiffness characteristics in order to achieve the ride quality of the vehicle. A differential evolution algorithm based approach is developed to optimize the rubber bushing through integrating a finite element code running in batch mode to compute the objective function values for each generation. Two case studies were given to illustrate the application of proposed approach. Optimum shape parameters of 2D bushing model were determined by shape optimization using differential evolution algorithm. PMID:25276848

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia.

PubMed

Gaudiano, Marcos E; Lenaerts, Tom; Pacheco, Jorge M

2016-12-01

Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can - on average - easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system. Copyright © 2016 Elsevier Inc. All rights reserved.

Template-free synthesis and structural evolution of discrete hydroxycancrinite zeolite nanorods from high-concentration hydrogels.

PubMed

Chen, Shaojiang; Sorge, Lukas P; Seo, Dong-Kyun

2017-12-07

We report the synthesis and characterization of hydroxycancrinite zeolite nanorods by a simple hydrothermal treatment of aluminosilicate hydrogels at high concentrations of precursors without the use of structure-directing agents. Transmission electron microscopy (TEM) analysis reveals that cancrinite nanorods, with lengths of 200-800 nm and diameters of 30-50 nm, exhibit a hexagonal morphology and are elongated along the crystallographic c direction. The powder X-ray diffraction (PXRD), Fourier transform infrared (FT-IR) and TEM studies revealed sequential events of hydrogel formation, the formation of aggregated sodalite nuclei, the conversion of sodalite to cancrinite and finally the growth of cancrinite nanorods into discrete particles. The aqueous dispersion of the discrete nanorods displays a good stability between pH 6-12 with the zeta potential no greater than -30 mV. The synthesis is unique in that the initial aggregated nanocrystals do not grow into microsized particles (aggregative growth) but into discrete nanorods. Our findings demonstrate an unconventional possibility that discrete zeolite nanocrystals could be produced from a concentrated hydrogel.

Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

NASA Astrophysics Data System (ADS)

Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

2017-11-01

In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

PubMed

Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L

2016-09-01

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

A hybrid model of cell cycle in mammals.

PubMed

Behaegel, Jonathan; Comet, Jean-Paul; Bernot, Gilles; Cornillon, Emilien; Delaunay, Franck

2016-02-01

Time plays an essential role in many biological systems, especially in cell cycle. Many models of biological systems rely on differential equations, but parameter identification is an obstacle to use differential frameworks. In this paper, we present a new hybrid modeling framework that extends René Thomas' discrete modeling. The core idea is to associate with each qualitative state "celerities" allowing us to compute the time spent in each state. This hybrid framework is illustrated by building a 5-variable model of the mammalian cell cycle. Its parameters are determined by applying formal methods on the underlying discrete model and by constraining parameters using timing observations on the cell cycle. This first hybrid model presents the most important known behaviors of the cell cycle, including quiescent phase and endoreplication.

Mean-Potential Law in Evolutionary Games.

PubMed

Nałęcz-Jawecki, Paweł; Miękisz, Jacek

2018-01-12

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1/3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

Parrondo's game using a discrete-time quantum walk

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.; Banerjee, Subhashish

2011-04-01

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A ( B) to have a winning probability more than player B ( A). Significance of the game strategy in information theory and physical applications are also discussed.

Analyzing neuronal networks using discrete-time dynamics

NASA Astrophysics Data System (ADS)

Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David

2010-05-01

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Evolution of specialization in resource utilization in structured metapopulations.

PubMed

Nurmi, Tuomas; Geritz, Stefan; Parvinen, Kalle; Gyllenberg, Mats

2008-07-01

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.

Joint evolution of specialization and dispersal in structured metapopulations.

PubMed

Nurmi, Tuomas; Parvinen, Kalle

2011-04-21

We study the joint evolution of dispersal and specialization concerning resource usage in a mechanistically underpinned structured discrete-time metapopulation model. We show that dispersal significantly affects the evolution of specialization and that specialization is a key factor that determines the possibility of evolutionary branching in dispersal propensity. Allowing both dispersal propensity and specialization to evolve as a consequence of natural selection is necessary in order to understand the evolutionary dynamics. The joint evolution of dispersal and specialization forms a natural evolutionary path leading to the coexistence of generalists and specialists. We show that in this process, the number of different patch types and the resource distribution are essential. Copyright © 2011 Elsevier Ltd. All rights reserved.

Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

PubMed Central

Gong, Haijun; Guo, Yusong; Linstedt, Adam

2017-01-01

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi—a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model—each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor SNARE proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size. PMID:20365406

Taking side effects into account for HIV medication.

PubMed

Costanza, Vicente; Rivadeneira, Pablo S; Biafore, Federico L; D'Attellis, Carlos E

2010-09-01

A control-theoretic approach to the problem of designing "low-side-effects" therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side effects during treatment is modeled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones. The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient and on the evolution of the viral load detected by periodical blood analysis. The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral morbidities caused by the medication. The optimization problem is solved by a hybrid dynamic programming scheme that adhere to discrete-time observation and control actions, but by maintaining the continuous-time setup for predicting states and side effects. The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months. If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterward, thus causing an apparent stabilization of the main variables. But in this case, the final viral load turns higher than acceptable.

The evolution and expression of the snaR family of small non-coding RNAs

PubMed Central

Parrott, Andrew M.; Tsai, Michael; Batchu, Priyanka; Ryan, Karen; Ozer, Harvey L.; Tian, Bin; Mathews, Michael B.

2011-01-01

We recently identified the snaR family of small non-coding RNAs that associate in vivo with the nuclear factor 90 (NF90/ILF3) protein. The major human species, snaR-A, is an RNA polymerase III transcript with restricted tissue distribution and orthologs in chimpanzee but not rhesus macaque or mouse. We report their expression in human tissues and their evolution in primates. snaR genes are exclusively in African Great Apes and some are unique to humans. Two novel families of snaR-related genetic elements were found in primates: CAS (catarrhine ancestor of snaR), limited to Old World Monkeys and apes; and ASR (Alu/snaR-related), present in all monkeys and apes. ASR and CAS appear to have spread by retrotransposition, whereas most snaR genes have spread by segmental duplication. snaR-A and snaR-G2 are differentially expressed in discrete regions of the human brain and other tissues, notably including testis. snaR-A is up-regulated in transformed and immortalized human cells, and is stably bound to ribosomes in HeLa cells. We infer that snaR evolved from the left monomer of the primate-specific Alu SINE family via ASR and CAS in conjunction with major primate speciation events, and suggest that snaRs participate in tissue- and species-specific regulation of cell growth and translation. PMID:20935053

A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

NASA Technical Reports Server (NTRS)

Weng, Fuzhong

1992-01-01

A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.

Nonconforming mortar element methods: Application to spectral discretizations

NASA Technical Reports Server (NTRS)

Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

1988-01-01

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

NASA Astrophysics Data System (ADS)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Cloud computing task scheduling strategy based on improved differential evolution algorithm

NASA Astrophysics Data System (ADS)

Ge, Junwei; He, Qian; Fang, Yiqiu

2017-04-01

In order to optimize the cloud computing task scheduling scheme, an improved differential evolution algorithm for cloud computing task scheduling is proposed. Firstly, the cloud computing task scheduling model, according to the model of the fitness function, and then used improved optimization calculation of the fitness function of the evolutionary algorithm, according to the evolution of generation of dynamic selection strategy through dynamic mutation strategy to ensure the global and local search ability. The performance test experiment was carried out in the CloudSim simulation platform, the experimental results show that the improved differential evolution algorithm can reduce the cloud computing task execution time and user cost saving, good implementation of the optimal scheduling of cloud computing tasks.

Discrete shear-transformation-zone plasticity modeling of notched bars

NASA Astrophysics Data System (ADS)

Kondori, Babak; Amine Benzerga, A.; Needleman, Alan

2018-02-01

Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear transformation zone plasticity. In this framework, the carriers of plastic deformation are shear transformation zones (STZs) which are modeled as Eshelby inclusions. Superposition is used to represent a boundary value problem solution in terms of discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.

Evolution of the Contact Area with Normal Load for Rough Surfaces: from Atomic to Macroscopic Scales.

PubMed

Huang, Shiping

2017-11-13

The evolution of the contact area with normal load for rough surfaces has great fundamental and practical importance, ranging from earthquake dynamics to machine wear. This work bridges the gap between the atomic scale and the macroscopic scale for normal contact behavior. The real contact area, which is formed by a large ensemble of discrete contacts (clusters), is proven to be much smaller than the apparent surface area. The distribution of the discrete contact clusters and the interaction between them are key to revealing the mechanism of the contacting solids. To this end, Green's function molecular dynamics (GFMD) is used to study both how the contact cluster evolves from the atomic scale to the macroscopic scale and the interaction between clusters. It is found that the interaction between clusters has a strong effect on their formation. The formation and distribution of the contact clusters is far more complicated than that predicted by the asperity model. Ignorance of the interaction between them leads to overestimating the contacting force. In real contact, contacting clusters are smaller and more discrete due to the interaction between the asperities. Understanding the exact nature of the contact area with the normal load is essential to the following research on friction.

Evolution of the Contact Area with Normal Load for Rough Surfaces: from Atomic to Macroscopic Scales

NASA Astrophysics Data System (ADS)

Huang, Shiping

2017-11-01

The evolution of the contact area with normal load for rough surfaces has great fundamental and practical importance, ranging from earthquake dynamics to machine wear. This work bridges the gap between the atomic scale and the macroscopic scale for normal contact behavior. The real contact area, which is formed by a large ensemble of discrete contacts (clusters), is proven to be much smaller than the apparent surface area. The distribution of the discrete contact clusters and the interaction between them are key to revealing the mechanism of the contacting solids. To this end, Green's function molecular dynamics (GFMD) is used to study both how the contact cluster evolves from the atomic scale to the macroscopic scale and the interaction between clusters. It is found that the interaction between clusters has a strong effect on their formation. The formation and distribution of the contact clusters is far more complicated than that predicted by the asperity model. Ignorance of the interaction between them leads to overestimating the contacting force. In real contact, contacting clusters are smaller and more discrete due to the interaction between the asperities. Understanding the exact nature of the contact area with the normal load is essential to the following research on friction.

T Cell Receptor Signaling in the Control of Regulatory T Cell Differentiation and Function

PubMed Central

Li, Ming O.; Rudensky, Alexander Y.

2016-01-01

Regulatory T cells (TReg cells), a specialized T cell lineage, have a pivotal function in the control of self-tolerance and inflammatory responses. Recent studies have revealed a discrete mode of TCR signaling that regulates Treg cell differentiation, maintenance and function and that impacts on gene expression, metabolism, cell adhesion and migration of these cells. Here, we discuss the emerging understanding of TCR-guided differentiation of Treg cells in the context of their function in health and disease. PMID:27026074

Stochastic Differential Games with Complexity Constrained Strategies.

DTIC Science & Technology

1982-03-01

Stochastic Differential Game ..... . 39 2.-1 A b.mp.C mcamp e ..... .... ................ . ..... qu CHAPTER 3 - PROBLEM OF STATE ESTDAATION IN TWO...similar to that used vith the differential game , e vould find that the optimal K has the form K T[T* + ( 2.58) This is not a surprising ansver in viev...Examle Example: Discrete-time, one-stage scalar game Transition equation: Y X + U - V P-offtfuntinl: J E + {5 2 CV Cc~ c>a> 0 Observation equations: Z x

CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane

2006-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations, just as differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as: mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang-Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either •contain significant additional new results and/or insights or •give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. Guidelines for preparation of contributions • The deadline for contributed papers will be 15 January 2007. •There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa •Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue: SIDE VII'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. •Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting 'J. Phys. A Special Issue: SIDE VII'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. •The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

NASA Astrophysics Data System (ADS)

Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek

2018-01-01

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.

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.

Improved Discretization of Grounding Lines and Calving Fronts using an Embedded-Boundary Approach in BISICLES

NASA Astrophysics Data System (ADS)

Martin, D. F.; Cornford, S. L.; Schwartz, P.; Bhalla, A.; Johansen, H.; Ng, E.

2017-12-01

Correctly representing grounding line and calving-front dynamics is of fundamental importance in modeling marine ice sheets, since the configuration of these interfaces exerts a controlling influence on the dynamics of the ice sheet. Traditional ice sheet models have struggled to correctly represent these regions without very high spatial resolution. We have developed a front-tracking discretization for grounding lines and calving fronts based on the Chombo embedded-boundary cut-cell framework. This promises better representation of these interfaces vs. a traditional stair-step discretization on Cartesian meshes like those currently used in the block-structured AMR BISICLES code. The dynamic adaptivity of the BISICLES model complements the subgrid-scale discretizations of this scheme, producing a robust approach for tracking the evolution of these interfaces. Also, the fundamental discontinuous nature of flow across grounding lines is respected by mathematically treating it as a material phase change. We present examples of this approach to demonstrate its effectiveness.

kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP

DTIC Science & Technology

2007-01-01

differentiability, fluid-solid interaction, error estimation, re-discretization, moving meshes 16. SECURITY CLASSIFICATION OF: 17 . LIMITATION OF 18. NUMBER...method the weight function is an indepen- dent function v = 0 6 4Ph , with v = 0 on F, if W = W0 on F1. 2. Galerkin method (GM): If Wh is an approximation...This can be demonstrated by considering a simple I-D case (like described above) in which the discretization 17 is uniform with characteristic length

Optimization of Operations Resources via Discrete Event Simulation Modeling

NASA Technical Reports Server (NTRS)

Joshi, B.; Morris, D.; White, N.; Unal, R.

1996-01-01

The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.

Competition drives trait evolution and character displacement between Mimulus species along an environmental gradient.

PubMed

Kooyers, Nicholas J; James, Brooke; Blackman, Benjamin K

2017-05-01

Closely related species may evolve to coexist stably in sympatry through niche differentiation driven by in situ competition, a process termed character displacement. Alternatively, past evolution in allopatry may have already sufficiently reduced niche overlap to permit establishment in sympatry, a process called ecological sorting. The relative importance of each process to niche differentiation is contentious even though they are not mutually exclusive and are both mediated via multivariate trait evolution. We explore how competition has impacted niche differentiation in two monkeyflowers, Mimulus alsinoides and M. guttatus, which often co-occur. Through field observations, common gardens, and competition experiments, we demonstrate that M. alsinoides is restricted to marginal habitats in sympatry and that the impacts of character displacement on niche differentiation are complex. Competition with M. guttatus alters selection gradients and has favored taller M. alsinoides with earlier seasonal flowering at low elevation and floral shape divergence at high elevation. However, no trait exhibits the pattern typically associated with character displacement, higher divergence between species in sympatry than allopatry. Thus, although character displacement was unlikely the process driving initial divergence along niche axes necessary for coexistence, we conclude that competition in sympatry has likely driven trait evolution along additional niche axes. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Application of differential evolution algorithm on self-potential data.

PubMed

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods.

Application of Differential Evolution Algorithm on Self-Potential Data

PubMed Central

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods. PMID:23240004

Characteristics and Significance of Magma Emplacement Horizons, Black Sturgeon Sill, Nipigon, Ontario

NASA Astrophysics Data System (ADS)

Zieg, M. J.; Hone, S. V.

2017-12-01

Spatial scales strongly control the timescales of processes in igneous intrusions, particularly through the thermal evolution of the magma, which in turn governs the evolution of crystallinity, viscosity, and other important physical and chemical properties of the system. In this study, we have collected a highly detailed data set comprising geochemical (bulk rock composition), textural (size and alignment of plagioclase crystals), and mineralogical (modal abundance) profiles through the central portion of the 250 m thick Black Sturgeon diabase sill. In this data, we have identified characteristic signals in texture (soft and somewhat diffuse chills), composition (reversals in differentiation trends), and mineralogy (olivine accumulations), all coinciding and recurring at roughly 10 meter intervals. Based on these signatures, we are able to map out multiple zones representing discrete pulses of magma that were emplaced sequentially as the intrusion was inflated. Simple thermal calculations suggest that each 10 meters of new crystallization would require repose times on the order of 10-100 years. To build up 250 meters of magma at this rate would only require approximately 250-2500 years, significantly less than the thermal lifetime of the entire sill. The soft chills we observe in the Black Sturgeon sill are therefore consistent with a system that remained warm throughout the emplacement process. Successive pulses were injected into partially crystalline mush, rather than pure liquid (which would result in hybridization) or solid (which would produce sharp hard chills). Episodic emplacement is by now widely recognized as a fundamental process in the formation of large felsic magma chambers; our results suggest that this also may be an important consideration in understanding the evolution of smaller mafic intrusions.

Wrinkling pattern evolution of cylindrical biological tissues with differential growth.

PubMed

Jia, Fei; Li, Bo; Cao, Yan-Ping; Xie, Wei-Hua; Feng, Xi-Qiao

2015-01-01

Three-dimensional surface wrinkling of soft cylindrical tissues induced by differential growth is explored. Differential volumetric growth can cause their morphological stability, leading to the formation of hexagonal and labyrinth wrinkles. During postbuckling, multiple bifurcations and morphological transitions may occur as a consequence of continuous growth in the surface layer. The physical mechanisms underpinning the morphological evolution are examined from the viewpoint of energy. Surface curvature is found to play a regulatory role in the pattern evolution. This study may not only help understand the morphogenesis of soft biological tissues, but also inspire novel routes for creating desired surface patterns of soft materials.

Automatic Clustering Using FSDE-Forced Strategy Differential Evolution

NASA Astrophysics Data System (ADS)

Yasid, A.

2018-01-01

Clustering analysis is important in datamining for unsupervised data, cause no adequate prior knowledge. One of the important tasks is defining the number of clusters without user involvement that is known as automatic clustering. This study intends on acquiring cluster number automatically utilizing forced strategy differential evolution (AC-FSDE). Two mutation parameters, namely: constant parameter and variable parameter are employed to boost differential evolution performance. Four well-known benchmark datasets were used to evaluate the algorithm. Moreover, the result is compared with other state of the art automatic clustering methods. The experiment results evidence that AC-FSDE is better or competitive with other existing automatic clustering algorithm.

Discrete X-Ray Source Populations and Star Formation History in Nearby Galaxies

NASA Technical Reports Server (NTRS)

Zezas, Andreas; Hasan, Hashima (Technical Monitor)

2005-01-01

This program aims in understanding the connection between the discrete X-ray source populations observed in nearby galaxies and the history of star-formation in these galaxies. The ultimate goal is to use this knowledge in order to constrain X-ray binary evolution channels. For this reason although the program is primarily observational it has a significant modeling component. During the second year of this study we focused on detailed studies of the Antennae galaxies and the Small Magellanic Cloud (SMC). We also performed the initial analysis of the 5 galaxies forming a starburst-age sequence.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Estimating Topology of Discrete Dynamical Networks

NASA Astrophysics Data System (ADS)

Guo, Shu-Juan; Fu, Xin-Chu

2010-07-01

In this paper, by applying Lasalle's invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, two examples, including a Hénon map and a central network, are illustrated to verify the theoretical results.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Evolution of tuf genes: ancient duplication, differential loss and gene conversion.

PubMed

Lathe, W C; Bork, P

2001-08-03

The tuf gene of eubacteria, encoding the EF-tu elongation factor, was duplicated early in the evolution of the taxon. Phylogenetic and genomic location analysis of 20 complete eubacterial genomes suggests that this ancient duplication has been differentially lost and maintained in eubacteria.

The Complete Mitochondrial Genome and Song Evolution of the Monotypic Genus U. Tarbinsky, 1932 (Orthoptera: Tettigoniidae).

PubMed

Wang, Yinliang; Zhao, Hanbo; Zhang, Xue; Ren, Bingzhong

2016-04-23

The insect Uvarovites inflatus Uvarov is highly appreciated in China. It is known for its distinctive songs and horn-like forewings and is raised commercially for insect lovers. U. inflatus was previously categorized as part of the monotypic genus Uvarovites; however, there was little molecular evidence to support this taxonomic classification. This study obtained and investigated the mitogenome of U. inflatus, and its songs were characterized and compared with other Ensifera species whose mitogenomes are available. By performing the mitochondrial analysis, we were able to assess the phylogenetic relationships between these species and discuss the evolution of Ensifera calling songs. The mitogenome of U. inflatus is 15,956 bp in length and contains 13 protein-coding genes, 22 tRNA genes, 2 rRNA genes, and 1 control region. The organization and orientation of the U. inflatus mitogenome are similar to those of other Tettigonioidea species. Phylogenetic analysis based on 13 protein-coding genes showed that the superfamily Tettigonioidea is monophyletic, as are the other six tested subfamilies from Tettigonioidea. Our results also indicated that Grylloidea is monophyletic. A Bayesian relaxed clock analysis showed that the differentiation of U. inflatus and Gampsocleis gratiosa Brunner occurred in the middle Miocene, suggesting that their speciation occurred over a long evolutionary period. The results provide significant support for the establishment of the monotypic genus Uvarovites. Calling song analysis showed that at least two discrete steps of independent evolution occurred during the change from pure tone to broadband noise, and that the ancestor of existing Ensifera was more likely to have emitted pure-tone songs than broadband signals. Together, the mitogenome, molecular clock, and acoustic data allowed us to clarify the taxonomic state of U. inflatus and propose a timeline for the evolution of Ensifera songs. © The Authors 2016. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Prediction of discretization error using the error transport equation

NASA Astrophysics Data System (ADS)

Celik, Ismail B.; Parsons, Don Roscoe

2017-06-01

This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier-Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the 'true error'. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process.

PubMed

Greenman, C D; Cooke, S L; Marshall, J; Stratton, M R; Campbell, P J

2016-01-01

Breakage-fusion-bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. Here we study the evolution space of breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are [Formula: see text] qualitatively distinct evolutions involving [Formula: see text] breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the process to show these evolutions are not equally likely, and also describe how amplicons become localized. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples.

Lattice Wigner equation.

PubMed

Solórzano, S; Mendoza, M; Succi, S; Herrmann, H J

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Lattice Wigner equation

NASA Astrophysics Data System (ADS)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Numerical modeling of fold-and-thrust belts: Applications to Kuqa foreland fold belt, China

NASA Astrophysics Data System (ADS)

Yin, H.; Morgan, J. K.; Zhang, J.; Wang, Z.

2009-12-01

We constructed discrete element models to simulate the evolution of fold-and-thrust belts. The impact of rock competence and decollement strength on the geometric pattern and deformation mechanics of fold-and-thrust belts has been investigated. The models reproduced some characteristic features of fold-and-thrust belts, such as faulted detachment folds, pop-ups, far-traveled thrust sheets, passive-roof duplexes, and back thrusts. In general, deformation propagates farther above a weak decollement than above a strong decollement. Our model results confirm that fold-and-thrust belts with strong frictional decollements develop relatively steep and narrow wedges formed by closely spaced imbricate thrust slices, whereas fold belts with weak decollements form wide low-taper wedges composed of faulted detachment folds, pop-ups, and back thrusts. Far-traveled thrust sheets and passive-roof duplexes are observed in the model with a strong lower decollement and a weak upper detachment. Model results also indicate that the thickness of the weak layer is critical. If it is thick enough, it acts as a ductile layer that is able to flow under differential stress, which helps to partition deformation above and below it. The discrete element modeling results were used to interpret the evolution of Kuqa Cenozoic fold-and-thrust belt along northern Tarim basin, China. Seismic and well data show that the widely distributed Paleogene rock salt has a significant impact on the deformation in this area. Structures beneath salt are closely spaced imbricate thrust and passive-roof duplex systems. Deformation above salt propagates much farther than below the salt. Faults above salt are relatively wide spaced. A huge controversy over the Kuqa fold-and-thrust belt is whether it is thin-skinned or thick-skinned. With the insights from DEM results, we suggest that Kuqa structures are mostly thin-skinned with Paleogene salt as decollement, except for the rear part near the backstop, where the faults below the salt are thick-skinned and involve the Paleozoic basement. We think that most basement-involved sub-salt faults, if not all, formed later than the above salt-detached thin-skinned structures.

Phytoplasma genomes: Evolution through mutually complimentary mechanisms, gene loss and horizontal acquisition

USDA-ARS?s Scientific Manuscript database

Phytoplasmas possess the smallest genomes known among plant pathogens. Yet, these biotrophic microbes exist as obligate parasites and pathogens of both plants and insects. After their evolutionary divergence from an acholeplasmalike ancestor and emergence as a discrete clade, phytoplasmas ev...

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

PubMed Central

Bianconi, Ginestra; Rahmede, Christoph

2015-01-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces. PMID:26356079

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free.

PubMed

Bianconi, Ginestra; Rahmede, Christoph

2015-09-10

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension d. We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the δ-faces of the d-dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the δ-faces.

Markov-modulated Markov chains and the covarion process of molecular evolution.

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

Computing anticipatory systems with incursion and hyperincursion

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

1998-07-01

An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

Contemporary evolution during invasion: evidence for differentiation, natural selection, and local adaptation.

PubMed

Colautti, Robert I; Lau, Jennifer A

2015-05-01

Biological invasions are 'natural' experiments that can improve our understanding of contemporary evolution. We evaluate evidence for population differentiation, natural selection and adaptive evolution of invading plants and animals at two nested spatial scales: (i) among introduced populations (ii) between native and introduced genotypes. Evolution during invasion is frequently inferred, but rarely confirmed as adaptive. In common garden studies, quantitative trait differentiation is only marginally lower (~3.5%) among introduced relative to native populations, despite genetic bottlenecks and shorter timescales (i.e. millennia vs. decades). However, differentiation between genotypes from the native vs. introduced range is less clear and confounded by nonrandom geographic sampling; simulations suggest this causes a high false-positive discovery rate (>50%) in geographically structured populations. Selection differentials (¦s¦) are stronger in introduced than in native species, although selection gradients (¦β¦) are not, consistent with introduced species experiencing weaker genetic constraints. This could facilitate rapid adaptation, but evidence is limited. For example, rapid phenotypic evolution often manifests as geographical clines, but simulations demonstrate that nonadaptive trait clines can evolve frequently during colonization (~two-thirds of simulations). Additionally, QST-FST studies may often misrepresent the strength and form of natural selection acting during invasion. Instead, classic approaches in evolutionary ecology (e.g. selection analysis, reciprocal transplant, artificial selection) are necessary to determine the frequency of adaptive evolution during invasion and its influence on establishment, spread and impact of invasive species. These studies are rare but crucial for managing biological invasions in the context of global change. © 2015 John Wiley & Sons Ltd.

Microscopic models for the study of taxpayer audit effects

NASA Astrophysics Data System (ADS)

Bertotti, Maria Letizia; Modanese, Giovanni

2016-03-01

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the audited taxpayer fraction and of the penalties imposed to noncompliant individuals. A complex systems perspective is adopted: society is considered as a system composed by a large number of heterogeneous individuals. These are divided into income classes and may as well have different tax evasion behaviors. The variation in time of the number of individuals in each class is described by a system of nonlinear differential equations of the kinetic discretized Boltzmann type involving transition probabilities. A priori, one could think that audits and fines should have a positive effect on the reduction of economic inequality and correspondingly of the Gini index G. According to our model, however, such effect is rather small. In contrast, the effect on the increase of the tax revenue may be significant.

Evolution of Subaerial Coastal Fluvial Delta Island Topography into Multiple Stable States Under Influence of Vegetation and Stochastic Hydrology

NASA Astrophysics Data System (ADS)

Moffett, K. B.; Smith, B. C.; O'Connor, M.; Mohrig, D. C.

2014-12-01

Coastal fluvial delta morphodynamics are prominently controlled by external fluvial sediment and water supplies; however, internal sediment-water-vegetation feedbacks are now being proposed as potentially equally significant in organizing and maintaining the progradation and aggradation of such systems. The time scales of fluvial and climate influences on these feedbacks, and of their responses, are also open questions. Historical remote sensing study of the Wax Lake Delta model system (Louisiana, USA) revealed trends in the evolution of the subaerial island surfaces from a non-systematic arrangement of elevations to a discrete set of levees and intra-island platforms with distinct vegetation types, designated as high marsh, low marsh, and mudflat habitat. We propose that this elevation zonation is consistent with multiple stable state theory, e.g. as applied to tidal salt marsh systems but not previously to deltas. According to zonally-distributed sediment core analyses, differentiation of island elevations was not due to organic matter accumulation as in salt marshes, but rather by differential mineral sediment accumulation with some organic contributions. Mineral sediment accumulation rates suggested that elevation growth was accelerating or holding steady over time, at least to date in this young delta, in contrast to theory suggesting rates should slow as elevation increases above mean water level. Hydrological analysis of island flooding suggested a prominent role of stochastic local storm events in raising island water levels and supplying mineral sediment to the subaerial island surfaces at short time scales; over longer time scales, the relative influences of local storms and inland/regional floods on the coupled sediment-water-vegetation system of the subaerial delta island surfaces remain the subject of ongoing study. These results help provide an empirical foundation for the next generation of coupled sediment-water-vegetation modeling and theory.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

NASA Astrophysics Data System (ADS)

Ravi Kanth, A. S. V.; Aruna, K.

2016-12-01

In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

Finite-difference models of ordinary differential equations - Influence of denominator functions

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.; Smith, Arthur

1990-01-01

This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Fourth-order partial differential equation noise removal on welding images

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

Halim, Suhaila Abd; Ibrahim, Arsmah; Sulong, Tuan Nurul Norazura Tuan

2015-10-22

Partial differential equation (PDE) has become one of the important topics in mathematics and is widely used in various fields. It can be used for image denoising in the image analysis field. In this paper, a fourth-order PDE is discussed and implemented as a denoising method on digital images. The fourth-order PDE is solved computationally using finite difference approach and then implemented on a set of digital radiographic images with welding defects. The performance of the discretized model is evaluated using Peak Signal to Noise Ratio (PSNR). Simulation is carried out on the discretized model on different level of Gaussianmore » noise in order to get the maximum PSNR value. The convergence criteria chosen to determine the number of iterations required is measured based on the highest PSNR value. Results obtained show that the fourth-order PDE model produced promising results as an image denoising tool compared with median filter.« less

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

An adaptively refined phase-space element method for cosmological simulations and collisionless dynamics

NASA Astrophysics Data System (ADS)

Hahn, Oliver; Angulo, Raul E.

2016-01-01

N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling collisionless systems. We introduce a new approach to simulate the gravitational evolution of cold collisionless fluids by solving the Vlasov-Poisson equations in terms of adaptively refineable `Lagrangian phase-space elements'. These geometrical elements are piecewise smooth maps between Lagrangian space and Eulerian phase-space and approximate the continuum structure of the distribution function. They allow for dynamical adaptive splitting to accurately follow the evolution even in regions of very strong mixing. We discuss in detail various one-, two- and three-dimensional test problems to demonstrate the performance of our method. Its advantages compared to N-body algorithms are: (I) explicit tracking of the fine-grained distribution function, (II) natural representation of caustics, (III) intrinsically smooth gravitational potential fields, thus (IV) eliminating the need for any type of ad hoc force softening. We show the potential of our method by simulating structure formation in a warm dark matter scenario. We discuss how spurious collisionality and large-scale discreteness noise of N-body methods are both strongly suppressed, which eliminates the artificial fragmentation of filaments. Therefore, we argue that our new approach improves on the N-body method when simulating self-gravitating cold and collisionless fluids, and is the first method that allows us to explicitly follow the fine-grained evolution in six-dimensional phase-space.

Evolutionary dynamics of collective action in spatially structured populations.

PubMed

Peña, Jorge; Nöldeke, Georg; Lehmann, Laurent

2015-10-07

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of spatial structure in biological collective action, the analysis of n-player games games in spatially structured populations has so far proved elusive. We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. This allows to conveniently identify convergence stable strategies and to capture the effect of population structure by a single structure coefficient, namely, the pairwise (scaled) relatedness among interacting individuals. As an application, we use our mathematical framework to investigate collective action problems associated with the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: "public goods" (both providers and shirkers can use the good, e.g., alarm calls), "club goods" (only providers can use the good, e.g., participation in collective hunting), and "charity goods" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness promotes the evolution of collective action in different ways depending on the kind of collective good and its economies of scale. Our findings highlight the importance of explicitly accounting for relatedness, the kind of collective good, and the economies of scale in theoretical and empirical studies of the evolution of collective action. Copyright © 2015 Elsevier Ltd. All rights reserved.

A POPULATION MEMETICS APPROACH TO CULTURAL EVOLUTION IN CHAFFINCH SONG: DIFFERENTIATION AMONG POPULATIONS.

PubMed

Lynch, Alejandro; Baker, Allan J

1994-04-01

We investigated cultural evolution in populations of common chaffinches (Fringilla coelebs) in the Atlantic islands (Azores, Madeira, and Canaries) and neighboring continental regions (Morocco and Iberia) by employing a population-memetic approach. To quantify differentiation, we used the concept of a song meme, defined as a single syllable or a series of linked syllables capable of being transmitted. The levels of cultural differentiation are higher among the Canaries populations than among the Azorean ones, even though the islands are on average closer to each other geographically. This is likely the result of reduced levels of migration, lower population sizes, and bottlenecks (possibly during the colonization of these populations) in the Canaries; all these factors produce a smaller effective population size and therefore accentuate the effects of differentiation by random drift. Significant levels of among-population differentiation in the Azores, in spite of substantial levels of migration, attest to the differentiating effects of high mutation rates of memes, which allow the accumulation of new mutants in different populations before migration can disperse them throughout the entire region. © 1994 The Society for the Study of Evolution.

Assessing competition in hospital care markets: the importance of accounting for quality differentiation.

PubMed

Tay, Abigail

2003-01-01

Quality differentiation is especially important in the hospital industry, where the choices of Medicare patients are unaffected by prices. Unlike previous studies that use geographic market concentration to estimate hospital competitiveness, this article emphasizes the importance of quality differentiation in this spatially differentiated market. I estimate a random-coefficients discrete-choice model that predicts patient flow to different hospitals and find that demand responses to both distance and quality are substantial. The estimates suggest that patients do not substitute toward alternative hospitals in proportion to current market shares, implying that geographic market concentration is an inappropriate measure of hospital competitiveness.

PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces

DOE PAGES

Sarmiento, Adel; Cortes, Adriano; Garcia, Daniel; ...

2016-10-07

We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.

Modeling evolution of the mind and cultures: emotional Sapir-Whorf hypothesis

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2009-05-01

Evolution of cultures is ultimately determined by mechanisms of the human mind. The paper discusses the mechanisms of evolution of language from primordial undifferentiated animal cries to contemporary conceptual contents. In parallel with differentiation of conceptual contents, the conceptual contents were differentiated from emotional contents of languages. The paper suggests the neural brain mechanisms involved in these processes. Experimental evidence and theoretical arguments are discussed, including mathematical approaches to cognition and language: modeling fields theory, the knowledge instinct, and the dual model connecting language and cognition. Mathematical results are related to cognitive science, linguistics, and psychology. The paper gives an initial mathematical formulation and mean-field equations for the hierarchical dynamics of both the human mind and culture. In the mind heterarchy operation of the knowledge instinct manifests through mechanisms of differentiation and synthesis. The emotional contents of language are related to language grammar. The conclusion is an emotional version of Sapir-Whorf hypothesis. Cultural advantages of "conceptual" pragmatic cultures, in which emotionality of language is diminished and differentiation overtakes synthesis resulting in fast evolution at the price of self doubts and internal crises are compared to those of traditional cultures where differentiation lags behind synthesis, resulting in cultural stability at the price of stagnation. Multi-language, multi-ethnic society might combine the benefits of stability and fast differentiation. Unsolved problems and future theoretical and experimental directions are discussed.

Spectral analysis of point-vortex dynamics: first application to vortex polygons in a circular domain

NASA Astrophysics Data System (ADS)

Speetjens, M. F. M.; Meleshko, V. V.; van Heijst, G. J. F.

2014-06-01

The present study addresses the classical problem of the dynamics and stability of a cluster of N-point vortices of equal strength arranged in a polygonal configuration (‘N-vortex polygons’). In unbounded domains, such N-vortex polygons are unconditionally stable for N\\leqslant 7. Confinement in a circular domain tightens the stability conditions to N\\leqslant 6 and a maximum polygon size relative to the domain radius. This work expands on existing studies on stability and integrability by a first giving an exploratory spectral analysis of the dynamics of N vortex polygons in circular domains. Key to this is that the spectral signature of the time evolution of vortex positions reflects their qualitative behaviour. Expressing vortex motion by a generic evolution operator (the so-called Koopman operator) provides a rigorous framework for such spectral analyses. This paves the way to further differentiation and classification of point-vortex behaviour beyond stability and integrability. The concept of Koopman-based spectral analysis is demonstrated for N-vortex polygons. This reveals that conditional stability can be seen as a local form of integrability and confirms an important generic link between spectrum and dynamics: discrete spectra imply regular (quasi-periodic) motion; continuous (sub-)spectra imply chaotic motion. Moreover, this exposes rich nonlinear dynamics as intermittency between regular and chaotic motion and quasi-coherent structures formed by chaotic vortices. Dedicated to the memory of Slava Meleshko, a dear friend and inspiring colleague.

Pigment cell interactions and differential xanthophore recruitment underlying zebrafish stripe reiteration and Danio pattern evolution

PubMed Central

Patterson, Larissa B.; Bain, Emily J.; Parichy, David M.

2014-01-01

Fishes have diverse pigment patterns, yet mechanisms of pattern evolution remain poorly understood. In zebrafish, Danio rerio, pigment-cell autonomous interactions generate dark stripes of melanophores that alternate with light interstripes of xanthophores and iridophores. Here, we identify mechanisms underlying the evolution of a uniform pattern in D. albolineatus in which all three pigment cell classes are intermingled. We show that in this species xanthophores differentiate precociously over a wider area, and that cis regulatory evolution has increased expression of xanthogenic Colony Stimulating Factor-1 (Csf1). Expressing Csf1 similarly in D. rerio has cascading effects, driving the intermingling of all three pigment cell classes and resulting in the loss of stripes, as in D. albolineatus. Our results identify novel mechanisms of pattern development and illustrate how pattern diversity can be generated when a core network of pigment-cell autonomous interactions is coupled with changes in pigment cell differentiation. PMID:25374113

A new discrete dipole kernel for quantitative susceptibility mapping.

PubMed

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Data approximation using a blending type spline construction

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

Dalmo, Rune; Bratlie, Jostein

2014-11-18

Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C{sup k}-smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which aremore » necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.« less

Drekar v.2.0

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

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows.

PubMed

Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Luo, Kai Hong; Li, Yingjun

2017-11-01

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific-heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

A mathematical model of the structure and evolution of small scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, C. E.

1990-01-01

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Effect of film thickness on morphological evolution in dewetting and crystallization of polystyrene/poly(ε-caprolactone) blend films.

PubMed

Ma, Meng; He, Zhoukun; Yang, Jinghui; Chen, Feng; Wang, Ke; Zhang, Qin; Deng, Hua; Fu, Qiang

2011-11-01

In this Article, the morphological evolution in the blend thin film of polystyrene (PS)/poly(ε-caprolactone) (PCL) was investigated via mainly AFM. It was found that an enriched two-layer structure with PS at the upper layer and PCL at the bottom layer was formed during spinning coating. By changing the solution concentration, different kinds of crystal morphologies, such as finger-like, dendritic, and spherulitic-like, could be obtained at the bottom PCL layer. These different initial states led to the morphological evolution processes to be quite different from each other, so the phase separation, dewetting, and crystalline morphology of PS/PCL blend films as a function of time were studied. It was interesting to find that the morphological evolution of PS at the upper layer was largely dependent on the film thickness. For the ultrathin (15 nm) blend film, a liquid-solid/liquid-liquid dewetting-wetting process was observed, forming ribbons that rupture into discrete circular PS islands on voronoi finger-like PCL crystal. For the thick (30 nm) blend film, the liquid-liquid dewetting of the upper PS layer from the underlying adsorbed PCL layer was found, forming interconnected rim structures that rupture into discrete circular PS islands embedded in the single lamellar PCL dendritic crystal due to Rayleigh instability. For the thicker (60 nm) blend film, a two-step liquid-liquid dewetting process with regular holes decorated with dendritic PCL crystal at early annealing stage and small holes decorated with spherulite-like PCL crystal among the early dewetting holes at later annealing stage was observed. The mechanism of this unusual morphological evolution process was discussed on the basis of the entropy effect and annealing-induced phase separation.

Parsing parallel evolution: ecological divergence and differential gene expression in the adaptive radiations of thick-lipped Midas cichlid fishes from Nicaragua.

PubMed

Manousaki, Tereza; Hull, Pincelli M; Kusche, Henrik; Machado-Schiaffino, Gonzalo; Franchini, Paolo; Harrod, Chris; Elmer, Kathryn R; Meyer, Axel

2013-02-01

The study of parallel evolution facilitates the discovery of common rules of diversification. Here, we examine the repeated evolution of thick lips in Midas cichlid fishes (the Amphilophus citrinellus species complex)-from two Great Lakes and two crater lakes in Nicaragua-to assess whether similar changes in ecology, phenotypic trophic traits and gene expression accompany parallel trait evolution. Using next-generation sequencing technology, we characterize transcriptome-wide differential gene expression in the lips of wild-caught sympatric thick- and thin-lipped cichlids from all four instances of repeated thick-lip evolution. Six genes (apolipoprotein D, myelin-associated glycoprotein precursor, four-and-a-half LIM domain protein 2, calpain-9, GTPase IMAP family member 8-like and one hypothetical protein) are significantly underexpressed in the thick-lipped morph across all four lakes. However, other aspects of lips' gene expression in sympatric morphs differ in a lake-specific pattern, including the magnitude of differentially expressed genes (97-510). Generally, fewer genes are differentially expressed among morphs in the younger crater lakes than in those from the older Great Lakes. Body shape, lower pharyngeal jaw size and shape, and stable isotopes (δ(13)C and δ(15)N) differ between all sympatric morphs, with the greatest differentiation in the Great Lake Nicaragua. Some ecological traits evolve in parallel (those related to foraging ecology; e.g. lip size, body and head shape) but others, somewhat surprisingly, do not (those related to diet and food processing; e.g. jaw size and shape, stable isotopes). Taken together, this case of parallelism among thick- and thin-lipped cichlids shows a mosaic pattern of parallel and nonparallel evolution. © 2012 Blackwell Publishing Ltd.

A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Numerical Stimulation of Multicomponent Chromatography Using Spreadsheets.

ERIC Educational Resources Information Center

Frey, Douglas D.

1990-01-01

Illustrated is the use of spreadsheet programs for implementing finite difference numerical simulations of chromatography as an instructional tool in a separations course. Discussed are differential equations, discretization and integration, spreadsheet development, computer requirements, and typical simulation results. (CW)

Group delay spread analysis of coupled-multicore fibers: A comparison between weak and tight bending conditions

NASA Astrophysics Data System (ADS)

Fujisawa, Takeshi; Saitoh, Kunimasa

2017-06-01

Group delay spread of coupled three-core fiber is investigated based on coupled-wave theory. The differences between supermode and discrete core mode models are thoroughly investigated to reveal applicability of both models for specific fiber bending condition. A macrobending with random twisting is taken into account for random modal mixing in the fiber. It is found that for weakly bent condition, both supermode and discrete core mode models are applicable. On the other hand, for strongly bent condition, the discrete core mode model should be used to account for increased differential modal group delay for the fiber without twisting and short correlation length, which were experimentally observed recently. Results presented in this paper indicate the discrete core mode model is superior to the supermode model for the analysis of coupled-multicore fibers for various bent condition. Also, for estimating GDS of coupled-multicore fiber, it is critically important to take into account the fiber bending condition.

Evolution of gene expression in fire ants: the effects of developmental stage, caste, and species

USDA-ARS?s Scientific Manuscript database

Ants provide remarkable examples of equivalent genotypes developing into divergent and discrete phenotypes. Diploid eggs can develop either into queens, which specialize in reproduction, or workers, which participate in cooperative tasks such as building the nest, collecting food, and rearing the yo...

Disparate modes of evolution shaped modern prion (PRNP) and prion-related doppel (PRND) variation in domestic cattle

USDA-ARS?s Scientific Manuscript database

Previous investigations aimed at determining whether the mammalian prion protein actually facilitates tangible molecular aspects of either a discrete or pleiotropic functional niche have been debated, especially given the apparent absence of overt behavioral or physiological phenotypes associated wi...

Microskills Training: Evolution, Reexamination, and Call for Reform

ERIC Educational Resources Information Center

Ridley, Charles R.; Kelly, Shannon M.; Mollen, Debra

2011-01-01

For more than four decades, the microskills approach has been the dominant paradigm for training entry-level counseling students. At its inception, the model met a critical need: instruction in discrete counseling behaviors, which at the time was conspicuously missing from training curricula. Although these behaviors have become essential…

Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces

NASA Astrophysics Data System (ADS)

Tal, Yuval; Hager, Bradford H.

2017-09-01

This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal-dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

NASA Technical Reports Server (NTRS)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Special relativity in a discrete quantum universe

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-10-01

The hypothesis of a discrete fabric of the universe, the "Planck scale," is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.

The SMM model as a boundary value problem using the discrete diffusion equation.

PubMed

Campbell, Joel

2007-12-01

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Time evolution of complexity in Abelian gauge theories

NASA Astrophysics Data System (ADS)

Hashimoto, Koji; Iizuka, Norihiro; Sugishita, Sotaro

2017-12-01

Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U (1 ) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ˜exp (entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.

Phenotypic models of evolution and development: geometry as destiny.

PubMed

François, Paul; Siggia, Eric D

2012-12-01

Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations). The expression-time to space map for Hox genes and the posterior dominance rule are phenotypes that naturally follow from computational evolution without considering the genetics of Hox regulation. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox

NASA Astrophysics Data System (ADS)

Perez, Alejandro

2015-04-01

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation during evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler), which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

Recent Progress in Discrete Dislocation Dynamics and Its Applications to Micro Plasticity

NASA Astrophysics Data System (ADS)

Po, Giacomo; Mohamed, Mamdouh S.; Crosby, Tamer; Erel, Can; El-Azab, Anter; Ghoniem, Nasr

2014-10-01

We present a self-contained review of the discrete dislocation dynamics (DDD) method for the numerical investigation of plasticity in crystals, focusing on recent development and implementation progress. The review covers the theoretical foundations of DDD within the framework of incompatible elasticity, its numerical implementation via the nodal method, the extension of the method to finite domains and several implementation details. Applications of the method to current topics in micro-plasticity are presented, including the size effects in nano-indentation, the evolution of the dislocation microstructure in persistent slip bands, and the phenomenon of dislocation avalanches in micro-pillar compression.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

β-Catenin signaling regulates temporally discrete phases of anterior taste bud development

PubMed Central

Thirumangalathu, Shoba; Barlow, Linda A.

2015-01-01

The sense of taste is mediated by multicellular taste buds located within taste papillae on the tongue. In mice, individual taste buds reside in fungiform papillae, which develop at mid-gestation as epithelial placodes in the anterior tongue. Taste placodes comprise taste bud precursor cells, which express the secreted factor sonic hedgehog (Shh) and give rise to taste bud cells that differentiate around birth. We showed previously that epithelial activation of β-catenin is the primary inductive signal for taste placode formation, followed by taste papilla morphogenesis and taste bud differentiation, but the degree to which these later elements were direct or indirect consequences of β-catenin signaling was not explored. Here, we define discrete spatiotemporal functions of β-catenin in fungiform taste bud development. Specifically, we show that early epithelial activation of β-catenin, before taste placodes form, diverts lingual epithelial cells from a taste bud fate. By contrast, β-catenin activation a day later within Shh+ placodes, expands taste bud precursors directly, but enlarges papillae indirectly. Further, placodal activation of β-catenin drives precocious differentiation of Type I glial-like taste cells, but not other taste cell types. Later activation of β-catenin within Shh+ precursors during papilla morphogenesis also expands taste bud precursors and accelerates Type I cell differentiation, but papilla size is no longer enhanced. Finally, although Shh regulates taste placode patterning, we find that it is dispensable for the accelerated Type I cell differentiation induced by β-catenin. PMID:26525674

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

Conceptual Comparison of Population Based Metaheuristics for Engineering Problems

PubMed Central

Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes. PMID:25874265

Conceptual comparison of population based metaheuristics for engineering problems.

PubMed

Adekanmbi, Oluwole; Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger absolute error values, it shows similar convergence rates as the other split schemes, but does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much to fast. Despite this, the finding of this new scheme illustrates the potential of our discretization framework as a toolbox to find and to study new FE schemes based on new combinations of FE spaces. [1] Bauer, W. [2016], A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM - International Journal on Geomathematics, 7(1), 31-101.

The "Polar Light Sign" is a useful tool to detect discrete membranous supravalvular mitral stenosis.

PubMed

Hertwig, Christine; Haas, Nikolaus A; Habash, Sheeraz; Hanslik, Andreas; Kececioglu, Deniz; Sandica, Eugen; Laser, Kai-Thorsten

2015-02-01

Mitral valve stenosis caused by a discrete supravalvular membrane is a rare congenital malformation haemodynamically leading to significant mitral valve stenosis. When the supravalvular mitral stenosis consists of a discrete supravalvular membrane adherent to the mitral valve, it is usually not clearly detectable by routine echocardiography. We report about the typical echocardiographic finding in three young patients with this rare form of a discrete membranous supravalvular stenosis caused by a membrane adherent to the mitral valve. These cases present a typical echocardiographic feature in colour Doppler generated by the pathognomonic supramitral flow acceleration. Whereas typical supravalvular mitral stenosis caused by cor triatriatum or a clearly visible supravalvular ring is easily detectable by echocardiography, a discrete supravalvular membrane adjacent to the mitral valve leaflets resembling valvular mitral stenosis is difficult to differentiate by routine echocardiography. In our opinion, this colour phenomenon does resemble the visual impression of polar lights in the northern hemisphere; owing to its typical appearance, it may therefore be named as "Polar Light Sign". This phenomenon may help to detect this anatomical entity by echocardiography in time and therefore improve the prognosis for repair.

The early thermal evolution of Mars

NASA Astrophysics Data System (ADS)

Bhatia, G. K.; Sahijpal, S.

2016-01-01

Hf-W isotopic systematics of Martian meteorites have provided evidence for the early accretion and rapid core formation of Mars. We present the results of numerical simulations performed to study the early thermal evolution and planetary scale differentiation of Mars. The simulations are confined to the initial 50 Myr (Ma) of the formation of solar system. The accretion energy produced during the growth of Mars and the decay energy due to the short-lived radio-nuclides 26Al, 60Fe, and the long-lived nuclides, 40K, 235U, 238U, and 232Th are incorporated as the heat sources for the thermal evolution of Mars. During the core-mantle differentiation of Mars, the molten metallic blobs were numerically moved using Stoke's law toward the center with descent velocity that depends on the local acceleration due to gravity. Apart from the accretion and the radioactive heat energies, the gravitational energy produced during the differentiation of Mars and the associated heat transfer is also parametrically incorporated in the present work to make an assessment of its contribution to the early thermal evolution of Mars. We conclude that the accretion energy alone cannot produce widespread melting and differentiation of Mars even with an efficient consumption of the accretion energy. This makes 26Al the prime source for the heating and planetary scale differentiation of Mars. We demonstrate a rapid accretion and core-mantle differentiation of Mars within the initial ~1.5 Myr. This is consistent with the chronological records of Martian meteorites.

The DSM-5 dissociative-PTSD subtype: can levels of depression, anxiety, hostility, and sleeping difficulties differentiate between dissociative-PTSD and PTSD in rape and sexual assault victims?

PubMed

Armour, Cherie; Elklit, Ask; Lauterbach, Dean; Elhai, Jon D

2014-05-01

The DSM-5 currently includes a dissociative-PTSD subtype within its nomenclature. Several studies have confirmed the dissociative-PTSD subtype in both American Veteran and American civilian samples. Studies have begun to assess specific factors which differentiate between dissociative vs. non-dissociative PTSD. The current study takes a novel approach to investigating the presence of a dissociative-PTSD subtype in its use of European victims of sexual assault and rape (N=351). Utilizing Latent Profile Analyses, we hypothesized that a discrete group of individuals would represent a dissociative-PTSD subtype. We additionally hypothesized that levels of depression, anger, hostility, and sleeping difficulties would differentiate dissociative-PTSD from a similarly severe form of PTSD in the absence of dissociation. Results concluded that there were four discrete groups termed baseline, moderate PTSD, high PTSD, and dissociative-PTSD. The dissociative-PTSD group encompassed 13.1% of the sample and evidenced significantly higher mean scores on measures of depression, anxiety, hostility, and sleeping difficulties. Implications are discussed in relation to both treatment planning and the newly published DSM-5. Copyright © 2014 Elsevier Ltd. All rights reserved.

Neuropathies of the optic nerve and visual evoked potentials with special reference to color vision and differential light threshold measured with the computer perimeter OCTOPUS.

PubMed

Wildberger, H

1984-10-31

The contrast evoked potentials (VEPs) to different check sizes were recorded in about 200 cases of discrete optic neuropathies (ON) of different origin. Differential light threshold (DLT) was tested with the computer perimeter OCTOPUS. Saturated and desaturated tests were applied to evaluate the degree of acquired color vision deficiency. Delayed VEP responses are not confined to optic neuritis (RBN) alone and the different latency times obtained from other ON are confluent. The delay may be due to demyelination, to an increasing dominance of paramacular VEP subcomponents or to an increasing dominance of the upper half-field responses. Recording with smaller check sizes has the advantage that discrete dysfunctions in the visual field (VF) center are more easily detected: a correlation between amplitudes and visual acuity is best in strabismic amblyopias, is less expressed in maculopathies of the retina and weak in ON. The absence or reduction of amplitudes to smaller check sizes, however, is an important indication of a disorder in the VF center of ON in an early or recovered stage. Acquired color vision defects of the tritan-like type are more confined to discrete ON, whereas the red/green type is reserved to more severe ON. The DLT of the VF center is reduced in a different, significant and non significant extent in discrete optic neuropathies and the correlation between DLT and visual acuity is weak. A careful numerical analysis is needed in types of discrete ON where the central DLT lies within normal statistical limits: a side difference of the DLT between the affected and the normal fellow eye is always present. Evaluation of visual fatigue effects and of the relative sensitivity loss of VF center and VF periphery may provide further diagnostic information.

Variationally consistent discretization schemes and numerical algorithms for contact problems

NASA Astrophysics Data System (ADS)

Wohlmuth, Barbara

We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Transit and lifespan in neutrophil production: implications for drug intervention.

PubMed

Câmara De Souza, Daniel; Craig, Morgan; Cassidy, Tyler; Li, Jun; Nekka, Fahima; Bélair, Jacques; Humphries, Antony R

2018-02-01

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino's extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. An extension to the Quartino model is provided by considering a general number of transit compartments and introducing an extra parameter that allows for the decoupling of the maturation time from the production rate of cells. An overview of the well established linear chain technique, used to reformulate transit compartment models with constant transit rates as distributed delay differential equations (DDEs), is then given. A state-dependent time rescaling of the Quartino model is performed to apply the linear chain technique and rewrite the Quartino model as a distributed DDE, yielding a discrete DDE model in a certain parameter limit. Next, stability and bifurcation analyses are undertaken in an effort to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension models incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment. This misspecification can have far reaching consequences on the development of future models of myelosuppression in PK/PD.

Rational Ruijsenaars Schneider hierarchy and bispectral difference operators

NASA Astrophysics Data System (ADS)

Iliev, Plamen

2007-05-01

We show that a monic polynomial in a discrete variable n, with coefficients depending on time variables t1,t2,…, is a τ-function for the discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These τ-functions were considered in [L. Haine, P. Iliev, Commutative rings of difference operators and an adelic flag manifold, Int. Math. Res. Not. 2000 (6) (2000) 281-323], where it was proved that they parametrize rank one solutions to a difference-differential version of the bispectral problem.

A radial basis function Galerkin method for inhomogeneous nonlocal diffusion

DOE PAGES

Lehoucq, Richard B.; Rowe, Stephen T.

2016-02-01

We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.

𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries

NASA Astrophysics Data System (ADS)

Krishna, S.

2017-04-01

We discuss a set of novel discrete symmetry transformations of the 𝒩 = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent 𝒩 = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions 𝜃α and 𝜃¯α onto (1, 4)-dimensional supermanifold.

Discrete-Event Simulation Models of Plasmodium falciparum Malaria

PubMed Central

McKenzie, F. Ellis; Wong, Roger C.; Bossert, William H.

2008-01-01

We develop discrete-event simulation models using a single “timeline” variable to represent the Plasmodium falciparum lifecycle in individual hosts and vectors within interacting host and vector populations. Where they are comparable our conclusions regarding the relative importance of vector mortality and the durations of host immunity and parasite development are congruent with those of classic differential-equation models of malaria, epidemiology. However, our results also imply that in regions with intense perennial transmission, the influence of mosquito mortality on malaria prevalence in humans may be rivaled by that of the duration of host infectivity. PMID:18668185

Parent-Child Communication and Marijuana Initiation: Evidence Using Discrete-Time Survival Analysis

PubMed Central

Nonnemaker, James M.; Silber-Ashley, Olivia; Farrelly, Matthew C.; Dench, Daniel

2012-01-01

This study supplements existing literature on the relationship between parent-child communication and adolescent drug use by exploring whether parental and/or adolescent recall of specific drug-related conversations differentially impact youth's likelihood of initiating marijuana use. Using discrete-time survival analysis, we estimated the hazard of marijuana initiation using a logit model to obtain an estimate of the relative risk of initiation. Our results suggest that parent-child communication about drug use is either not protective (no effect) or—in the case of youth reports of communication—potentially harmful (leading to increased likelihood of marijuana initiation). PMID:22958867

Covariant information-density cutoff in curved space-time.

PubMed

Kempf, Achim

2004-06-04

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

Planarian cholinesterase: in vitro characterization of an evolutionarily ancient enzyme to study organophosphorus pesticide toxicity and reactivation.

PubMed

Hagstrom, Danielle; Hirokawa, Hideto; Zhang, Limin; Radic, Zoran; Taylor, Palmer; Collins, Eva-Maria S

2017-08-01

The freshwater planarian Dugesia japonica has recently emerged as an animal model for developmental neurotoxicology and found to be sensitive to organophosphorus (OP) pesticides. While previous activity staining of D. japonica, which possess a discrete cholinergic nervous system, has shown acylthiocholine catalysis, it is unknown whether this is accomplished through an acetylcholinesterase (AChE), butyrylcholinesterase (BChE), or a hybrid esterase and how OP exposure affects esterase activity. Here, we show that the majority of D. japonica cholinesterase (DjChE) activity departs from conventional AChE and BChE classifications. Inhibition by classic protonable amine and quaternary reversible inhibitors (ethopropazine, donepezil, tacrine, edrophonium, BW284c51, propidium) shows that DjChE is far less sensitive to these inhibitors than human AChE, suggesting discrete differences in active center and peripheral site recognition and structures. Additionally, we find that different OPs (chlorpyrifos oxon, paraoxon, dichlorvos, diazinon oxon, malaoxon) and carbamylating agents (carbaryl, neostigmine, physostigmine, pyridostigmine) differentially inhibit DjChE activity in vitro. DjChE was most sensitive to diazinon oxon and neostigmine and least sensitive to malaoxon and carbaryl. Diazinon oxon-inhibited DjChE could be reactivated by the quaternary oxime, pralidoxime (2-PAM), and the zwitterionic oxime, RS194B, with RS194B being significantly more potent. Sodium fluoride (NaF) reactivates OP-DjChE faster than 2-PAM. As one of the most ancient true cholinesterases, DjChE provides insight into the evolution of a hybrid enzyme before the separation into distinct AChE and BChE enzymes found in higher vertebrates. The sensitivity of DjChE to OPs and capacity for reactivation validate the use of planarians for OP toxicology studies.

Application of Markov Models for Analysis of Development of Psychological Characteristics

ERIC Educational Resources Information Center

Kuravsky, Lev S.; Malykh, Sergey B.

2004-01-01

A technique to study combined influence of environmental and genetic factors on the base of changes in phenotype distributions is presented. Histograms are exploited as base analyzed characteristics. A continuous time, discrete state Markov process with piece-wise constant interstate transition rates is associated with evolution of each histogram.…

Duplicated genes evolve independently in allopolyploid cotton.

Treesearch

Richard C. Cronn; Randall L. Small; Jonathan F. Wendel

1999-01-01

Of the many processes that generate gene duplications, polyploidy is unique in that entire genomes are duplicated. This process has been important in the evolution of many eukaryotic groups, and it occurs with high frequency in plants. Recent evidence suggests that polyploidization may be accompanied by rapid genomic changes, but the evolutionary fate of discrete loci...

Evolution of Self-Reporting Methods for Identifying Discrete Emotions in Science Classrooms

ERIC Educational Resources Information Center

Ritchie, Stephen M.; Hudson, Peter; Bellocchi, Alberto; Henderson, Senka; King, Donna; Tobin, Kenneth

2016-01-01

Emotion researchers have grappled with challenging methodological issues in capturing emotions of participants in naturalistic settings such as school or university classrooms. Self-reporting methods have been used frequently, yet these methods are inadequate when used alone. We argue that the self-reporting methods of emotion diaries and…

Iconicity and the Emergence of Combinatorial Structure in Language

ERIC Educational Resources Information Center

Verhoef, Tessa; Kirby, Simon; de Boer, Bart

2016-01-01

In language, recombination of a discrete set of meaningless building blocks forms an unlimited set of possible utterances. How such combinatorial structure emerged in the evolution of human language is increasingly being studied. It has been shown that it can emerge when languages culturally evolve and adapt to human cognitive biases. How the…

Lunar initial Nd-143/Nd-144 - Differential evolution of the lunar crust and mantle

NASA Technical Reports Server (NTRS)

Lugmair, G. W.; Marti, K.

1978-01-01

The Sm-Nd evolution of Apollo 15 green glass is discussed. The ICE age (intercept with chondritic evolution) of 3.8 + or - 0.4 eons overlaps the range of reported (Ar-39)-(Ar-40) ages and implies a distinct source region for green glass, characterized by very low and unfractionated REE abundances. Evidence is presented that LINd (lunar initial Nd) is compatible with a 'chondritic'-type Nd isotopic evolution as observed in the Juvinas meteorite. This normalization is used to study the Sm-Nd system of various lunar rock types. The results obtained from a limited number of rocks clearly indicate differential Sm-Nd evolution for the lunar crust and mantle. High-Ti basalts returned by the Apollo 11 and 17 missions were derived from distinct source regions. The Nd-143 evolution in KREEP requires a source region which is clearly distinct from any mantle reservoir.

Measurements of Discrete Symmetries in the Neutral Kaon System with the CPLEAR (PS195) Experiment

NASA Astrophysics Data System (ADS)

Ruf, Thomas

2015-07-01

The antiproton storage ring LEAR offered unique opportunities to study the symmetries which exist between matter and antimatter. At variance with other approaches at this facility, CPLEAR was an experiment devoted to the study of T, \\{CPT} and \\{CP} symmetries in the neutral kaon system. It measured with high precision the time evolution of initially strangeness-tagged K0 and overline K ^0 states to determine the size of violations with respect to these symmetries in the context of a systematic study. In parallel, limits concerning quantum-mechanical predictions (EPR paradox, coherence of the wave function) or the equivalence principle of general relativity have been obtained. This article will first discuss briefly the unique low energy antiproton storage ring LEAR followed by a description of the CPLEAR experiment, including the basic formalism necessary to understand the time evolution of a neutral kaon state and the main results related to measurements of discrete symmetries in the neutral kaon system. An excellent and exhaustive review of the CPLEAR experiment and all its measurements is given in Ref. 1.

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Ecological symmetry breaking can favour the evolution of altruism in an action-response game.

PubMed

Di Paolo, E A

2000-03-21

The evolution of altruistic behaviour is studied in a simple action-response game with a tunable degree of conflict of interest. It is shown that for the continuous, mixed-medium approach no stable polymorphism favours altruism. Ecological dynamics are explored with the addition of a spatial dimension and a local energy variable. A continuous spatial model with finite local range does not introduce any substantial difference in the results with respect to the level of altruism. However, the model illustrates how ecological coupling may lead to the formation of stable spatial patterns in the form of discrete and isolated clusters of players as a consequence of inverse density dependence. A discrete, individual-based model is built in which local interactions are also modelled as occurring within a finite neighbourhood of each individual and spatial positions are not restricted as in lattice models. This model shows substantially different results. A high level of altruism is observed for low (but positive) degrees of conflict and this level decreases linearly for higher degrees of conflict. The evolution of altruism is explained by studying the broken symmetries introduced by the spatial clusters themselves, mainly between their central and peripheral regions which, in combination with the discrete and the stochastic nature of the model, result in the stabilization of strategies in which players behave altruistically towards the same type. As a consequence of the activity of the players, energy resources at the centre of an altruistic cluster are very depleted; so much so that, for low conflict, fitter non-altruistic mutants may initially invade only to become locally extinct due to their less efficient use of energy as their numbers increase. In peripheral regions invader may subsist; however, for geometrical reasons long-lasting genealogies tend to originate only at the centre of a cluster. Copyright 2000 Academic Press.

Cosmology of biased discrete symmetry breaking

NASA Technical Reports Server (NTRS)

Gelmini, Graciela B.; Gleiser, Marcelo; Kolb, Edward W.

1988-01-01

The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.

Exact Markov chains versus diffusion theory for haploid random mating.

PubMed

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

Effect of differential speed rolling on the texture evolution of Mg-4Zn-1Gd alloy

NASA Astrophysics Data System (ADS)

Shim, Myeong-Shik; Suh, Byeong-Chan; Kim, Jae H.; Kim, Nack J.

2015-05-01

The microstructural and texture evolution during differential speed rolling process of Mg 4Zn-1Gd (wt%) alloy have been investigated by means of electron backscatter diffraction observation and texture analysis. The angular distribution of basal poles are inclined about 10° from the normal direction towards the rolling direction and the maximum intensities of basal poles are decreased, compared to the conventional rolling process. Such an inclination of angular distribution of basal poles can be induced by the operation of shear stress along the rolling direction, as much as one quarter of tensile stress along the RD and one quarter of compressive stress along the ND. When the reduction ratios in differential speed rolling increase, there is no difference in texture evolution although there is a significant change in activated twinning systems. In addition, the engineering stresses after differential speed rolling are also similar to that after conventional rolling process, while ductility and stretch formability in the former are worse than those in the latter.

Dynamic Noise and its Role in Understanding Epidemiological Processes

NASA Astrophysics Data System (ADS)

Stollenwerk, Nico; Aguiar, Maíra

2010-09-01

We investigate the role of dynamic noise in understanding epidemiological systems, such as influenza or dengue fever by deriving stochastic ordinary differential equations from markov processes for discrete populations. This approach allows for an easy analysis of dynamical noise transitions between co-existing attractors.

Heat transfer at microscopic level in a MHD fractional inertial flow confined between non-isothermal boundaries

NASA Astrophysics Data System (ADS)

Shoaib Anwar, Muhammad; Rasheed, Amer

2017-07-01

Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Sensory trait variation in an echolocating bat suggests roles for both selection and plasticity

PubMed Central

2014-01-01

Background Across heterogeneous environments selection and gene flow interact to influence the rate and extent of adaptive trait evolution. This complex relationship is further influenced by the rarely considered role of phenotypic plasticity in the evolution of adaptive population variation. Plasticity can be adaptive if it promotes colonization and survival in novel environments and in doing so may increase the potential for future population differentiation via selection. Gene flow between selectively divergent environments may favour the evolution of phenotypic plasticity or conversely, plasticity itself may promote gene flow, leading to a pattern of trait differentiation in the presence of gene flow. Variation in sensory traits is particularly informative in testing the role of environment in trait and population differentiation. Here we test the hypothesis of ‘adaptive differentiation with minimal gene flow’ in resting echolocation frequencies (RF) of Cape horseshoe bats (Rhinolophus capensis) across a gradient of increasingly cluttered habitats. Results Our analysis reveals a geographically structured pattern of increasing RF from open to highly cluttered habitats in R. capensis; however genetic drift appears to be a minor player in the processes influencing this pattern. Although Bayesian analysis of population structure uncovered a number of spatially defined mitochondrial groups and coalescent methods revealed regional-scale gene flow, phylogenetic analysis of mitochondrial sequences did not correlate with RF differentiation. Instead, habitat discontinuities between biomes, and not genetic and geographic distances, best explained echolocation variation in this species. We argue that both selection for increased detection distance in relatively less cluttered habitats and adaptive phenotypic plasticity may have influenced the evolution of matched echolocation frequencies and habitats across different populations. Conclusions Our study reveals significant sensory trait differentiation in the presence of historical gene flow and suggests roles for both selection and plasticity in the evolution of echolocation variation in R. capensis. These results highlight the importance of population level analyses to i) illuminate the subtle interplay between selection, plasticity and gene flow in the evolution of adaptive traits and ii) demonstrate that evolutionary processes may act simultaneously and that their relative influence may vary across different environments. PMID:24674227

Sensory trait variation in an echolocating bat suggests roles for both selection and plasticity.

PubMed

Odendaal, Lizelle J; Jacobs, David S; Bishop, Jacqueline M

2014-03-27

Across heterogeneous environments selection and gene flow interact to influence the rate and extent of adaptive trait evolution. This complex relationship is further influenced by the rarely considered role of phenotypic plasticity in the evolution of adaptive population variation. Plasticity can be adaptive if it promotes colonization and survival in novel environments and in doing so may increase the potential for future population differentiation via selection. Gene flow between selectively divergent environments may favour the evolution of phenotypic plasticity or conversely, plasticity itself may promote gene flow, leading to a pattern of trait differentiation in the presence of gene flow. Variation in sensory traits is particularly informative in testing the role of environment in trait and population differentiation. Here we test the hypothesis of 'adaptive differentiation with minimal gene flow' in resting echolocation frequencies (RF) of Cape horseshoe bats (Rhinolophus capensis) across a gradient of increasingly cluttered habitats. Our analysis reveals a geographically structured pattern of increasing RF from open to highly cluttered habitats in R. capensis; however genetic drift appears to be a minor player in the processes influencing this pattern. Although Bayesian analysis of population structure uncovered a number of spatially defined mitochondrial groups and coalescent methods revealed regional-scale gene flow, phylogenetic analysis of mitochondrial sequences did not correlate with RF differentiation. Instead, habitat discontinuities between biomes, and not genetic and geographic distances, best explained echolocation variation in this species. We argue that both selection for increased detection distance in relatively less cluttered habitats and adaptive phenotypic plasticity may have influenced the evolution of matched echolocation frequencies and habitats across different populations. Our study reveals significant sensory trait differentiation in the presence of historical gene flow and suggests roles for both selection and plasticity in the evolution of echolocation variation in R. capensis. These results highlight the importance of population level analyses to i) illuminate the subtle interplay between selection, plasticity and gene flow in the evolution of adaptive traits and ii) demonstrate that evolutionary processes may act simultaneously and that their relative influence may vary across different environments.

Overview of MAVEN Particle and Fields Package (PFP) Measurements During Observations of Discrete Aurora at Mars by the MAVEN Imaging Ultraviolet Spectrograph (IUVS)

NASA Astrophysics Data System (ADS)

Soobiah, Y. I. J.; Espley, J. R.; Connerney, J. E. P.; Gruesbeck, J.; DiBraccio, G. A.; Schneider, N.; Jain, S.; Brain, D.; Andersson, L.; Halekas, J. S.; Lillis, R. J.; McFadden, J. P.; Mitchell, D. L.; Mazelle, C. X.; Deighan, J.; McClintock, W. E.; Ergun, R.; Jakosky, B. M.

2016-12-01

NASA's Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft has observed a variety of aurora at Mars and related processes that impact the escape of the Martian atmosphere. So far MAVEN's Imaging Ultraviolet Spectrograph (IUVS) instrument has observed 1) Diffuse aurora over widespread regions of Mars' northern hemisphere; 2) Discrete aurora that is spatially confined to localized patches around regions of crustal magnetic field; and 3) Proton aurora from the limb brightening of Lyman-α emission. MAVEN's Solar Energetic Particle (SEP) instrument has shown the diffuse aurora to be coincident with outbursts of solar energetic particles and disturbed solar wind and magnetospheric conditions. MAVEN Particle and Fields Package (PFP) Solar Wind Ion Analyzer (SWIA) has shown the limb brightening of Lyman-α to correlate with increased upstream solar wind dynamic pressure as associated with increased penetrating protons. So far a conclusive explanation for the discrete aurora has yet to be determined. This study aims to explore the plasma processes related to discrete Martian aurora in greater detail by presenting an overview of PFP measurements during orbits when IUVS observed discrete aurora at Mars. Initial observations from orbit 1600 of MAVEN has shown the almost side-by-side occurrence of a crustal magnetic field associated current sheet measured by MAVEN's Magnetometer Investigation (MAG) near the Mars terminator and IUVS limb observations of discrete aurora in Mars shadow (similar co-latitudes but separated by nearly 1800 km across longitude). This study includes further analysis of magnetic field current sheets and the particle acceleration/energization to investigate the space plasma processes involved in discrete aurora at Mars.

β-Catenin signaling regulates temporally discrete phases of anterior taste bud development.

PubMed

Thirumangalathu, Shoba; Barlow, Linda A

2015-12-15

The sense of taste is mediated by multicellular taste buds located within taste papillae on the tongue. In mice, individual taste buds reside in fungiform papillae, which develop at mid-gestation as epithelial placodes in the anterior tongue. Taste placodes comprise taste bud precursor cells, which express the secreted factor sonic hedgehog (Shh) and give rise to taste bud cells that differentiate around birth. We showed previously that epithelial activation of β-catenin is the primary inductive signal for taste placode formation, followed by taste papilla morphogenesis and taste bud differentiation, but the degree to which these later elements were direct or indirect consequences of β-catenin signaling was not explored. Here, we define discrete spatiotemporal functions of β-catenin in fungiform taste bud development. Specifically, we show that early epithelial activation of β-catenin, before taste placodes form, diverts lingual epithelial cells from a taste bud fate. By contrast, β-catenin activation a day later within Shh(+) placodes, expands taste bud precursors directly, but enlarges papillae indirectly. Further, placodal activation of β-catenin drives precocious differentiation of Type I glial-like taste cells, but not other taste cell types. Later activation of β-catenin within Shh(+) precursors during papilla morphogenesis also expands taste bud precursors and accelerates Type I cell differentiation, but papilla size is no longer enhanced. Finally, although Shh regulates taste placode patterning, we find that it is dispensable for the accelerated Type I cell differentiation induced by β-catenin. © 2015. Published by The Company of Biologists Ltd.

DVS-SOFTWARE: An Effective Tool for Applying Highly Parallelized Hardware To Computational Geophysics

NASA Astrophysics Data System (ADS)

Herrera, I.; Herrera, G. S.

2015-12-01

Most geophysical systems are macroscopic physical systems. The behavior prediction of such systems is carried out by means of computational models whose basic models are partial differential equations (PDEs) [1]. Due to the enormous size of the discretized version of such PDEs it is necessary to apply highly parallelized super-computers. For them, at present, the most efficient software is based on non-overlapping domain decomposition methods (DDM). However, a limiting feature of the present state-of-the-art techniques is due to the kind of discretizations used in them. Recently, I. Herrera and co-workers using 'non-overlapping discretizations' have produced the DVS-Software which overcomes this limitation [2]. The DVS-software can be applied to a great variety of geophysical problems and achieves very high parallel efficiencies (90%, or so [3]). It is therefore very suitable for effectively applying the most advanced parallel supercomputers available at present. In a parallel talk, in this AGU Fall Meeting, Graciela Herrera Z. will present how this software is being applied to advance MOD-FLOW. Key Words: Parallel Software for Geophysics, High Performance Computing, HPC, Parallel Computing, Domain Decomposition Methods (DDM)REFERENCES [1]. Herrera Ismael and George F. Pinder, Mathematical Modelling in Science and Engineering: An axiomatic approach", John Wiley, 243p., 2012. [2]. Herrera, I., de la Cruz L.M. and Rosas-Medina A. "Non Overlapping Discretization Methods for Partial, Differential Equations". NUMER METH PART D E, 30: 1427-1454, 2014, DOI 10.1002/num 21852. (Open source) [3]. Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Introduction to Numerical Methods

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

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Non-smooth saddle-node bifurcations III: Strange attractors in continuous time

NASA Astrophysics Data System (ADS)

Fuhrmann, G.

2016-08-01

Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a non-smooth bifurcation. By a previous result on the occurrence of non-smooth bifurcations in forced discrete time dynamical systems, this yields that within the class of families of quasiperiodically driven differential equations, non-smooth saddle-node bifurcations occur in a set with non-empty C2-interior.

Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench.

PubMed

Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P

2012-10-26

Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

A Discrete Probability Function Method for the Equation of Radiative Transfer

NASA Technical Reports Server (NTRS)

Sivathanu, Y. R.; Gore, J. P.

1993-01-01

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

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

Xiao, Jianyuan; Liu, Jian; He, Yang

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactlymore » soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.« less

Local and global dynamics of Ramsey model: From continuous to discrete time.

PubMed

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Particle and Fields Observations Associated with Discrete Aurora at Mars: A Dual Spacecraft Perspective Using MAVEN and MEX

NASA Astrophysics Data System (ADS)

Soobiah, Y. I. J.; Espley, J. R.; Connerney, J. E. P.; Gruesbeck, J.; DiBraccio, G. A.; Schneider, N. M.; Jain, S.; Mitchell, D. L.; Mazelle, C. X.; Halekas, J. S.; Andersson, L.; Brain, D.; Lillis, R. J.; McFadden, J. P.; Deighan, J.; McClintock, B.; Jakosky, B. M.; Frahm, R.; Winningham, D.; Coates, A. J.; Holmstrom, M.

2017-12-01

NASA's Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft has observed a variety of distinct auroral types at Mars and related processes relevant to the escape of the Martian atmosphere. MAVEN's Imaging Ultraviolet Spectrograph (IUVS) instrument has measured 1) diffuse aurora over widespread regions of Mars' northern hemisphere, 2) discrete aurora spatially confined to localized patches around regions of strong crustal magnetic field and 3) proton aurora from limb brightening of Lyman-α emission. The processes involved in the occurrence of discrete aurora at Mars are not yet well understood. This study presents MAVEN IUVS and Particle and Fields Package (PFP) observations of contemporaneous particle and field signatures and discrete aurora at Mars. Discrete aurora observed in limb scans occur in association with patches of electrons in the optical shadow of Mars. The electron signatures display a range of field aligned (toward Mars) electron energy spectra, from electrons that are not accelerated (sometimes including photoelectron peaks) to accelerated electrons. These are observed in association with a range of magnetic field orientations, from horizontal to radial magnetic field directions. Observations obtained at low altitude over the nightside by MAVEN and the more distant Mars Express' (MEX) Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) are compared to investigate transport of electrons from plasma sheet and `inverted-V' electron signatures from the magnetotail to low altitudes.

Local and global dynamics of Ramsey model: From continuous to discrete time

NASA Astrophysics Data System (ADS)

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction

NASA Astrophysics Data System (ADS)

Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi

This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Adaptive array technique for differential-phase reflectometry in QUEST

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

Idei, H., E-mail: idei@triam.kyushu-u.ac.jp; Hanada, K.; Zushi, H.

2014-11-15

A Phased Array Antenna (PAA) was considered as launching and receiving antennae in reflectometry to attain good directivity in its applied microwave range. A well-focused beam was obtained in a launching antenna application, and differential-phase evolution was properly measured by using a metal reflector plate in the proof-of-principle experiment at low power test facilities. Differential-phase evolution was also evaluated by using the PAA in the Q-shu University Experiment with Steady State Spherical Tokamak (QUEST). A beam-forming technique was applied in receiving phased-array antenna measurements. In the QUEST device that should be considered as a large oversized cavity, standing wave effectmore » was significantly observed with perturbed phase evolution. A new approach using derivative of measured field on propagating wavenumber was proposed to eliminate the standing wave effect.« less

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

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

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

Interface modeling in incompressible media using level sets in Escript

NASA Astrophysics Data System (ADS)

Gross, L.; Bourgouin, L.; Hale, A. J.; Mühlhaus, H.-B.

2007-08-01

We use a finite element (FEM) formulation of the level set method to model geological fluid flow problems involving interface propagation. Interface problems are ubiquitous in geophysics. Here we focus on a Rayleigh-Taylor instability, namely mantel plumes evolution, and the growth of lava domes. Both problems require the accurate description of the propagation of an interface between heavy and light materials (plume) or between high viscous lava and low viscous air (lava dome), respectively. The implementation of the models is based on Escript which is a Python module for the solution of partial differential equations (PDEs) using spatial discretization techniques such as FEM. It is designed to describe numerical models in the language of PDEs while using computational components implemented in C and C++ to achieve high performance for time-intensive, numerical calculations. A critical step in the solution geological flow problems is the solution of the velocity-pressure problem. We describe how the Escript module can be used for a high-level implementation of an efficient variant of the well-known Uzawa scheme. We begin with a brief outline of the Escript modules and then present illustrations of its usage for the numerical solutions of the problems mentioned above.

An RBF-FD closest point method for solving PDEs on surfaces

NASA Astrophysics Data System (ADS)

Petras, A.; Ling, L.; Ruuth, S. J.

2018-10-01

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

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

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less

Permutation flow-shop scheduling problem to optimize a quadratic objective function

NASA Astrophysics Data System (ADS)

Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

2017-09-01

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

75 FR 12597 - Endangered and Threatened Species; Proposed Listing of Nine Distinct Population Segments of...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-16

... result in a significant gap in the range of the taxon; (c) evidence that the discrete segment represents... appear to have shaped the evolution of these two matriarchal lineages with the onset of glacial cycles...-directional invasion by the temperate-adapted loggerheads into the respective basins (Bowen et al., 1994; J.S...

Discrete virus infection model of hepatitis B virus.

PubMed

Zhang, Pengfei; Min, Lequan; Pian, Jianwei

2015-01-01

In 1996 Nowak and his colleagues proposed a differential equation virus infection model, which has been widely applied in the study for the dynamics of hepatitis B virus (HBV) infection. Biological dynamics may be described more practically by discrete events rather than continuous ones. Using discrete systems to describe biological dynamics should be reasonable. Based on one revised Nowak et al's virus infection model, this study introduces a discrete virus infection model (DVIM). Two equilibriums of this model, E1 and E2, represents infection free and infection persistent, respectively. Similar to the case of the basic virus infection model, this study deduces a basic virus reproductive number R0 independing on the number of total cells of an infected target organ. A proposed theorem proves that if the basic virus reproductive number R0<1 then the virus free equilibrium E1 is locally stable. The DVIM is more reasonable than an abstract discrete susceptible-infected-recovered model (SIRS) whose basic virus reproductive number R0 is relevant to the number of total cells of the infected target organ. As an application, this study models the clinic HBV DNA data of a patient who was accepted via anti-HBV infection therapy with drug lamivudine. The results show that the numerical simulation is good in agreement with the clinic data.

Effects of sintering temperature on the microstructural evolution and wear behavior of WCp reinforced Ni-based coatings

NASA Astrophysics Data System (ADS)

Chen, Chuan-hui; Bai, Yang; Ye, Xu-chu

2014-12-01

This article focuses on the microstructural evolution and wear behavior of 50wt%WC reinforced Ni-based composites prepared onto 304 stainless steel substrates by vacuum sintering at different sintering temperatures. The microstructure and chemical composition of the coatings were investigated by X-ray diffraction (XRD), differential thermal analysis (DTA), scanning and transmission electron microscopy (SEM and TEM) equipped with energy-dispersive X-ray spectroscopy (EDS). The wear resistance of the coatings was tested by thrust washer testing. The mechanisms of the decomposition, dissolution, and precipitation of primary carbides, and their influences on the wear resistance have been discussed. The results indicate that the coating sintered at 1175°C is composed of fine WC particles, coarse M6C (M=Ni, Fe, Co, etc.) carbides, and discrete borides dispersed in solid solution. Upon increasing the sintering temperature to 1225°C, the microstructure reveals few incompletely dissolved WC particles trapped in larger M6C, Cr-rich lamellar M23C6, and M3C2 in the austenite matrix. M23C6 and M3C2 precipitates are formed in both the γ/M6C grain boundary and the matrix. These large-sized and lamellar brittle phases tend to weaken the wear resistance of the composite coatings. The wear behavior is controlled simultaneously by both abrasive wear and adhesive wear. Among them, abrasive wear plays a major role in the wear process of the coating sintered at 1175°C, while the effect of adhesive wear is predominant in the coating sintered at 1225°C.

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

DOE PAGES

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2016-10-21

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less

An Alternative Approach to Zero Tolerance Policies.

ERIC Educational Resources Information Center

Ilg, Timothy J.; Russo, Charles J.

2001-01-01

School officials should adopt no-tolerance policies that require educators' discretion in punishing misbehaving students (based on due process and fundamental fairness), rather than relying on the zero-tolerance approach, which fails to differentiate among different levels of offenses. Even disruptive students deserve due process and appropriate…

An electronic circuit for sensing malfunctions in test instrumentation

NASA Technical Reports Server (NTRS)

Miller, W. M., Jr.

1969-01-01

Monitoring device differentiates between malfunctions occurring in the system undergoing test and malfunctions within the test instrumentation itself. Electronic circuits in the monitor use transistors to commutate silicon controlled rectifiers by removing the drive voltage, display circuits are then used to monitor multiple discrete lines.

A discrete classical space-time could require 6 extra-dimensions

NASA Astrophysics Data System (ADS)

Guillemant, Philippe; Medale, Marc; Abid, Cherifa

2018-01-01

We consider a discrete space-time in which conservation laws are computed in such a way that the density of information is kept bounded. We use a 2D billiard as a toy model to compute the uncertainty propagation in ball positions after every shock and the corresponding loss of phase information. Our main result is the computation of a critical time step above which billiard calculations are no longer deterministic, meaning that a multiverse of distinct billiard histories begins to appear, caused by the lack of information. Then, we highlight unexpected properties of this critical time step and the subsequent exponential evolution of the number of histories with time, to observe that after certain duration all billiard states could become possible final states, independent of initial conditions. We conclude that if our space-time is really a discrete one, one would need to introduce extra-dimensions in order to provide supplementary constraints that specify which history should be played.

Landau-Zener transitions and Dykhne formula in a simple continuum model

NASA Astrophysics Data System (ADS)

Dunham, Yujin; Garmon, Savannah

The Landau-Zener model describing the interaction between two linearly driven discrete levels is useful in describing many simple dynamical systems; however, no system is completely isolated from the surrounding environment. Here we examine a generalizations of the original Landau-Zener model to study simple environmental influences. We consider a model in which one of the discrete levels is replaced with a energy continuum, in which we find that the survival probability for the initially occupied diabatic level is unaffected by the presence of the continuum. This result can be predicted by assuming that each step in the evolution for the diabatic state evolves independently according to the Landau-Zener formula, even in the continuum limit. We also show that, at least for the simplest model, this result can also be predicted with the natural generalization of the Dykhne formula for open systems. We also observe dissipation as the non-escape probability from the discrete levels is no longer equal to one.

Evolution of plant conducting cells: perspectives from key regulators of vascular cell differentiation.

PubMed

Ohtani, Misato; Akiyoshi, Nobuhiro; Takenaka, Yuto; Sano, Ryosuke; Demura, Taku

2017-01-01

One crucial problem that plants faced during their evolution, particularly during the transition to growth on land, was how to transport water, nutrients, metabolites, and small signaling molecules within a large, multicellular body. As a solution to this problem, land plants developed specific tissues for conducting molecules, called water-conducting cells (WCCs) and food-conducting cells (FCCs). The well-developed WCCs and FCCs in extant plants are the tracheary elements and sieve elements, respectively, which are found in vascular plants. Recent molecular genetic studies revealed that transcriptional networks regulate the differentiation of tracheary and sieve elements, and that the networks governing WCC differentiation are largely conserved among land plant species. In this review, we discuss the molecular evolution of plant conducting cells. By focusing on the evolution of the key transcription factors that regulate vascular cell differentiation, the NAC transcription factor VASCULAR-RELATED NAC-DOMAIN for WCCs and the MYB-coiled-coil (CC)-type transcription factor ALTERED PHLOEM DEVELOPMENT for sieve elements, we describe how land plants evolved molecular systems to produce the specialized cells that function as WCCs and FCCs. © The Author 2016. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved. For permissions, please email: journals.permissions@oup.com.

Pulse retrieval algorithm for interferometric frequency-resolved optical gating based on differential evolution.

PubMed

Hyyti, Janne; Escoto, Esmerando; Steinmeyer, Günter

2017-10-01

A novel algorithm for the ultrashort laser pulse characterization method of interferometric frequency-resolved optical gating (iFROG) is presented. Based on a genetic method, namely, differential evolution, the algorithm can exploit all available information of an iFROG measurement to retrieve the complex electric field of a pulse. The retrieval is subjected to a series of numerical tests to prove the robustness of the algorithm against experimental artifacts and noise. These tests show that the integrated error-correction mechanisms of the iFROG method can be successfully used to remove the effect from timing errors and spectrally varying efficiency in the detection. Moreover, the accuracy and noise resilience of the new algorithm are shown to outperform retrieval based on the generalized projections algorithm, which is widely used as the standard method in FROG retrieval. The differential evolution algorithm is further validated with experimental data, measured with unamplified three-cycle pulses from a mode-locked Ti:sapphire laser. Additionally introducing group delay dispersion in the beam path, the retrieval results show excellent agreement with independent measurements with a commercial pulse measurement device based on spectral phase interferometry for direct electric-field retrieval. Further experimental tests with strongly attenuated pulses indicate resilience of differential-evolution-based retrieval against massive measurement noise.

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free parameter is then given in such a way that the fluxes are limited towards the low-order solver until positivity is attained. Given the lack of additional degrees of freedom in the system, this positivity limiter lacks energy conservation where the limiter turns on. However, this ingredient can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems including a smooth Alfvén wave (to verify formal order of accuracy), shock tube problems (to test the shock-capturing ability of the scheme), Orszag-Tang, and cloud shock interactions. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

The History of Bordetella pertussis Genome Evolution Includes Structural Rearrangement

PubMed Central

Peng, Yanhui; Loparev, Vladimir; Batra, Dhwani; Bowden, Katherine E.; Burroughs, Mark; Cassiday, Pamela K.; Davis, Jamie K.; Johnson, Taccara; Juieng, Phalasy; Knipe, Kristen; Mathis, Marsenia H.; Pruitt, Andrea M.; Rowe, Lori; Sheth, Mili; Tondella, M. Lucia; Williams, Margaret M.

2017-01-01

ABSTRACT Despite high pertussis vaccine coverage, reported cases of whooping cough (pertussis) have increased over the last decade in the United States and other developed countries. Although Bordetella pertussis is well known for its limited gene sequence variation, recent advances in long-read sequencing technology have begun to reveal genomic structural heterogeneity among otherwise indistinguishable isolates, even within geographically or temporally defined epidemics. We have compared rearrangements among complete genome assemblies from 257 B. pertussis isolates to examine the potential evolution of the chromosomal structure in a pathogen with minimal gene nucleotide sequence diversity. Discrete changes in gene order were identified that differentiated genomes from vaccine reference strains and clinical isolates of various genotypes, frequently along phylogenetic boundaries defined by single nucleotide polymorphisms. The observed rearrangements were primarily large inversions centered on the replication origin or terminus and flanked by IS481, a mobile genetic element with >240 copies per genome and previously suspected to mediate rearrangements and deletions by homologous recombination. These data illustrate that structural genome evolution in B. pertussis is not limited to reduction but also includes rearrangement. Therefore, although genomes of clinical isolates are structurally diverse, specific changes in gene order are conserved, perhaps due to positive selection, providing novel information for investigating disease resurgence and molecular epidemiology. IMPORTANCE Whooping cough, primarily caused by Bordetella pertussis, has resurged in the United States even though the coverage with pertussis-containing vaccines remains high. The rise in reported cases has included increased disease rates among all vaccinated age groups, provoking questions about the pathogen's evolution. The chromosome of B. pertussis includes a large number of repetitive mobile genetic elements that obstruct genome analysis. However, these mobile elements facilitate large rearrangements that alter the order and orientation of essential protein-encoding genes, which otherwise exhibit little nucleotide sequence diversity. By comparing the complete genome assemblies from 257 isolates, we show that specific rearrangements have been conserved throughout recent evolutionary history, perhaps by eliciting changes in gene expression, which may also provide useful information for molecular epidemiology. PMID:28167525

Comparative Sex Chromosome Genomics in Snakes: Differentiation, Evolutionary Strata, and Lack of Global Dosage Compensation

PubMed Central

Zektser, Yulia; Mahajan, Shivani; Bachtrog, Doris

2013-01-01

Snakes exhibit genetic sex determination, with female heterogametic sex chromosomes (ZZ males, ZW females). Extensive cytogenetic work has suggested that the level of sex chromosome heteromorphism varies among species, with Boidae having entirely homomorphic sex chromosomes, Viperidae having completely heteromorphic sex chromosomes, and Colubridae showing partial differentiation. Here, we take a genomic approach to compare sex chromosome differentiation in these three snake families. We identify homomorphic sex chromosomes in boas (Boidae), but completely heteromorphic sex chromosomes in both garter snakes (Colubridae) and pygmy rattlesnake (Viperidae). Detection of W-linked gametologs enables us to establish the presence of evolutionary strata on garter and pygmy rattlesnake sex chromosomes where recombination was abolished at different time points. Sequence analysis shows that all strata are shared between pygmy rattlesnake and garter snake, i.e., recombination was abolished between the sex chromosomes before the two lineages diverged. The sex-biased transmission of the Z and its hemizygosity in females can impact patterns of molecular evolution, and we show that rates of evolution for Z-linked genes are increased relative to their pseudoautosomal homologs, both at synonymous and amino acid sites (even after controlling for mutational biases). This demonstrates that mutation rates are male-biased in snakes (male-driven evolution), but also supports faster-Z evolution due to differential selective effects on the Z. Finally, we perform a transcriptome analysis in boa and pygmy rattlesnake to establish baseline levels of sex-biased expression in homomorphic sex chromosomes, and show that heteromorphic ZW chromosomes in rattlesnakes lack chromosome-wide dosage compensation. Our study provides the first full scale overview of the evolution of snake sex chromosomes at the genomic level, thus greatly expanding our knowledge of reptilian and vertebrate sex chromosomes evolution. PMID:24015111

Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays.

PubMed

Wang, Leimin; Zeng, Zhigang; Ge, Ming-Feng; Hu, Junhao

2018-05-02

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Parent-child communication and marijuana initiation: evidence using discrete-time survival analysis.

PubMed

Nonnemaker, James M; Silber-Ashley, Olivia; Farrelly, Matthew C; Dench, Daniel

2012-12-01

This study supplements existing literature on the relationship between parent-child communication and adolescent drug use by exploring whether parental and/or adolescent recall of specific drug-related conversations differentially impact youth's likelihood of initiating marijuana use. Using discrete-time survival analysis, we estimated the hazard of marijuana initiation using a logit model to obtain an estimate of the relative risk of initiation. Our results suggest that parent-child communication about drug use is either not protective (no effect) or - in the case of youth reports of communication - potentially harmful (leading to increased likelihood of marijuana initiation). Copyright © 2012 Elsevier Ltd. All rights reserved.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Eruptive stratigraphy of the Tatara-San Pedro complex, 36°S, sourthern volcanic zone, Chilean Andes: reconstruction method and implications for magma evolution at long-lived arc volcanic centers

USGS Publications Warehouse

Dungan, M.A.; Wulff, A.; Thompson, R.

2001-01-01

The Quaternary Tatara-San Pedro volcanic complex (36°S, Chilean Andes) comprises eight or more unconformity-bound volcanic sequences, representing variably preserved erosional remnants of volcanic centers generated during 930 ky of activity. The internal eruptive histories of several dominantly mafic to intermediate sequences have been reconstructed, on the basis of correlations of whole-rock major and trace element chemistry of flows between multiple sampled sections, but with critical contributions from photogrammetric, geochronologic, and paleomagnetic data. Many groups of flows representing discrete eruptive events define internal variation trends that reflect extrusion of heterogeneous or rapidly evolving magna batches from conduit-reservoir systems in which open-system processes typically played a large role. Long-term progressive evolution trends are extremely rare and the magma compositions of successive eruptive events rarely lie on precisely the same differentiation trend, even where they have evolved from similar parent magmas by similar processes. These observations are not consistent with magma differentiation in large long-lived reservoirs, but they may be accommodated by diverse interactions between newly arrived magma inputs and multiple resident pockets of evolved magma and / or crystal mush residing in conduit-dominated subvolcanic reservoirs. Without constraints provided by the reconstructed stratigraphic relations, the framework for petrologic modeling would be far different. A well-established eruptive stratigraphy may provide independent constraints on the petrologic processes involved in magma evolution-simply on the basis of the specific order in which diverse, broadly cogenetic magmas have been erupted. The Tatara-San Pedro complex includes lavas ranging from primitive basalt to high-SiO2 rhyolite, and although the dominant erupted magma type was basaltic andesite ( 52-55 wt % SiO2) each sequence is characterized by unique proportions of mafic, intermediate, and silicic eruptive products. Intermediate lava compositions also record different evolution paths, both within and between sequences. No systematic long-term pattern is evident from comparisons at the level of sequences. The considerable diversity of mafic and evolved magmas of the Tatara-San Pedro complex bears on interpretations of regional geochemical trends. The variable role of open-system processes in shaping the compositions of evolved Tatara-San Pedro complex magmas, and even some basaltic magmas, leads to the conclusion that addressing problems such as are magma genesis and elemental fluxes through subduction zones on the basis of averaged or regressed reconnaissance geochemical datasets is a tenuous exercise. Such compositional indices are highly instructive for identifying broad regional trends and first-order problems, but they should be used with extreme caution in attempts to quantify processes and magma sources, including crustal components, implicated in these trends.

Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

NASA Astrophysics Data System (ADS)

Karpfinger, Florian; Gurevich, Boris; Valero, Henri-Pierre; Bakulin, Andrey; Sinha, Bikash

2010-11-01

This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

The Brassica oleracea genome reveals the asymmetrical evolution of polyploid genomes

PubMed Central

Liu, Shengyi; Liu, Yumei; Yang, Xinhua; Tong, Chaobo; Edwards, David; Parkin, Isobel A. P.; Zhao, Meixia; Ma, Jianxin; Yu, Jingyin; Huang, Shunmou; Wang, Xiyin; Wang, Junyi; Lu, Kun; Fang, Zhiyuan; Bancroft, Ian; Yang, Tae-Jin; Hu, Qiong; Wang, Xinfa; Yue, Zhen; Li, Haojie; Yang, Linfeng; Wu, Jian; Zhou, Qing; Wang, Wanxin; King, Graham J; Pires, J. Chris; Lu, Changxin; Wu, Zhangyan; Sampath, Perumal; Wang, Zhuo; Guo, Hui; Pan, Shengkai; Yang, Limei; Min, Jiumeng; Zhang, Dong; Jin, Dianchuan; Li, Wanshun; Belcram, Harry; Tu, Jinxing; Guan, Mei; Qi, Cunkou; Du, Dezhi; Li, Jiana; Jiang, Liangcai; Batley, Jacqueline; Sharpe, Andrew G; Park, Beom-Seok; Ruperao, Pradeep; Cheng, Feng; Waminal, Nomar Espinosa; Huang, Yin; Dong, Caihua; Wang, Li; Li, Jingping; Hu, Zhiyong; Zhuang, Mu; Huang, Yi; Huang, Junyan; Shi, Jiaqin; Mei, Desheng; Liu, Jing; Lee, Tae-Ho; Wang, Jinpeng; Jin, Huizhe; Li, Zaiyun; Li, Xun; Zhang, Jiefu; Xiao, Lu; Zhou, Yongming; Liu, Zhongsong; Liu, Xuequn; Qin, Rui; Tang, Xu; Liu, Wenbin; Wang, Yupeng; Zhang, Yangyong; Lee, Jonghoon; Kim, Hyun Hee; Denoeud, France; Xu, Xun; Liang, Xinming; Hua, Wei; Wang, Xiaowu; Wang, Jun; Chalhoub, Boulos; Paterson, Andrew H

2014-01-01

Polyploidization has provided much genetic variation for plant adaptive evolution, but the mechanisms by which the molecular evolution of polyploid genomes establishes genetic architecture underlying species differentiation are unclear. Brassica is an ideal model to increase knowledge of polyploid evolution. Here we describe a draft genome sequence of Brassica oleracea, comparing it with that of its sister species B. rapa to reveal numerous chromosome rearrangements and asymmetrical gene loss in duplicated genomic blocks, asymmetrical amplification of transposable elements, differential gene co-retention for specific pathways and variation in gene expression, including alternative splicing, among a large number of paralogous and orthologous genes. Genes related to the production of anticancer phytochemicals and morphological variations illustrate consequences of genome duplication and gene divergence, imparting biochemical and morphological variation to B. oleracea. This study provides insights into Brassica genome evolution and will underpin research into the many important crops in this genus. PMID:24852848

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

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

PubMed

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Reconstructed ancestral enzymes reveal that negative selection drove the evolution of substrate specificity in ADP-dependent kinases.

PubMed

Castro-Fernandez, Víctor; Herrera-Morande, Alejandra; Zamora, Ricardo; Merino, Felipe; Gonzalez-Ordenes, Felipe; Padilla-Salinas, Felipe; Pereira, Humberto M; Brandão-Neto, Jose; Garratt, Richard C; Guixe, Victoria

2017-09-22

One central goal in molecular evolution is to pinpoint the mechanisms and evolutionary forces that cause an enzyme to change its substrate specificity; however, these processes remain largely unexplored. Using the glycolytic ADP-dependent kinases of archaea, including the orders Thermococcales , Methanosarcinales , and Methanococcales , as a model and employing an approach involving paleoenzymology, evolutionary statistics, and protein structural analysis, we could track changes in substrate specificity during ADP-dependent kinase evolution along with the structural determinants of these changes. To do so, we studied five key resurrected ancestral enzymes as well as their extant counterparts. We found that a major shift in function from a bifunctional ancestor that could phosphorylate either glucose or fructose 6-phosphate (fructose-6-P) as a substrate to a fructose 6-P-specific enzyme was started by a single amino acid substitution resulting in negative selection with a ground-state mode against glucose and a subsequent 1,600-fold change in specificity of the ancestral protein. This change rendered the residual phosphorylation of glucose a promiscuous and physiologically irrelevant activity, highlighting how promiscuity may be an evolutionary vestige of ancestral enzyme activities, which have been eliminated over time. We also could reconstruct the evolutionary history of substrate utilization by using an evolutionary model of discrete binary characters, indicating that substrate uses can be discretely lost or acquired during enzyme evolution. These findings exemplify how negative selection and subtle enzyme changes can lead to major evolutionary shifts in function, which can subsequently generate important adaptive advantages, for example, in improving glycolytic efficiency in Thermococcales . © 2017 by The American Society for Biochemistry and Molecular Biology, Inc.

On Some Parabolic Type Problems from Thin Film Theory and Chemical Reaction-Diffusion Networks

NASA Astrophysics Data System (ADS)

Mohamed, Fatma Naser Ali

This dissertation considers some parabolic type problems from thin film theory and chemical reaction-diffusion networks. The dissertation consists of two parts: In the first part, we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove an existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that, in this case, the surface-tension energy dissipation is the mechanism responsible for the H1-norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type, are also successfully treated by the same means. [special characters omitted]. In the second part, we are concerned with the convergence of a certain space-discretization scheme -the so-called method of lines- for mass-action reaction-diffusion systems. First, we start with a toy model, namely. [special characters omitted]. and prove convergence of method of lines for this linear case. Here weak convergence in L2(0,1) is enough to prove convergence of the method of lines. Then we adopt the framework for convergence analysis introduced in [23] and concentrate on the proof-of-concept reaction. within 1D space, while at the same time noting that our techniques are readily generalizable to other reaction-diffusion networks and to more than one space dimension. Indeed, it will be obvious how to extend our proofs to the multi-dimensional case; we only note that the proof of the comparison principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream numerical tool and the specialized literature is rather scarce. The method amounts to discretizing evolutionary PDE's in space only, so it produces a semi-discrete numerical scheme which consists of a system of ODE's (in the time variable). To prove convergence of the semi-discrete MOL scheme to the original PDE one needs to perform some more or less traditional analysis: it is necessary to show that the scheme is consistent with the continuous problem and that the discretized version of the spatial differential operator retains sufficient dissipative properties in order to allow an application of Gronwall's Lemma to the error term. As shown in [23], a uniform (in time) consistency estimate is sufficient to obtain convergence; however, the consistency estimate we proved is not uniform for a small time, so we cannot directly employ the results in [23] to prove convergence in our case. Instead, we prove all the required estimates "from the scratch", then we use their exact quantitative form in order to conclude convergence.

From quantum to classical modeling of radiation reaction: A focus on stochasticity effects

NASA Astrophysics Data System (ADS)

Niel, F.; Riconda, C.; Amiranoff, F.; Duclous, R.; Grech, M.

2018-04-01

Radiation reaction in the interaction of ultrarelativistic electrons with a strong external electromagnetic field is investigated using a kinetic approach in the nonlinear moderately quantum regime. Three complementary descriptions are discussed considering arbitrary geometries of interaction: a deterministic one relying on the quantum-corrected radiation reaction force in the Landau and Lifschitz (LL) form, a linear Boltzmann equation for the electron distribution function, and a Fokker-Planck (FP) expansion in the limit where the emitted photon energies are small with respect to that of the emitting electrons. The latter description is equivalent to a stochastic differential equation where the effect of the radiation reaction appears in the form of the deterministic term corresponding to the quantum-corrected LL friction force, and by a diffusion term accounting for the stochastic nature of photon emission. By studying the evolution of the energy moments of the electron distribution function with the three models, we are able to show that all three descriptions provide similar predictions on the temporal evolution of the average energy of an electron population in various physical situations of interest, even for large values of the quantum parameter χ . The FP and full linear Boltzmann descriptions also allow us to correctly describe the evolution of the energy variance (second-order moment) of the distribution function, while higher-order moments are in general correctly captured with the full linear Boltzmann description only. A general criterion for the limit of validity of each description is proposed, as well as a numerical scheme for the inclusion of the FP description in particle-in-cell codes. This work, not limited to the configuration of a monoenergetic electron beam colliding with a laser pulse, allows further insight into the relative importance of various effects of radiation reaction and in particular of the discrete and stochastic nature of high-energy photon emission and its back-reaction in the deformation of the particle distribution function.

Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions

ERIC Educational Resources Information Center

Wroughton, Jacqueline; Cole, Tarah

2013-01-01

Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

Bykova, Nadezda A; Favorov, Alexander V; Mironov, Andrey A

2013-01-01

The problem of reconstruction of ancestral states given a phylogeny and data from extant species arises in a wide range of biological studies. The continuous-time Markov model for the discrete states evolution is generally used for the reconstruction of ancestral states. We modify this model to account for a case when the states of the extant species are uncertain. This situation appears, for example, if the states for extant species are predicted by some program and thus are known only with some level of reliability; it is common for bioinformatics field. The main idea is formulation of the problem as a hidden Markov model on a tree (tree HMM, tHMM), where the basic continuous-time Markov model is expanded with the introduction of emission probabilities of observed data (e.g. prediction scores) for each underlying discrete state. Our tHMM decoding algorithm allows us to predict states at the ancestral nodes as well as to refine states at the leaves on the basis of quantitative comparative genomics. The test on the simulated data shows that the tHMM approach applied to the continuous variable reflecting the probabilities of the states (i.e. prediction score) appears to be more accurate then the reconstruction from the discrete states assignment defined by the best score threshold. We provide examples of applying our model to the evolutionary analysis of N-terminal signal peptides and transcription factor binding sites in bacteria. The program is freely available at http://bioinf.fbb.msu.ru/~nadya/tHMM and via web-service at http://bioinf.fbb.msu.ru/treehmmweb.

Emerging principles of regulatory evolution.

PubMed

Prud'homme, Benjamin; Gompel, Nicolas; Carroll, Sean B

2007-05-15

Understanding the genetic and molecular mechanisms governing the evolution of morphology is a major challenge in biology. Because most animals share a conserved repertoire of body-building and -patterning genes, morphological diversity appears to evolve primarily through changes in the deployment of these genes during development. The complex expression patterns of developmentally regulated genes are typically controlled by numerous independent cis-regulatory elements (CREs). It has been proposed that morphological evolution relies predominantly on changes in the architecture of gene regulatory networks and in particular on functional changes within CREs. Here, we discuss recent experimental studies that support this hypothesis and reveal some unanticipated features of how regulatory evolution occurs. From this growing body of evidence, we identify three key operating principles underlying regulatory evolution, that is, how regulatory evolution: (i) uses available genetic components in the form of preexisting and active transcription factors and CREs to generate novelty; (ii) minimizes the penalty to overall fitness by introducing discrete changes in gene expression; and (iii) allows interactions to arise among any transcription factor and downstream CRE. These principles endow regulatory evolution with a vast creative potential that accounts for both relatively modest morphological differences among closely related species and more profound anatomical divergences among groups at higher taxonomical levels.

Vesta Evolution from Surface Mineralogy: Mafic and Ultramafic Mineral Distribution

NASA Technical Reports Server (NTRS)

DeSanctis, M. C.; Ammannito, E.; Palomba, E.; Longobardo, A.; Mittlefehldt, D. W.; McSween, H. Y; Marchi, S.; Capria, M. T.; Capaccioni, F.; Frigeri, A.;

Internal constitution and evolution of the moon.

NASA Technical Reports Server (NTRS)

Solomon, S. C.; Toksoz, M. N.

1973-01-01

The composition, structure and evolution of the moon's interior are narrowly constrained by a large assortment of physical and chemical data. Models of the thermal evolution of the moon that fit the chronology of igneous activity on the lunar surface, the stress history of the lunar lithosphere implied by the presence of mascons, and the surface concentrations of radioactive elements, involve extensive differentiation early in lunar history. This differentiation may be the result of rapid accretion and large-scale melting or of primary chemical layering during accretion; differences in present-day temperatures for these two possibilities are significant only in the inner 1000 km of the moon and may not be resolvable.

Single nucleotide polymorphisms unravel hierarchical divergence and signatures of selection among Alaskan sockeye salmon (Oncorhynchus nerka) populations.

PubMed

Gomez-Uchida, Daniel; Seeb, James E; Smith, Matt J; Habicht, Christopher; Quinn, Thomas P; Seeb, Lisa W

2011-02-18

Disentangling the roles of geography and ecology driving population divergence and distinguishing adaptive from neutral evolution at the molecular level have been common goals among evolutionary and conservation biologists. Using single nucleotide polymorphism (SNP) multilocus genotypes for 31 sockeye salmon (Oncorhynchus nerka) populations from the Kvichak River, Alaska, we assessed the relative roles of geography (discrete boundaries or continuous distance) and ecology (spawning habitat and timing) driving genetic divergence in this species at varying spatial scales within the drainage. We also evaluated two outlier detection methods to characterize candidate SNPs responding to environmental selection, emphasizing which mechanism(s) may maintain the genetic variation of outlier loci. For the entire drainage, Mantel tests suggested a greater role of geographic distance on population divergence than differences in spawn timing when each variable was correlated with pairwise genetic distances. Clustering and hierarchical analyses of molecular variance indicated that the largest genetic differentiation occurred between populations from distinct lakes or subdrainages. Within one population-rich lake, however, Mantel tests suggested a greater role of spawn timing than geographic distance on population divergence when each variable was correlated with pairwise genetic distances. Variable spawn timing among populations was linked to specific spawning habitats as revealed by principal coordinate analyses. We additionally identified two outlier SNPs located in the major histocompatibility complex (MHC) class II that appeared robust to violations of demographic assumptions from an initial pool of eight candidates for selection. First, our results suggest that geography and ecology have influenced genetic divergence between Alaskan sockeye salmon populations in a hierarchical manner depending on the spatial scale. Second, we found consistent evidence for diversifying selection in two loci located in the MHC class II by means of outlier detection methods; yet, alternative scenarios for the evolution of these loci were also evaluated. Both conclusions argue that historical contingency and contemporary adaptation have likely driven differentiation between Kvichak River sockeye salmon populations, as revealed by a suite of SNPs. Our findings highlight the need for conservation of complex population structure, because it provides resilience in the face of environmental change, both natural and anthropogenic.

Single nucleotide polymorphisms unravel hierarchical divergence and signatures of selection among Alaskan sockeye salmon (Oncorhynchus nerka) populations

PubMed Central

2011-01-01

Background Disentangling the roles of geography and ecology driving population divergence and distinguishing adaptive from neutral evolution at the molecular level have been common goals among evolutionary and conservation biologists. Using single nucleotide polymorphism (SNP) multilocus genotypes for 31 sockeye salmon (Oncorhynchus nerka) populations from the Kvichak River, Alaska, we assessed the relative roles of geography (discrete boundaries or continuous distance) and ecology (spawning habitat and timing) driving genetic divergence in this species at varying spatial scales within the drainage. We also evaluated two outlier detection methods to characterize candidate SNPs responding to environmental selection, emphasizing which mechanism(s) may maintain the genetic variation of outlier loci. Results For the entire drainage, Mantel tests suggested a greater role of geographic distance on population divergence than differences in spawn timing when each variable was correlated with pairwise genetic distances. Clustering and hierarchical analyses of molecular variance indicated that the largest genetic differentiation occurred between populations from distinct lakes or subdrainages. Within one population-rich lake, however, Mantel tests suggested a greater role of spawn timing than geographic distance on population divergence when each variable was correlated with pairwise genetic distances. Variable spawn timing among populations was linked to specific spawning habitats as revealed by principal coordinate analyses. We additionally identified two outlier SNPs located in the major histocompatibility complex (MHC) class II that appeared robust to violations of demographic assumptions from an initial pool of eight candidates for selection. Conclusions First, our results suggest that geography and ecology have influenced genetic divergence between Alaskan sockeye salmon populations in a hierarchical manner depending on the spatial scale. Second, we found consistent evidence for diversifying selection in two loci located in the MHC class II by means of outlier detection methods; yet, alternative scenarios for the evolution of these loci were also evaluated. Both conclusions argue that historical contingency and contemporary adaptation have likely driven differentiation between Kvichak River sockeye salmon populations, as revealed by a suite of SNPs. Our findings highlight the need for conservation of complex population structure, because it provides resilience in the face of environmental change, both natural and anthropogenic. PMID:21332997

Predicting network modules of cell cycle regulators using relative protein abundance statistics.

PubMed

Oguz, Cihan; Watson, Layne T; Baumann, William T; Tyson, John J

2017-02-28

Parameter estimation in systems biology is typically done by enforcing experimental observations through an objective function as the parameter space of a model is explored by numerical simulations. Past studies have shown that one usually finds a set of "feasible" parameter vectors that fit the available experimental data equally well, and that these alternative vectors can make different predictions under novel experimental conditions. In this study, we characterize the feasible region of a complex model of the budding yeast cell cycle under a large set of discrete experimental constraints in order to test whether the statistical features of relative protein abundance predictions are influenced by the topology of the cell cycle regulatory network. Using differential evolution, we generate an ensemble of feasible parameter vectors that reproduce the phenotypes (viable or inviable) of wild-type yeast cells and 110 mutant strains. We use this ensemble to predict the phenotypes of 129 mutant strains for which experimental data is not available. We identify 86 novel mutants that are predicted to be viable and then rank the cell cycle proteins in terms of their contributions to cumulative variability of relative protein abundance predictions. Proteins involved in "regulation of cell size" and "regulation of G1/S transition" contribute most to predictive variability, whereas proteins involved in "positive regulation of transcription involved in exit from mitosis," "mitotic spindle assembly checkpoint" and "negative regulation of cyclin-dependent protein kinase by cyclin degradation" contribute the least. These results suggest that the statistics of these predictions may be generating patterns specific to individual network modules (START, S/G2/M, and EXIT). To test this hypothesis, we develop random forest models for predicting the network modules of cell cycle regulators using relative abundance statistics as model inputs. Predictive performance is assessed by the areas under receiver operating characteristics curves (AUC). Our models generate an AUC range of 0.83-0.87 as opposed to randomized models with AUC values around 0.50. By using differential evolution and random forest modeling, we show that the model prediction statistics generate distinct network module-specific patterns within the cell cycle network.

Population genomics of the killer whale indicates ecotype evolution in sympatry involving both selection and drift.

PubMed

Moura, Andre E; Kenny, John G; Chaudhuri, Roy; Hughes, Margaret A; J Welch, Andreanna; Reisinger, Ryan R; de Bruyn, P J Nico; Dahlheim, Marilyn E; Hall, Neil; Hoelzel, A Rus

2014-11-01

The evolution of diversity in the marine ecosystem is poorly understood, given the relatively high potential for connectivity, especially for highly mobile species such as whales and dolphins. The killer whale (Orcinus orca) has a worldwide distribution, and individual social groups travel over a wide geographic range. Even so, regional populations have been shown to be genetically differentiated, including among different foraging specialists (ecotypes) in sympatry. Given the strong matrifocal social structure of this species together with strong resource specializations, understanding the process of differentiation will require an understanding of the relative importance of both genetic drift and local adaptation. Here we provide a high-resolution analysis based on nuclear single-nucleotide polymorphic markers and inference about differentiation at both neutral loci and those potentially under selection. We find that all population comparisons, within or among foraging ecotypes, show significant differentiation, including populations in parapatry and sympatry. Loci putatively under selection show a different pattern of structure compared to neutral loci and are associated with gene ontology terms reflecting physiologically relevant functions (e.g. related to digestion). The pattern of differentiation for one ecotype in the North Pacific suggests local adaptation and shows some fixed differences among sympatric ecotypes. We suggest that differential habitat use and resource specializations have promoted sufficient isolation to allow differential evolution at neutral and functional loci, but that the process is recent and dependent on both selection and drift. © 2014 The Authors. Molecular Ecology published by John Wiley & Sons Ltd.

Population genomics of the killer whale indicates ecotype evolution in sympatry involving both selection and drift

PubMed Central

Moura, Andre E; Kenny, John G; Chaudhuri, Roy; Hughes, Margaret A; J Welch, Andreanna; Reisinger, Ryan R; de Bruyn, P J Nico; Dahlheim, Marilyn E; Hall, Neil; Hoelzel, A Rus

2014-01-01

The evolution of diversity in the marine ecosystem is poorly understood, given the relatively high potential for connectivity, especially for highly mobile species such as whales and dolphins. The killer whale (Orcinus orca) has a worldwide distribution, and individual social groups travel over a wide geographic range. Even so, regional populations have been shown to be genetically differentiated, including among different foraging specialists (ecotypes) in sympatry. Given the strong matrifocal social structure of this species together with strong resource specializations, understanding the process of differentiation will require an understanding of the relative importance of both genetic drift and local adaptation. Here we provide a high-resolution analysis based on nuclear single-nucleotide polymorphic markers and inference about differentiation at both neutral loci and those potentially under selection. We find that all population comparisons, within or among foraging ecotypes, show significant differentiation, including populations in parapatry and sympatry. Loci putatively under selection show a different pattern of structure compared to neutral loci and are associated with gene ontology terms reflecting physiologically relevant functions (e.g. related to digestion). The pattern of differentiation for one ecotype in the North Pacific suggests local adaptation and shows some fixed differences among sympatric ecotypes. We suggest that differential habitat use and resource specializations have promoted sufficient isolation to allow differential evolution at neutral and functional loci, but that the process is recent and dependent on both selection and drift. PMID:25244680

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Repeated evolution of soldier sub-castes suggests parasitism drives social complexity in stingless bees.

PubMed

Grüter, Christoph; Segers, Francisca H I D; Menezes, Cristiano; Vollet-Neto, Ayrton; Falcón, Tiago; von Zuben, Lucas; Bitondi, Márcia M G; Nascimento, Fabio S; Almeida, Eduardo A B

2017-02-23

The differentiation of workers into morphological castes represents an important evolutionary innovation that is thought to improve division of labor in insect societies. Given the potential benefits of task-related worker differentiation, it is puzzling that physical worker castes, such as soldiers, are extremely rare in social bees and absent in wasps. Following the recent discovery of soldiers in a stingless bee, we studied the occurrence of worker differentiation in 28 stingless bee species from Brazil and found that several species have specialized soldiers for colony defence. Our results reveal that worker differentiation evolved repeatedly during the last ~ 25 million years and coincided with the emergence of parasitic robber bees, a major threat to many stingless bee species. Furthermore, our data suggest that these robbers are a driving force behind the evolution of worker differentiation as targets of robber bees are four times more likely to have nest guards of increased size than non-targets. These findings reveal unexpected diversity in the social organization of stingless bees.Although common in ants and termites, worker differentiation into physical castes is rare in social bees and unknown in wasps. Here, Grüter and colleagues find a guard caste in ten species of stingless bees and show that the evolution of the guard caste is associated with parasitization by robber bees.

Nitrogen-Bearing, Indigenous Carbonaceous Matter in the Nakhla Mars Meteorite

NASA Technical Reports Server (NTRS)

Thomas-Keprta, K. L.; Clemett, S. J.; Messenger, S.; Rahman, Z.; Gibson, E. K.; Wentworth, S. J.; McKay, D. S.

2017-01-01

We report the identification of discrete assemblages of nitrogen (N)-rich organic matter entrapped within interior fracture surfaces of the martian meteorite Nakhla. Based on context, composition and isotopic measurements this organic matter is of demonstrably martian origin. The presence of N-bearing organic species is of considerable importance to the habitable potential and chemical evolution of the martian regolith.

A finite volume method for trace element diffusion and partitioning during crystal growth

NASA Astrophysics Data System (ADS)

Hesse, Marc A.

2012-09-01

A finite volume method on a uniform grid is presented to compute the polythermal diffusion and partitioning of a trace element during the growth of a porphyroblast crystal in a uniform matrix and in linear, cylindrical and spherical geometry. The motion of the crystal-matrix interface and the thermal evolution are prescribed functions of time. The motion of the interface is discretized and it advances from one cell boundary to next as the prescribed interface position passes the cell center. The appropriate conditions for the flux across the crystal-matrix interface are derived from discrete mass conservation. Numerical results are benchmarked against steady and transient analytic solutions for isothermal diffusion with partitioning and growth. Two applications illustrate the ability of the model to reproduce observed rare-earth element patterns in garnets (Skora et al., 2006) and water concentration profiles around spherulites in obsidian (Watkins et al., 2009). Simulations with diffusion inside the growing crystal show complex concentration evolutions for trace elements with high diffusion coefficients, such as argon or hydrogen, but demonstrate that rare-earth element concentrations in typical metamorphic garnets are not affected by intracrystalline diffusion.

Generic emergence of power law distributions and Lévy-Stable intermittent fluctuations in discrete logistic systems

NASA Astrophysics Data System (ADS)

Biham, Ofer; Malcai, Ofer; Levy, Moshe; Solomon, Sorin

1998-08-01

The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form wi(t+1)=λ(t)wi(t)+aw¯(t)-bwi(t)w¯(t) is studied by computer simulations. The variables wi, i=1,...,N, are the individual system components and w¯(t)=(1/N)∑iwi(t) is their average. The parameters a and b are constants, while λ(t) is randomly chosen at each time step from a given distribution. Models of this type describe the temporal evolution of a large variety of systems such as stock markets and city populations. These systems are characterized by a large number of interacting objects and the dynamics is dominated by multiplicative processes. The instantaneous probability distribution P(w,t) of the system components wi turns out to fulfill a Pareto power law P(w,t)~w-1-α. The time evolution of w¯(t) presents intermittent fluctuations parametrized by a Lévy-stable distribution with the same index α, showing an intricate relation between the distribution of the wi's at a given time and the temporal fluctuations of their average.

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

PubMed

Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N

2015-12-01

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.

Discrete event performance prediction of speculatively parallel temperature-accelerated dynamics

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

Zamora, Richard James; Voter, Arthur F.; Perez, Danny

Due to its unrivaled ability to predict the dynamical evolution of interacting atoms, molecular dynamics (MD) is a widely used computational method in theoretical chemistry, physics, biology, and engineering. Despite its success, MD is only capable of modeling time scales within several orders of magnitude of thermal vibrations, leaving out many important phenomena that occur at slower rates. The Temperature Accelerated Dynamics (TAD) method overcomes this limitation by thermally accelerating the state-to-state evolution captured by MD. Due to the algorithmically complex nature of the serial TAD procedure, implementations have yet to improve performance by parallelizing the concurrent exploration of multiplemore » states. Here we utilize a discrete event-based application simulator to introduce and explore a new Speculatively Parallel TAD (SpecTAD) method. We investigate the SpecTAD algorithm, without a full-scale implementation, by constructing an application simulator proxy (SpecTADSim). Finally, following this method, we discover that a nontrivial relationship exists between the optimal SpecTAD parameter set and the number of CPU cores available at run-time. Furthermore, we find that a majority of the available SpecTAD boost can be achieved within an existing TAD application using relatively simple algorithm modifications.« less

Discrete event performance prediction of speculatively parallel temperature-accelerated dynamics

DOE PAGES

Zamora, Richard James; Voter, Arthur F.; Perez, Danny; ...

2016-12-01

Due to its unrivaled ability to predict the dynamical evolution of interacting atoms, molecular dynamics (MD) is a widely used computational method in theoretical chemistry, physics, biology, and engineering. Despite its success, MD is only capable of modeling time scales within several orders of magnitude of thermal vibrations, leaving out many important phenomena that occur at slower rates. The Temperature Accelerated Dynamics (TAD) method overcomes this limitation by thermally accelerating the state-to-state evolution captured by MD. Due to the algorithmically complex nature of the serial TAD procedure, implementations have yet to improve performance by parallelizing the concurrent exploration of multiplemore » states. Here we utilize a discrete event-based application simulator to introduce and explore a new Speculatively Parallel TAD (SpecTAD) method. We investigate the SpecTAD algorithm, without a full-scale implementation, by constructing an application simulator proxy (SpecTADSim). Finally, following this method, we discover that a nontrivial relationship exists between the optimal SpecTAD parameter set and the number of CPU cores available at run-time. Furthermore, we find that a majority of the available SpecTAD boost can be achieved within an existing TAD application using relatively simple algorithm modifications.« less

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

NASA Astrophysics Data System (ADS)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

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

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking.

PubMed

Doolittle, W Ford; Inkpen, S Andrew

2018-04-17

Many practicing biologists accept that nothing in their discipline makes sense except in the light of evolution, and that natural selection is evolution's principal sense-maker. But what natural selection actually is (a force or a statistical outcome, for example) and the levels of the biological hierarchy (genes, organisms, species, or even ecosystems) at which it operates directly are still actively disputed among philosophers and theoretical biologists. Most formulations of evolution by natural selection emphasize the differential reproduction of entities at one or the other of these levels. Some also recognize differential persistence, but in either case the focus is on lineages of material things: even species can be thought of as spatiotemporally restricted, if dispersed, physical beings. Few consider-as "units of selection" in their own right-the processes implemented by genes, cells, species, or communities. "It's the song not the singer" (ITSNTS) theory does that, also claiming that evolution by natural selection of processes is more easily understood and explained as differential persistence than as differential reproduction. ITSNTS was formulated as a response to the observation that the collective functions of microbial communities (the songs) are more stably conserved and ecologically relevant than are the taxa that implement them (the singers). It aims to serve as a useful corrective to claims that "holobionts" (microbes and their animal or plant hosts) are aggregate "units of selection," claims that often conflate meanings of that latter term. But ITSNS also seems broadly applicable, for example, to the evolution of global biogeochemical cycles and the definition of ecosystem function.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

PubMed

Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

2017-01-01

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Towards an integrated numerical simulator for crack-seal vein microstructure: Coupling phase-field with the Discrete Element Method

NASA Astrophysics Data System (ADS)

Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.

2016-04-01

Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that translate the spatial domain of the model from DEM to the phase-field and vice versa. This will allow the fracturing process to be modeled with DEM and the sealing processes to be modeled with phase-field approach. With this bidirectional coupling, the strengths of these two numerical methods will be combined into a unified model of iterative crack-seal that will be able to model the complex feedback mechanisms between fracturing and sealing processes and assess the influence of thermal, mechanical, chemical and hydraulic parameters on the evolution of vein microstructures. References: Ankit, K., Nestler, B., Selzer, M., and Reichardt, M., 2013, Phase-field study of grain boundary tracking behavior in crack-seal microstructures: Contributions to Mineralogy and Petrology, v. 166, no. 6, p. 1709-1723 Ankit, K., Selzer, M., Hilgers, C., and Nestler, B., 2015a, Phase-field modeling of fracture cementation processes in 3-D: Journal of Petroleum Science Research, v. 4, no. 2, p. 79-96 Ankit, K., Urai, J.L., and Nestler, B., 2015b, Microstructural evolution in bitaxial crack-seal veins: A phase-field study: Journal of Geophysical Research: Solid Earth, v. 120, no. 5, p. 3096-3118. Virgo, S., Abe, S., and Urai, J.L., 2013, Extension fracture propagation in rocks with veins: Insight into the crack-seal process using Discrete Element Method modeling: Journal of Geophysical Research: Solid Earth, v. 118, no. 10 Virgo, S., Abe, S., and Urai, J.L., 2014, The evolution of crack seal vein and fracture networks in an evolving stress field: Insights from Discrete Element Models of fracture sealing: Journal of Geophysical Research: Solid Earth, p. 2014JB011520

Determining Regulatory Networks Governing the Differentiation of Embryonic Stem Cells to Pancreatic Lineage

NASA Astrophysics Data System (ADS)

Banerjee, Ipsita

2009-03-01

Knowledge of pathways governing cellular differentiation to specific phenotype will enable generation of desired cell fates by careful alteration of the governing network by adequate manipulation of the cellular environment. With this aim, we have developed a novel method to reconstruct the underlying regulatory architecture of a differentiating cell population from discrete temporal gene expression data. We utilize an inherent feature of biological networks, that of sparsity, in formulating the network reconstruction problem as a bi-level mixed-integer programming problem. The formulation optimizes the network topology at the upper level and the network connectivity strength at the lower level. The method is first validated by in-silico data, before applying it to the complex system of embryonic stem (ES) cell differentiation. This formulation enables efficient identification of the underlying network topology which could accurately predict steps necessary for directing differentiation to subsequent stages. Concurrent experimental verification demonstrated excellent agreement with model prediction.

Stellar differential rotation and coronal time-scales

NASA Astrophysics Data System (ADS)

Gibb, G. P. S.; Jardine, M. M.; Mackay, D. H.

2014-10-01

We investigate the time-scales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion time-scale through the relation τ_Form ∝ √{τ_Lapτ_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (τLife∝τLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae.

Sexual and reproductive behaviour of Drosophila melanogaster from a microclimatically interslope differentiated population of "Evolution Canyon" (Mount Carmel, Israel).

PubMed

Iliadi, K; Iliadi, N; Rashkovetsky, E; Minkov, I; Nevo, E; Korol, A

2001-11-22

The strong microscale interslope environmental differences in "Evolution Canyon" provide an excellent natural model for sympatric speciation. Our previous studies revealed significant slope-specific differences for a fitness complex of Drosophila. This complex involved either adaptation traits (tolerance to high temperature, different viability and longevity pattern) or behavioural differentiation, manifested in habitat choice and non-random mating. This remarkable differentiation has evolved despite a very small interslope distance (a few hundred metres only). Our hypothesis is that strong interslope microclimatic contrast caused differential selection for fitness-related traits accompanied by behavioural differentiation and reinforced by some sexual isolation, which started incipient speciation. Here we describe the results of a systematic analysis of sexual behaviour in a non-choice situation and several reproductive parameters of D. melanogaster populations from the opposite slopes of "Evolution Canyon". The evidence indicates that: (i) mate choice derives from differences in mating propensity and discrimination; (ii) females from the milder north-facing slope discriminate strongly against males of the opposite slope; (iii) both sexes of the south-facing slope display distinct reproductive and behavioural patterns with females showing increased fecundity, shorter time before remating and relatively higher receptivity, and males showing higher mating propensity. These patterns represent adaptive life strategies contributing to higher fitness.

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

NASA Astrophysics Data System (ADS)

Negri, Federico; Manzoni, Andrea; Amsallem, David

2015-12-01

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the empirical interpolation method (EIM) and its discrete variant DEIM. In this paper we show that MDEIM represents a very efficient approach to deal with complex physical and geometrical parametrizations in a non-intrusive, efficient and purely algebraic way. We propose different strategies to combine MDEIM with a state approximation resulting either from a reduced basis greedy approach or Proper Orthogonal Decomposition. A posteriori error estimates accounting for the MDEIM error are also developed in the case of parametrized elliptic and parabolic equations. Finally, the capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems.

Crystallization in Two Dimensions and a Discrete Gauss-Bonnet Theorem

NASA Astrophysics Data System (ADS)

De Luca, L.; Friesecke, G.

2018-02-01

We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential V(r)=+∞ if r<1, -1 if r=1, 0 if r>1. This is done by endowing the bond graph of a general particle configuration with a suitable notion of discrete curvature, and appealing to a discrete Gauss-Bonnet theorem (Knill in Elem Math 67:1-7, 2012) which, as its continuous cousins, relates the sum/integral of the curvature to topological invariants. This leads to an exact geometric decomposition of the Heitmann-Radin energy into (i) a combinatorial bulk term, (ii) a combinatorial perimeter, (iii) a multiple of the Euler characteristic, and (iv) a natural topological energy contribution due to defects. An analogous exact geometric decomposition is also established for soft potentials such as the Lennard-Jones potential V(r)=r^{-6}-2r^{-12}, where two additional contributions arise, (v) elastic energy and (vi) energy due to non-bonded interactions.

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

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

Xiao, Jianyuan; Qin, Hong; Liu, Jian

2015-11-01

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces fivemore » exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.« less

Numerical uncertainty in computational engineering and physics

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

Hemez, Francois M

2009-01-01

Obtaining a solution that approximates ordinary or partial differential equations on a computational mesh or grid does not necessarily mean that the solution is accurate or even 'correct'. Unfortunately assessing the quality of discrete solutions by questioning the role played by spatial and temporal discretizations generally comes as a distant third to test-analysis comparison and model calibration. This publication is contributed to raise awareness of the fact that discrete solutions introduce numerical uncertainty. This uncertainty may, in some cases, overwhelm in complexity and magnitude other sources of uncertainty that include experimental variability, parametric uncertainty and modeling assumptions. The concepts ofmore » consistency, convergence and truncation error are overviewed to explain the articulation between the exact solution of continuous equations, the solution of modified equations and discrete solutions computed by a code. The current state-of-the-practice of code and solution verification activities is discussed. An example in the discipline of hydro-dynamics illustrates the significant effect that meshing can have on the quality of code predictions. A simple method is proposed to derive bounds of solution uncertainty in cases where the exact solution of the continuous equations, or its modified equations, is unknown. It is argued that numerical uncertainty originating from mesh discretization should always be quantified and accounted for in the overall uncertainty 'budget' that supports decision-making for applications in computational physics and engineering.« less

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Natural selection and neutral evolution jointly drive population divergence between alpine and lowland ecotypes of the allopolyploid plant Anemone multifida (Ranunculaceae).

PubMed

McEwen, Jamie R; Vamosi, Jana C; Rogers, Sean M

2013-01-01

Population differentiation can be driven in large part by natural selection, but selectively neutral evolution can play a prominent role in shaping patters of population divergence. The decomposition of the evolutionary history of populations into the relative effects of natural selection and selectively neutral evolution enables an understanding of the causes of population divergence and adaptation. In this study, we examined heterogeneous genomic divergence between alpine and lowland ecotypes of the allopolyploid plant, Anemone multifida. Using peak height and dominant AFLP data, we quantified population differentiation at non-outlier (neutral) and outlier loci to determine the potential contribution of natural selection and selectively neutral evolution to population divergence. We found 13 candidate loci, corresponding to 2.7% of loci, with signatures of divergent natural selection between alpine and lowland populations and between alpine populations (Fst  = 0.074-0.445 at outlier loci), but neutral population differentiation was also evident between alpine populations (FST  = 0.041-0.095 at neutral loci). By examining population structure at both neutral and outlier loci, we determined that the combined effects of selection and neutral evolution are associated with the divergence of alpine populations, which may be linked to extreme abiotic conditions and isolation between alpine sites. The presence of outlier levels of genetic variation in structured populations underscores the importance of separately analyzing neutral and outlier loci to infer the relative role of divergent natural selection and neutral evolution in population divergence.

A Study of Multigrid Preconditioners Using Eigensystem Analysis

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Swanson, R. C.

2005-01-01

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

The Allusion of the Gene: Misunderstandings of the Concepts Heredity and Gene

ERIC Educational Resources Information Center

Falk, Raphael

2014-01-01

Life sciences became Biology, a formal scientific discipline, at the turn of the nineteenth century, when it adopted the methods of reductive physics and chemistry. Mendel's hypothesis of inheritance of discrete factors further introduced a quantitative reductionist dimension into biology. In 1910 Johannsen differentiated between the…

Differentiating Processes of Control and Understanding in the Early Development of Emotion and Cognition

ERIC Educational Resources Information Center

Blankson, A. Nayena; O'Brien, Marion; Leerkes, Esther M.; Marcovitch, Stuart; Calkins, Susan D.

2012-01-01

In this study, we examined the hypothesis that preschoolers' performance on emotion and cognitive tasks is organized into discrete processes of control and understanding within the domains of emotion and cognition. Additionally, we examined the relations among component processes using mother report, behavioral observation, and physiological…

Metastability of Reversible Random Walks in Potential Fields

NASA Astrophysics Data System (ADS)

Landim, C.; Misturini, R.; Tsunoda, K.

2015-09-01

Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.

Path integrals and large deviations in stochastic hybrid systems.

PubMed

Bressloff, Paul C; Newby, Jay M

2014-04-01

We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

NASA Astrophysics Data System (ADS)

Krishna, S.; Shukla, D.; Malik, R. P.

2016-07-01

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

Identification and Single-Cell Functional Characterization of an Endodermally Biased Pluripotent Substate in Human Embryonic Stem Cells.

PubMed

Allison, Thomas F; Smith, Andrew J H; Anastassiadis, Konstantinos; Sloane-Stanley, Jackie; Biga, Veronica; Stavish, Dylan; Hackland, James; Sabri, Shan; Langerman, Justin; Jones, Mark; Plath, Kathrin; Coca, Daniel; Barbaric, Ivana; Gokhale, Paul; Andrews, Peter W

2018-05-09

Human embryonic stem cells (hESCs) display substantial heterogeneity in gene expression, implying the existence of discrete substates within the stem cell compartment. To determine whether these substates impact fate decisions of hESCs we used a GFP reporter line to investigate the properties of fractions of putative undifferentiated cells defined by their differential expression of the endoderm transcription factor, GATA6, together with the hESC surface marker, SSEA3. By single-cell cloning, we confirmed that substates characterized by expression of GATA6 and SSEA3 include pluripotent stem cells capable of long-term self-renewal. When clonal stem cell colonies were formed from GATA6-positive and GATA6-negative cells, more of those derived from GATA6-positive cells contained spontaneously differentiated endoderm cells than similar colonies derived from the GATA6-negative cells. We characterized these discrete cellular states using single-cell transcriptomic analysis, identifying a potential role for SOX17 in the establishment of the endoderm-biased stem cell state. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

PubMed

Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

2012-01-01

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Modeling of the WSTF frictional heating apparatus in high pressure systems

NASA Technical Reports Server (NTRS)

Skowlund, Christopher T.

1992-01-01

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Implementation of high-gain observer on low-cost fused IR-OS sensor embedded in UAV system

NASA Astrophysics Data System (ADS)

Nor, E. Mohd; Noor, S. B. Mohd; Bahiki, M. R.; Azrad, S.

2017-12-01

This paper presents discrete time implementation of a high gain observer (HGO) and extended term to estimate the state velocity and acceleration from the position measured by a low-cost sensor installed on-board the unmanned aerial vehicle (UAV). Owing to the low-cost sensor, the signal produced from fused IR-OS is noisy and therefore, additional filters are used to remove the noise. This study proposes an alternative to this standard and tedious procedure using HGO. The discrete time implementation of HGO and its extended term is presented and ground tests are conducted to verify the algorithm by inducing a dynamic motion on the UAV platform embedded with the fusion IR-OS onboard. A comparison study is conducted using standard numerical differentiation and ground truth measurement by OptiTrack. The results show that EHGO can produce a velocity signal with the same quality as that of differentiated signal from fused IR-OS using Kalman filter. The novelty of HGO lies in its simplicity and its minimal tuning of parameters.

Neural potentials disorder during differential psychoacoustic experiment evaluated by discrete wavelet analysis.

PubMed

Tsakiraki, Eleni S; Tsiaparas, Nikolaos N; Christopoulou, Maria I; Papageorgiou, Charalabos Ch; Nikita, Konstantina S

2014-01-01

The aim of the paper is the assessment of neural potentials disorder during a differential sensitivity psychoacoustic procedure. Ten volunteers were asked to compare the duration of two acoustic pulses: one reference with stable duration of 500 ms and one trial which varied from 420 ms to 620 ms. During the discrimination task, Electroencephalogram (EEG) and Event Related Potential (ERP) signals were recorded. The mean Relative Wavelet Energy (mRWE) and the normalized Shannon Wavelet Entropy (nSWE) are computed based on the Discrete Wavelet analysis. The results are correlated to the data derived by the psychoacoustic analysis on the volunteers responses. In most of the electrodes, when the duration of the trial pulse is 460 ms and 560 ms, there is an increase and a decrease in nSWE value, respectively, which is determined mostly by the mRWE in delta rhythm. These extrema are correlated to the Just Noticeable Difference (JND) in pulses duration, calculated by psychoacoustic analysis. The dominance of delta rhythm during the whole auditory experiment is noteworthy. The lowest values of nSWE are noted in temporal lobe.